\chapter{Mathematical symbols} \label{math-symbols} \idxbothbegin{mathematical}{symbols} \tablesections Most, but not all, of the symbols in this chapter are math-mode only. That is, they yield a ``\texttt{Missing~\$ inserted}''\index{Missing \$ inserted=``\texttt{Missing~\$ inserted}''} error message if not used within \verb|$|$\ldots$\verb|$|, \verb|\[|$\ldots$\verb|\]|, or another math-mode environment. Operators marked as ``variable-sized'' are taller in displayed formulas, shorter in in-text formulas, and possibly shorter still when used in various levels of superscripts and subscripts. \ifcomplete Stylized letters such as ``$\!\mathscr{L}\,$'' and ``$\varmathbb{Z}$'' are usually produced using one of the math alphabets in \ref{alphabets} rather than with an explicit symbol command. Look there first if you need a symbol for a transform, number set, or some other alphanumeric. Although there have been many requests on \ctt for a contradiction\idxboth{contradiction}{symbols} symbol, the ensuing discussion invariably reveals innumerable ways to represent contradiction in a proof, including ``\blitza''~(\cmdI{\blitza}), ``$\Rightarrow\Leftarrow$''~(\cmdX{\Rightarrow}\cmdX{\Leftarrow}),\index{arrows} ``$\bot$''~(\cmdX{\bot}), ``$\nleftrightarrow$''~(\cmdX{\nleftrightarrow}), and ``\textreferencemark''~(\cmdI{\textreferencemark}). Because of the lack of notational consensus, it is probably better to spell out ``Contradiction!''\ than to use a symbol for this purpose. Similarly, discussions on \ctt have revealed that there are a variety of ways to indicate the mathematical notion of ``is defined\idxboth{definition}{symbols} as''. Common candidates include ``$\triangleq$''~(\cmdX{\triangleq}), ``$\equiv$''~(\cmdX{\equiv}), ``$\coloneqq$''~(\emph{various}\footnote{In \TX, \PX, and \MTOOLS\ the symbol is called \cmdX{\coloneqq}. In \ABX\ and \MNS\ it's called \cmdI[$\string\ABXcoloneq$]{\coloneq}. In \CEQ\ it's called \cmdX{\colonequals}.}), and ``\STIXeqdef''~(\cmdI[\STIXeqdef]{\eqdef}). See also the example of \cmd{\equalsfill} \vpageref[below]{equalsfill-ex}. Depending upon the context, disjoint union % \index{disjoint union=disjoint union ($\coprod$)}% \index{disjoint union=disjoint union ($\sqcup$)}% \index{disjoint union=disjoint union ($\dotcup$)}% \index{disjoint union=disjoint union ($\oplus$)}% \index{disjoint union=disjoint union ($\amalg$)}% % may be represented as ``$\coprod$''~(\cmdX{\coprod}), ``$\sqcup$''~(\cmdX{\sqcup}), ``$\dotcup$''~(\cmdX{\dotcup}), ``$\oplus$''~(\cmdX{\oplus}), ``$\amalg$''~(\cmdX{\amalg}), or any of a number of other symbols.\footnote{\person{Bob}{Tennent} listed these and other disjoint-union symbol possibilities in a November~2007 post to \ctt.} Finally, the average\index{average} value of a variable~$x$ is written by some people as ``$\overline{x}$''~(\verb|\overline{x}|)\incsyms\indexaccent[$\string\blackacc{\string\overline}$]{\overline}, by some people as ``$\langle x \rangle$''~(\cmdX{\langle} \texttt{x} \cmdX{\rangle}), and by some people as ``$\diameter x$'' or ``$\varnothing x$''~(\cmdX{\diameter} \texttt{x} or \cmdX{\varnothing} \texttt{x}). The moral of the story is that you should be careful always to explain your notation to avoid confusing your readers. \fi % Matches \ifcomplete \bigskip \begin{symtable}{Math-mode Versions of Text Symbols} \index{underline} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \label{math-text-vers} \begin{tabular}{*3{ll}} \X\mathdollar & \X\mathparagraph & \X\mathsterling \\ \X\mathellipsis & \X\mathsection & \X\mathunderscore \\ \end{tabular} \bigskip \usetextmathmessage \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Math-mode Versions of Text Symbols} \index{tilde} \index{underline} \index{copyright} \index{quotation marks} \index{question mark=question mark (\Queston)} \idxboth{currency}{symbols} \idxboth{monetary}{symbols} \label{logix-math-text-vers} \begin{tabular}{*4{ll}} \K\AAnd & \K\Cpyrght & \K\Exclaim & \K\Semicln \\ \K\Ampersand & \K\Dagger & \K\LeftSlash & \K\SingleQuote \\ \K[\LOGIXAt]\At & \K\Daggerr & \K\LngVrtBar & \K\Tild \\ \K\BackQuote & \K\Ddagger & \K\Numbr & \K\TripleQuote \\ \K\BndBar & \K\Ddaggerr & \K\Percnt & \K\Underscore \\ \K\Circumflex & \K\Dollar & \K\Queston & \\ \K\Coma & \K\DoubleQuote & \K\RightSlash & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Basic Operators} \idxboth{binary}{operators} \index{asterisks} \index{asterisks>circled} \index{asterisks>dotted} \index{plusses} \label{logix-basic} \begin{tabular}{*4{ll}} \K\Asterick & \K\CircMinusPlus & \K\Divd & \K\Minus \\ \K\CircAsterick & \K\CircPls & \K\Divide & \K\MinusPlus \\ \K\CircDivd & \K\CircPlusMinus & \K\DMinus & \K\Pls \\ \K\CircDivide & \K\CircTimes & \K\DPlus & \K\PlusMinus \\ \K\CircMinus & \K\DAsterisk & \K\DTimes & \K\Times \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[UTFSYM]{\UTFSYM\ Basic Operators} \idxboth{binary}{operators} \label{utfsym-basic} \begin{tabular}{lll@{\qquad}lll} \Tutfsym{2715}{multiplication X} & \Tutfsym{2797}{heavy division sign} \\ \Tutfsym{2716}{heavy multiplication X} & \Tutfsymw{2796}{heavy minus sign} \\ \Tutfsym{2795}{heavy plus sign} & \\ \end{tabular} \bigskip \begin{tablenote} \utfsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[TWEM]{\TWEM\ Basic Operators} \idxboth{binary}{operators} \index{plusses} \label{twemojis-basic} \begin{tabular}{*2{ll}} \Ttwem{divide}{2797} & \Ttwem{multiply}{2716} \\ \Ttwem{heavy equals sign}{1f7f0} & \Ttwem{plus}{2795} \\ \Ttwem{minus}{2796} & \\ \end{tabular} \bigskip \begin{tablenote} \twemojismessage. \end{tablenote} \end{symtable} \begin{symtable}[CMLL]{\CMLL\ Unary Operators} \idxboth{unary}{operators} \idxboth{linear logic}{symbols} \label{cmll-unary} \begin{tabular}{*2{ll@{\qquad}}ll} \K[!]\oc$^*$ & \K[\CMLLshneg]\shneg & \K[?]\wn$^*$ \\ \K[\CMLLshift]\shift & \K[\CMLLshpos]\shpos & \\ \end{tabular} \bigskip \begin{tablenote}[*] \cmdI[!]{\oc} and \cmdI[?]{\wn} differ from~``!'' and~``?'' in terms of their math-mode spacing: \verb|$A=!B$| produces ``$A=!B$'', for example, while \verb|$A=\oc B$| produces ``$A=\mathord{!}B$''. \end{tablenote} \end{symtable} \begin{symtable}{Binary Operators} \idxboth{binary}{operators} \index{division} \idxboth{logic}{symbols} \index{rhombuses} \index{circles} \label{bin} \begin{tabular}{*4{ll}} \X\amalg & \X\cup & \X\oplus & \X\times \\ \X\ast & \X\dagger & \X\oslash & \X\triangleleft \\ \X\bigcirc & \X\ddagger & \X\otimes & \X\triangleright \\ \X\bigtriangledown & \X\diamond & \X\pm & \X\unlhd$^*$ \\ \X\bigtriangleup & \X\div & \X\rhd$^*$ & \X\unrhd$^*$ \\ \X\bullet & \X\lhd$^*$ & \X\setminus & \X\uplus \\ \X\cap & \X\mp & \X\sqcap & \X\vee \\ \X\cdot & \X\odot & \X\sqcup & \X\wedge \\ \X\circ & \X\ominus & \X\star & \X\wr \\ \end{tabular} \bigskip \notpredefinedmessage \end{symtable} \begin{symtable}[AMS]{\AMS\ Binary Operators} \idxboth{binary}{operators} \idxboth{boxed}{symbols} \index{semidirect products} \label{ams-bin} \begin{tabular}{*3{ll}} \X\barwedge & \X\circledcirc & \X\intercal$^*$ \\ \X\boxdot & \X\circleddash & \X\leftthreetimes \\ \X\boxminus & \X\Cup & \X\ltimes \\ \X\boxplus & \X\curlyvee & \X\rightthreetimes \\ \X\boxtimes & \X\curlywedge & \X\rtimes \\ \X\Cap & \X\divideontimes & \X\smallsetminus \\ \X\centerdot & \X\dotplus & \X\veebar \\ \X\circledast & \X\doublebarwedge \\ \end{tabular} \bigskip \begin{tablenote}[*] \newcommand{\trpose}{{\mathpalette\raiseT{\intercal}}} \newcommand{\raiseT}[2]{\raisebox{0.25ex}{$#1#2$}} % Some people use a superscripted \cmdX{\intercal} for matrix transpose\index{transpose}: ``\verb|A^\intercal|''~$\mapsto$ ``$A^\intercal$''. (See the May~2009 \ctt thread, ``raising math symbols'', for suggestions about altering the height of the superscript.) \cmdX{\top} (\vref{letter-like}), \verb|T|, and \verb|\mathsf{T}| are other popular choices: ``$A^\top$'', ``$A^T$'', ``$A^{\text{\textsf{T}}}$''. \end{tablenote} \end{symtable} \begin{symtable}[ST]{\ST\ Binary Operators} \idxboth{binary}{operators} \idxboth{logic}{symbols} \idxboth{boxed}{symbols} \index{arrows} \label{st-bin} \begin{tabular}{*3{ll}} \X\baro & \X\interleave & \X\varoast \\ \X\bbslash & \X\leftslice & \X\varobar \\ \X\binampersand & \X\merge & \X\varobslash \\ \X\bindnasrepma & \X\minuso & \X\varocircle \\ \X\boxast & \X\moo & \X\varodot \\ \X\boxbar & \X\nplus & \X\varogreaterthan \\ \X\boxbox & \X\obar & \X\varolessthan \\ \X\boxbslash & \X\oblong & \X\varominus \\ \X\boxcircle & \X\obslash & \X\varoplus \\ \X\boxdot & \X\ogreaterthan & \X\varoslash \\ \X\boxempty & \X\olessthan & \X\varotimes \\ \X\boxslash & \X\ovee & \X\varovee \\ \X\curlyveedownarrow & \X\owedge & \X\varowedge \\ \X\curlyveeuparrow & \X\rightslice & \X\vartimes \\ \X\curlywedgedownarrow & \X\sslash & \X\Ydown \\ \X\curlywedgeuparrow & \X\talloblong & \X\Yleft \\ \X\fatbslash & \X\varbigcirc & \X\Yright \\ \X\fatsemi & \X\varcurlyvee & \X\Yup \\ \X\fatslash & \X\varcurlywedge \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{\WASY\ Binary Operators} \idxboth{binary}{operators} \label{wasy-bin} \begin{tabular}{*4{ll}} \X\lhd & \X\ocircle & \X\RHD & \X\unrhd \\ \X\LHD & \X\rhd & \X\unlhd \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Binary Operators} \idxboth{binary}{operators} \idxboth{logic}{symbols} \index{circles} \label{txpx-bin} \begin{tabular}{*3{ll}} \X\circledbar & \X\circledwedge & \X\medcirc \\ \X\circledbslash & \X\invamp & \X\sqcapplus \\ \X\circledvee & \X\medbullet & \X\sqcupplus \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Binary Operators} \idxboth{binary}{operators} \index{asterisks} \index{semidirect products} \index{rhombuses} \index{plusses} \index{squares} \label{abx-bin} \begin{tabular}{*3{ll}} \X[\ABXast]\ast & \X[\ABXcurlywedge]\curlywedge & \X[\ABXsqcap]\sqcap \\ \X[\ABXAsterisk]\Asterisk & \X[\ABXdivdot]\divdot & \X[\ABXsqcup]\sqcup \\ \X[\ABXbarwedge]\barwedge & \X[\ABXdivideontimes]\divideontimes & \X[\ABXsqdoublecap]\sqdoublecap \\ \X[\ABXbigstar]\bigstar & \X[\ABXdotdiv]\dotdiv & \X[\ABXsqdoublecup]\sqdoublecup \\ \X[\ABXbigvarstar]\bigvarstar & \X[\ABXdotplus]\dotplus & \X[\ABXsquare]\square \\ \X[\ABXblackdiamond]\blackdiamond & \X[\ABXdottimes]\dottimes & \X[\ABXsquplus]\squplus \\ \X[\ABXcap]\cap & \X[\ABXdoublebarwedge]\doublebarwedge & \X[\ABXudot]\udot \\ \X[\ABXcircplus]\circplus & \X[\ABXdoublecap]\doublecap & \X[\ABXuplus]\uplus \\ \X[\ABXcoasterisk]\coasterisk & \X[\ABXdoublecup]\doublecup & \X[\ABXvarstar]\varstar \\ \X[\ABXcoAsterisk]\coAsterisk & \X[\ABXltimes]\ltimes & \X[\ABXvee]\vee \\ \X[\ABXconvolution]\convolution & \X[\ABXpluscirc]\pluscirc & \X[\ABXveebar]\veebar \\ \X[\ABXcup]\cup & \X[\ABXrtimes]\rtimes & \X[\ABXveedoublebar]\veedoublebar \\ \X[\ABXcurlyvee]\curlyvee & \X[\ABXsqbullet]\sqbullet & \X[\ABXwedge]\wedge \\ \end{tabular} \bigskip \begin{tablenote} Many of the preceding glyphs go by multiple names. \cmdI[$\string\ABXcenterdot$]{\centerdot} is equivalent to \cmdI[$\string\ABXsqbullet$]{\sqbullet}, and \cmdI[$\string\ABXast$]{\ast} is equivalent to \cmdI{*}. \cmdI[$\string\ABXasterisk$]{\asterisk} produces the same glyph as \cmdI[$\string\ABXast$]{\ast}, but as an ordinary symbol, not a binary operator. Similarly, \cmdI[$\string\ABXbigast$]{\bigast} produces a large-operator version of the \cmdI[$\string\ABXAsterisk$]{\Asterisk} binary operator, and \cmdI[$\string\ABXbigcoast$]{\bigcoast} produces a large-operator version of the \cmdI[$\string\ABXcoAsterisk$]{\coAsterisk} binary operator. \end{tablenote} \end{symtable} \begin{longsymtable}[MNS]{\MNS\ Binary Operators} \ltidxboth{binary}{operators} \ltindex{plusses} \ltindex{circles} \ltindex{rhombuses} \ltidxboth{database}{symbols} \label{mns-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\MNSamalg]\amalg & \K[\MNSdoublesqcup]\doublesqcup & \K[\MNSrighttherefore]\righttherefore \\ \K[\MNSast]\ast & \K[\MNSdoublevee]\doublevee & \K[\MNSrightthreetimes]\rightthreetimes \\ \K[\MNSbackslashdiv]\backslashdiv & \K[\MNSdoublewedge]\doublewedge & \K[\MNSrightY]\rightY \\ \K[\MNSbowtie]\bowtie & \K[\MNSdowntherefore]\downtherefore & \K[\MNSrtimes]\rtimes \\ \K[\MNSbullet]\bullet & \K[\MNSdownY]\downY & \K[\MNSslashdiv]\slashdiv \\ \K[\MNScap]\cap & \K[\MNSdtimes]\dtimes & \K[\MNSsmallprod]\smallprod \\ \K[\MNScapdot]\capdot & \K[\MNSfivedots]\fivedots & \K[\MNSsqcap]\sqcap \\ \K[\MNScapplus]\capplus & \K[\MNShbipropto]\hbipropto & \K[\MNSsqcapdot]\sqcapdot \\ \K[\MNScdot]\cdot & \K[\MNShdotdot]\hdotdot & \K[\MNSsqcapplus]\sqcapplus \\ \K[\MNScirc]\circ & \K[\MNSlefthalfcap]\lefthalfcap & \K[\MNSsqcup]\sqcup \\ \K[\MNSclosedcurlyvee]\closedcurlyvee & \K[\MNSlefthalfcup]\lefthalfcup & \K[\MNSsqcupdot]\sqcupdot \\ \K[\MNSclosedcurlywedge]\closedcurlywedge & \K[\MNSlefttherefore]\lefttherefore & \K[\MNSsqcupplus]\sqcupplus \\ \K[\MNScup]\cup & \K[\MNSleftthreetimes]\leftthreetimes & \K[\MNSsquaredots]\squaredots \\ \K[\MNScupdot]\cupdot & \K[\MNSleftY]\leftY & \K[\MNStimes]\times \\ \K[\MNScupplus]\cupplus & \K[\MNSltimes]\ltimes & \K[\MNSudotdot]\udotdot \\ \K[\MNScurlyvee]\curlyvee & \K[\MNSmedbackslash]\medbackslash & \K[\MNSuptherefore]\uptherefore \\ \K[\MNScurlyveedot]\curlyveedot & \K[\MNSmedcircle]\medcircle & \K[\MNSupY]\upY \\ \K[\MNScurlywedge]\curlywedge & \K[\MNSmedslash]\medslash & \K[\MNSutimes]\utimes \\ \K[\MNScurlywedgedot]\curlywedgedot & \K[\MNSmedvert]\medvert & \K[\MNSvbipropto]\vbipropto \\ \K[\MNSddotdot]\ddotdot & \K[\MNSmedvertdot]\medvertdot & \K[\MNSvdotdot]\vdotdot \\ \K[\MNSdiamonddots]\diamonddots & \K[\MNSminus]\minus & \K[\MNSvee]\vee \\ \K[\MNSdiv]\div & \K[\MNSminusdot]\minusdot & \K[\MNSveedot]\veedot \\ \K[\MNSdotmedvert]\dotmedvert & \K[\MNSmp]\mp & \K[\MNSvertbowtie]\vertbowtie \\ \K[\MNSdotminus]\dotminus & \K[\MNSneswbipropto]\neswbipropto & \K[\MNSvertdiv]\vertdiv \\ \K[\MNSdoublecap]\doublecap & \K[\MNSnwsebipropto]\nwsebipropto & \K[\MNSwedge]\wedge \\ \K[\MNSdoublecup]\doublecup & \K[\MNSplus]\plus & \K[\MNSwedgedot]\wedgedot \\ \K[\MNSdoublecurlyvee]\doublecurlyvee & \K[\MNSpm]\pm & \K[\MNSwreath]\wreath \\ \K[\MNSdoublecurlywedge]\doublecurlywedge & \K[\MNSrighthalfcap]\righthalfcap & \\ \K[\MNSdoublesqcap]\doublesqcap & \K[\MNSrighthalfcup]\righthalfcup & \\ \end{longtable} \bigskip \begin{tablenote} \MNS\ defines \cmdI[\MNSmedbackslash]{\setminus} and \cmdI[\MNSmedbackslash]{\smallsetminus} as synonyms for \cmdI[\MNSmedbackslash]{\medbackslash}; \cmdI[\MNSbowtie]{\Join} as a synonym for \cmdI[\MNSbowtie]{\bowtie}; \cmdI[\MNSwreath]{\wr} as a synonym for \cmdI[\MNSwreath]{\wreath}; \cmdI[\MNSmedvert]{\shortmid} as a synonym for \cmdI[\MNSmedvert]{\medvert}; \cmdI[\MNSdoublecap]{\Cap} as a synonym for \cmdI[\MNSdoublecap]{\doublecap}; \cmdI[\MNSdoublecup]{\Cup} as a synonym for \cmdI[\MNSdoublecup]{\doublecup}; and, \cmdI[\MNScupplus]{\uplus} as a synonym for \cmdI[\MNScupplus]{\cupplus}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Binary Operators} \ltidxboth{binary}{operators} \ltindex{plusses} \ltidxboth{database}{symbols} \label{fdsym-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMamalg]\amalg & \K[\FDSYMdoublesqcup]\doublesqcup & \K[\FDSYMrightY]\rightY \\ \K[\FDSYMast]\ast & \K[\FDSYMdoublevee]\doublevee & \K[\FDSYMrtimes]\rtimes \\ \K[\FDSYMbarwedge]\barwedge & \K[\FDSYMdoublewedge]\doublewedge & \K[\FDSYMsetminus]\setminus \\ \K[\FDSYMbowtie]\bowtie & \K[\FDSYMdownY]\downY & \K[\FDSYMsqcap]\sqcap \\ \K[\FDSYMcap]\cap & \K[\FDSYMdtimes]\dtimes & \K[\FDSYMsqcapdot]\sqcapdot \\ \K[\FDSYMcapdot]\capdot & \K[\FDSYMhdotdot]\hdotdot & \K[\FDSYMsqcapplus]\sqcapplus \\ \K[\FDSYMcapplus]\capplus & \K[\FDSYMintercal]\intercal & \K[\FDSYMsqcup]\sqcup \\ \K[\FDSYMcdot]\cdot & \K[\FDSYMintprod]\intprod & \K[\FDSYMsqcupdot]\sqcupdot \\ \X[\FDSYMcenterdot]\centerdot & \K[\FDSYMintprodr]\intprodr & \K[\FDSYMsqcupplus]\sqcupplus \\ \K[\FDSYMcup]\cup & \K[\FDSYMleftthreetimes]\leftthreetimes & \K[\FDSYMtimes]\times \\ \K[\FDSYMcupdot]\cupdot & \K[\FDSYMleftY]\leftY & \K[\FDSYMtimesbar]\timesbar \\ \K[\FDSYMcupplus]\cupplus & \K[\FDSYMltimes]\ltimes & \K[\FDSYMudotdot]\udotdot \\ \K[\FDSYMcurlyvee]\curlyvee & \K[\FDSYMmedbackslash]\medbackslash & \K[\FDSYMupbowtie]\upbowtie \\ \K[\FDSYMcurlywedge]\curlywedge & \K[\FDSYMmedslash]\medslash & \K[\FDSYMupY]\upY \\ \K[\FDSYMddotdot]\ddotdot & \K[\FDSYMminus]\minus & \K[\FDSYMutimes]\utimes \\ \K[\FDSYMdiv]\div & \K[\FDSYMminusdot]\minusdot & \K[\FDSYMvaramalg]\varamalg \\ \K[\FDSYMdivideontimes]\divideontimes & \K[\FDSYMminusfdots]\minusfdots & \K[\FDSYMvdotdot]\vdotdot \\ \K[\FDSYMdivslash]\divslash & \K[\FDSYMminusrdots]\minusrdots & \K[\FDSYMvdots]\vdots \\ \K[\FDSYMdotminus]\dotminus & \K[\FDSYMmp]\mp & \K[\FDSYMvee]\vee \\ \K[\FDSYMdotplus]\dotplus & \K[\FDSYMplus]\plus & \K[\FDSYMveebar]\veebar \\ \K[\FDSYMdottimes]\dottimes & \K[\FDSYMplusdot]\plusdot & \K[\FDSYMveedot]\veedot \\ \K[\FDSYMdoublebarwedge]\doublebarwedge & \K[\FDSYMpm]\pm & \K[\FDSYMveedoublebar]\veedoublebar \\ \K[\FDSYMdoublecap]\doublecap & \K[\FDSYMpullback]\pullback & \K[\FDSYMwedge]\wedge \\ \K[\FDSYMdoublecup]\doublecup & \K[\FDSYMpushout]\pushout & \K[\FDSYMwedgedot]\wedgedot \\ \K[\FDSYMdoublesqcap]\doublesqcap & \K[\FDSYMrightthreetimes]\rightthreetimes & \K[\FDSYMwreath]\wreath \\ \end{longtable} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMbtimes]{\btimes} as a synonym for \cmdI[\string\FDSYMdtimes]{\dtimes}; \cmdI[\string\FDSYMCap]{\Cap} as a synonym for \cmdI[\string\FDSYMdoublecap]{\doublecap}; \cmdI[\string\FDSYMCup]{\Cup} as a synonym for \cmdI[\string\FDSYMdoublecup]{\doublecup}; \cmdI[\string\FDSYMhookupminus]{\hookupminus} as a synonym for \cmdI[\string\FDSYMintprodr]{\intprodr}; \cmdI[\string\FDSYMhourglass]{\hourglass} as a synonym for \cmdI[\string\FDSYMupbowtie]{\upbowtie}; \cmdI[\string\FDSYMland]{\land} as a synonym for \cmdI[\string\FDSYMwedge]{\wedge}; \cmdI[\string\FDSYMlor]{\lor} as a synonym for \cmdI[\string\FDSYMvee]{\vee}; \cmdI[\string\FDSYMminushookup]{\minushookup} as a synonym for \cmdI[\string\FDSYMintprod]{\intprod}; \cmdI[\string\FDSYMsmalldivslash]{\smalldivslash} as a synonym for \cmdI[\string\FDSYMmedslash]{\medslash}; \cmdI[\string\FDSYMsmallsetminus]{\smallsetminus} as a synonym for \cmdI[\string\FDSYMmedbackslash]{\medbackslash}; \cmdI[\string\FDSYMSqcap]{\Sqcap} as a synonym for \cmdI[\string\FDSYMdoublesqcap]{\doublesqcap}; \cmdI[\string\FDSYMSqcup]{\Sqcup} as a synonym for \cmdI[\string\FDSYMdoublesqcup]{\doublesqcup}; \cmdI[\string\FDSYMttimes]{\ttimes} as a synonym for \cmdI[\string\FDSYMutimes]{\utimes}; \cmdI[\string\FDSYMlJoin]{\lJoin} as a synonym for \cmdI[\string\FDSYMltimes]{\ltimes}; \cmdI[\string\FDSYMrJoin]{\rJoin} as a synonym for \cmdI[\string\FDSYMrtimes]{\rtimes}; \cmdI[\string\FDSYMJoin]{\Join} and \cmdI[\string\FDSYMlrtimes]{\lrtimes} as synonyms for \cmdI[\string\FDSYMbowtie]{\bowtie}; \cmdI[\string\FDSYMuplus]{\uplus} as a synonym for \cmdI[\string\FDSYMcupplus]{\cupplus}; \cmdI[\string\FDSYMveeonvee]{\veeonvee} as a synonym for \cmdI[\string\FDSYMdoublevee]{\doublevee}; \cmdI[\string\FDSYMwedgeonwedge]{\wedgeonwedge} as a synonym for \cmdI[\string\FDSYMdoublewedge]{\doublewedge}; and \cmdI[\string\FDSYMwr]{\wr} as a synonym for \cmdI[\string\FDSYMwreath]{\wreath}). \end{tablenote} \end{longsymtable} \begin{longsymtable}[BSK]{\BSK\ Binary Operators} \ltidxboth{binary}{operators} \ltindex{plusses} \ltindex{asterisks} \label{bsk-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\BSKast]\ast & \K[\BSKdottimes]\dottimes & \K[\BSKrtimesblack]\rtimesblack \\ \K[\BSKbaro]\baro & \K[\BSKdoublebarwedge]\doublebarwedge & \K[\BSKsmallsetminus]\smallsetminus \\ \K[\BSKbarwedge]\barwedge & \K[\BSKfatsemi]\fatsemi & \K[\BSKsmashtimes]\smashtimes \\ \K[\BSKbbslash]\bbslash & \K[\BSKgtrdot]\gtrdot & \K[\BSKsquplus]\squplus \\ \K[\BSKbinampersand]\binampersand & \K[\BSKintercal]\intercal & \K[\BSKsslash]\sslash \\ \K[\BSKbindnasrepma]\bindnasrepma & \K[\BSKlbag]\lbag & \K[\BSKtimes]\times \\ \K[\BSKblackbowtie]\blackbowtie & \K[\BSKlblackbowtie]\lblackbowtie & \K[\BSKuplus]\uplus \\ \K[\BSKbowtie]\bowtie & \K[\BSKleftslice]\leftslice & \K[\BSKvarcap]\varcap \\ \K[\BSKcap]\cap & \K[\BSKleftthreetimes]\leftthreetimes & \K[\BSKvarcup]\varcup \\ \K[\BSKCap]\Cap & \K[\BSKlessdot]\lessdot & \K[\BSKvarintercal]\varintercal \\ \K[\BSKcdot]\cdot & \K[\BSKltimes]\ltimes & \K[\BSKvarsqcap]\varsqcap \\ \K[\BSKcenterdot]\centerdot & \K[\BSKltimesblack]\ltimesblack & \K[\BSKvarsqcup]\varsqcup \\ \K[\BSKcircplus]\circplus & \K[\BSKmerge]\merge & \K[\BSKvartimes]\vartimes \\ \K[\BSKcoAsterisk]\coAsterisk & \K[\BSKminuso]\minuso & \K[\BSKvee]\vee \\ \K[\BSKconvolution]\convolution & \K[\BSKmoo]\moo & \K[\BSKVee]\Vee \\ \K[\BSKcup]\cup & \K[\BSKmp]\mp & \K[\BSKveebar]\veebar \\ \K[\BSKCup]\Cup & \K[\BSKnplus]\nplus & \K[\BSKveeonvee]\veeonvee \\ \K[\BSKcupleftarrow]\cupleftarrow & \K[\BSKpluscirc]\pluscirc & \K[\BSKwedge]\wedge \\ \K[\BSKcurlyvee]\curlyvee & \K[\BSKplustrif]\plustrif & \K[\BSKWedge]\Wedge \\ \K[\BSKcurlywedge]\curlywedge & \K[\BSKpm]\pm & \K[\BSKYdown]\Ydown \\ \K[\BSKdagger]\dagger & \K[\BSKrbag]\rbag & \K[\BSKYleft]\Yleft \\ \K[\BSKddagger]\ddagger & \K[\BSKrblackbowtie]\rblackbowtie & \K[\BSKYright]\Yright \\ \K[\BSKdiv]\div & \K[\BSKrightslice]\rightslice & \K[\BSKYup]\Yup \\ \K[\BSKdivideontimes]\divideontimes & \K[\BSKrightthreetimes]\rightthreetimes & \\ \K[\BSKdotplus]\dotplus & \K[\BSKrtimes]\rtimes & \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[STIX]{\STIX\ Binary Operators} \ltidxboth{binary}{operators} \ltindex{plusses} \label{stix-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXamalg]\amalg & \K[\STIXfcmp]\fcmp & \K[\STIXsqcup]\sqcup \\ \K[\STIXast]\ast & \K[\STIXfracslash]\fracslash & \K[\STIXSqcup]\Sqcup \\ \K[\STIXbarcap]\barcap & \K[\STIXintercal]\intercal & \K[\STIXsslash]\sslash \\ \K[\STIXbarcup]\barcup & \K[\STIXinterleave]\interleave & \K[\STIXthreedotcolon]\threedotcolon \\ \K[\STIXbarvee]\barvee & \K[\STIXintprod]\intprod & \K[\STIXtimes]\times \\ \K[\STIXbarwedge]\barwedge & \K[\STIXintprodr]\intprodr & \K[\STIXtimesbar]\timesbar \\ \K[\STIXbigslopedvee]\bigslopedvee & \K[\STIXinvlazys]\invlazys & \K[\STIXtminus]\tminus \\ \K[\STIXbigslopedwedge]\bigslopedwedge & \K[\STIXleftthreetimes]\leftthreetimes & \K[\STIXtplus]\tplus \\ \K[\STIXbtimes]\btimes & \K[\STIXlhd]\lhd & \K[\STIXtripleplus]\tripleplus \\ \K[\STIXcap]\cap & \K[\STIXltimes]\ltimes & \K[\STIXtrslash]\trslash \\ \K[\STIXCap]\Cap & \K[\STIXmidbarvee]\midbarvee & \K[\STIXtwocaps]\twocaps \\ \K[\STIXcapbarcup]\capbarcup & \K[\STIXmidbarwedge]\midbarwedge & \K[\STIXtwocups]\twocups \\ \K[\STIXcapdot]\capdot & \K[\STIXminusdot]\minusdot & \K[\STIXtypecolon]\typecolon \\ \K[\STIXcapovercup]\capovercup & \K[\STIXminusfdots]\minusfdots & \K[\STIXuminus]\uminus \\ \K[\STIXcapwedge]\capwedge & \K[\STIXminusrdots]\minusrdots & \K[\STIXunlhd]\unlhd \\ \K[\STIXclosedvarcap]\closedvarcap & \K[\STIXmp]\mp & \K[\STIXunrhd]\unrhd \\ \K[\STIXclosedvarcup]\closedvarcup & \K[\STIXnhVvert]\nhVvert & \K[\STIXupand]\upand \\ \K[\STIXclosedvarcupsmashprod]\closedvarcupsmashprod & \K[\STIXopluslhrim]\opluslhrim & \K[\STIXuplus]\uplus \\ \K[\STIXcommaminus]\commaminus & \K[\STIXoplusrhrim]\oplusrhrim & \K[\STIXvarbarwedge]\varbarwedge \\ \K[\STIXcup]\cup & \K[\STIXotimeslhrim]\otimeslhrim & \K[\STIXvardoublebarwedge]\vardoublebarwedge \\ \K[\STIXCup]\Cup & \K[\STIXotimesrhrim]\otimesrhrim & \K[\STIXvarveebar]\varveebar \\ \K[\STIXcupbarcap]\cupbarcap & \K[\STIXplusdot]\plusdot & \K[\STIXvectimes]\vectimes \\ \K[\STIXcupdot]\cupdot & \K[\STIXpluseqq]\pluseqq & \K[\STIXVee]\Vee \\ \K[\STIXcupleftarrow]\cupleftarrow & \K[\STIXplushat]\plushat & \K[\STIXvee]\vee \\ \K[\STIXcupovercap]\cupovercap & \K[\STIXplussim]\plussim & \K[\STIXveebar]\veebar \\ \K[\STIXcupvee]\cupvee & \K[\STIXplussubtwo]\plussubtwo & \K[\STIXveedot]\veedot \\ \K[\STIXcurlyvee]\curlyvee & \K[\STIXplustrif]\plustrif & \K[\STIXveedoublebar]\veedoublebar \\ \K[\STIXcurlywedge]\curlywedge & \K[\STIXpm]\pm & \K[\STIXveemidvert]\veemidvert \\ \K[\STIXdagger]\dagger & \K[\STIXrhd]\rhd & \K[\STIXveeodot]\veeodot \\ \K[\STIXddagger]\ddagger & \K[\STIXrightthreetimes]\rightthreetimes & \K[\STIXveeonvee]\veeonvee \\ \K[\STIXdiv]\div & \K[\STIXringplus]\ringplus & \K[\STIXWedge]\Wedge \\ \K[\STIXdivideontimes]\divideontimes & \K[\STIXrsolbar]\rsolbar & \K[\STIXwedge]\wedge \\ \K[\STIXdotminus]\dotminus & \K[\STIXrtimes]\rtimes & \K[\STIXwedgebar]\wedgebar \\ \K[\STIXdotplus]\dotplus & \K[\STIXsetminus]\setminus & \K[\STIXwedgedot]\wedgedot \\ \K[\STIXdottimes]\dottimes & \K[\STIXshuffle]\shuffle & \K[\STIXwedgedoublebar]\wedgedoublebar \\ \K[\STIXdoublebarvee]\doublebarvee & \K[\STIXsimplus]\simplus & \K[\STIXwedgemidvert]\wedgemidvert \\ \K[\STIXdoublebarwedge]\doublebarwedge & \K[\STIXsmallsetminus]\smallsetminus & \K[\STIXwedgeodot]\wedgeodot \\ \K[\STIXdoubleplus]\doubleplus & \K[\STIXsmashtimes]\smashtimes & \K[\STIXwedgeonwedge]\wedgeonwedge \\ \K[\STIXdsol]\dsol & \K[\STIXsqcap]\sqcap & \K[\STIXwr]\wr \\ \K[\STIXeqqplus]\eqqplus & \K[\STIXSqcap]\Sqcap & \\ \end{longtable} \begin{tablenote} \STIX\ defines \cmdI[\string\STIXland]{\land} as a synonym for \cmdI[\string\STIXwedge]{\wedge}, \cmdI[\string\STIXlor]{\lor} as a synonym for \cmdI[\string\STIXvee]{\vee}, \cmdI[\string\STIXdoublecap]{\doublecap} as a synonym for \cmdI[\string\STIXCap]{\Cap}, and \cmdI[\string\STIXdoublecup]{\doublecup} as a synonym for \cmdI[\string\STIXCup]{\Cup}. \end{tablenote} \end{longsymtable} \begin{symtable}[MDES]{\MDES\ Binary Operators} \idxboth{binary}{operators} \label{mdes-bin} \begin{tabular}{*3{ll}} \K[\MDESdtimes]\dtimes & \K[\MDESudtimes]\udtimes & \K[\MDESutimes]\utimes \\ \end{tabular} \bigskip \begin{tablenote} \ifAMS The \MDES\ package additionally provides versions of each of the binary operators shown in \vref{ams-bin}. \else The \MDES\ package additionally provides versions of each of the \AMS\ binary operators. \fi \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Binary Operators} \idxboth{binary}{operators} \label{pdfmsym-bin} \begin{tabular}{*3{ll}} \X\circwedge & \X\divs & \X\ndivs \\ \X\dcup & \X\dwedge & \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[CMLL]{\CMLL\ Binary Operators} \idxboth{binary}{operators} \label{cmll-bin} \begin{tabular}{ll@{\qquad}ll} \K[\CMLLparr]\parr$^*$ & \K[\&]\with$^\dag$ \\ \end{tabular} \bigskip \begin{tablenote}[*] \CMLL\ defines \cmdI[\CMLLparr]{\invamp} as a synonym for \cmdI[\CMLLparr]{\parr}. \end{tablenote} \medskip \begin{tablenote}[\dag] \cmdI[\&]{\with} differs from~\cmdI{\&} in terms of its math-mode spacing: \verb|$A \& B$| produces ``$A \& B$'', for example, while \verb|$A \with B$| produces ``$A\mathbin{\&}B$''. \end{tablenote} \end{symtable} \begin{symtable}[SHUF]{\SHUF\ Binary Operators} \idxboth{binary}{operators} \index{shuffle product=shuffle product (\shuffle)} \index{complete shuffle product=complete shuffle product (\cshuffle)} \label{shuf-bin} \begin{tabular}{ll@{\qquad}ll} \K\cshuffle & \K\shuffle \\ \end{tabular} \end{symtable} \begin{symtable}[RESMES]{\RESMES\ Binary Operators} \idxboth{binary}{operators} \index{restriction of a measure} \label{resmes-bin} \begin{tabular}{ll} \X\resmes \\ \end{tabular} \bigskip \begin{tablenote} This symbol notates the restriction of a measure to a set, as in $\phi \resmes Y$. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Logical Operators} \idxboth{binary}{operators} \idxboth{logic}{symbols} \label{logix-bin} \begin{tabular}{*4{ll}} \K\CircInvNt & \K\CircXor & \K\Nand & \K\SbNd \\ \K\CircNand & \K\Dnd & \K\Nd & \K\SbNor \\ \K\CircNd & \K\Dnt & \K\Ngt & \K\SbOr \\ \K\CircNgt & \K\Dor & \K\Nor & \K\SbXor \\ \K\CircNor & \K\InvNt & \K\Nt & \K\Shfr \\ \K\CircNt & \K\Lnand & \K\Or & \K\Xor \\ \K\CircOr & \K\Lnor & \K\SbNand & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[ULSY]{\ULSY\ Geometric Binary Operators} \idxboth{binary}{operators} \label{ulsy-geometric-bin} \begin{tabular}{ll} \K\odplus \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Geometric Binary Operators} \idxboth{binary}{operators} \idxboth{logic}{symbols} \idxboth{boxed}{symbols} \index{asterisks} \index{asterisks>boxed} \index{asterisks>circled} \label{abx-geometric-bin} \begin{tabular}{*3{ll}} \X[\ABXblacktriangledown]\blacktriangledown & \X[\ABXboxright]\boxright & \X[\ABXominus]\ominus \\ \X[\ABXblacktriangleleft]\blacktriangleleft & \X[\ABXboxslash]\boxslash & \X[\ABXoplus]\oplus \\ \X[\ABXblacktriangleright]\blacktriangleright & \X[\ABXboxtimes]\boxtimes & \X[\ABXoright]\oright \\ \X[\ABXblacktriangleup]\blacktriangleup & \X[\ABXboxtop]\boxtop & \X[\ABXoslash]\oslash \\ \X[\ABXboxasterisk]\boxasterisk & \X[\ABXboxtriangleup]\boxtriangleup & \X[\ABXotimes]\otimes \\ \X[\ABXboxbackslash]\boxbackslash & \X[\ABXboxvoid]\boxvoid & \X[\ABXotop]\otop \\ \X[\ABXboxbot]\boxbot & \X[\ABXoasterisk]\oasterisk & \X[\ABXotriangleup]\otriangleup \\ \X[\ABXboxcirc]\boxcirc & \X[\ABXobackslash]\obackslash & \X[\ABXovoid]\ovoid \\ \X[\ABXboxcoasterisk]\boxcoasterisk & \X[\ABXobot]\obot & \X[\ABXsmalltriangledown]\smalltriangledown \\ \X[\ABXboxdiv]\boxdiv & \X[\ABXocirc]\ocirc & \X[\ABXsmalltriangleleft]\smalltriangleleft \\ \X[\ABXboxdot]\boxdot & \X[\ABXocoasterisk]\ocoasterisk & \X[\ABXsmalltriangleright]\smalltriangleright \\ \X[\ABXboxleft]\boxleft & \X[\ABXodiv]\odiv & \X[\ABXsmalltriangleup]\smalltriangleup \\ \X[\ABXboxminus]\boxminus & \X[\ABXodot]\odot \\ \X[\ABXboxplus]\boxplus & \X[\ABXoleft]\oleft \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Geometric Binary Operators} \idxboth{binary}{operators} \idxboth{logic}{symbols} \index{rhombuses} \label{mns-geometric-bin} \begin{tabular}{*3{ll}} \K[\MNSboxbackslash]\boxbackslash & \K[\MNSfilledmedtriangledown]\filledmedtriangledown & \K[\MNSocirc]\ocirc \\ \K[\MNSboxbox]\boxbox & \K[\MNSfilledmedtriangleleft]\filledmedtriangleleft & \K[\MNSodot]\odot \\ \K[\MNSboxdot]\boxdot & \K[\MNSfilledmedtriangleright]\filledmedtriangleright & \K[\MNSominus]\ominus \\ \K[\MNSboxminus]\boxminus & \K[\MNSfilledmedtriangleup]\filledmedtriangleup & \K[\MNSoplus]\oplus \\ \K[\MNSboxplus]\boxplus & \K[\MNSfilledsquare]\filledsquare & \K[\MNSoslash]\oslash \\ \K[\MNSboxslash]\boxslash & \K[\MNSfilledstar]\filledstar & \K[\MNSostar]\ostar \\ \K[\MNSboxtimes]\boxtimes & \K[\MNSfilledtriangledown]\filledtriangledown & \K[\MNSotimes]\otimes \\ \K[\MNSboxvert]\boxvert & \K[\MNSfilledtriangleleft]\filledtriangleleft & \K[\MNSotriangle]\otriangle \\ \K[\MNSdiamondbackslash]\diamondbackslash & \K[\MNSfilledtriangleright]\filledtriangleright & \K[\MNSovert]\overt \\ \K[\MNSdiamonddiamond]\diamonddiamond & \K[\MNSfilledtriangleup]\filledtriangleup & \K[\MNSpentagram]\pentagram \\ \K[\MNSdiamonddot]\diamonddot & \K[\MNSmeddiamond]\meddiamond & \K[\MNSsmalldiamond]\smalldiamond \\ \K[\MNSdiamondminus]\diamondminus & \K[\MNSmedsquare]\medsquare & \K[\MNSsmallsquare]\smallsquare \\ \K[\MNSdiamondplus]\diamondplus & \K[\MNSmedstar]\medstar & \K[\MNSsmallstar]\smallstar \\ \K[\MNSdiamondslash]\diamondslash & \K[\MNSmedtriangledown]\medtriangledown & \K[\MNSsmalltriangledown]\smalltriangledown \\ \K[\MNSdiamondtimes]\diamondtimes & \K[\MNSmedtriangleleft]\medtriangleleft & \K[\MNSsmalltriangleleft]\smalltriangleleft \\ \K[\MNSdiamondvert]\diamondvert & \K[\MNSmedtriangleright]\medtriangleright & \K[\MNSsmalltriangleright]\smalltriangleright \\ \K[\MNSdownslice]\downslice & \K[\MNSmedtriangleup]\medtriangleup & \K[\MNSsmalltriangleup]\smalltriangleup \\ \K[\MNSfilleddiamond]\filleddiamond & \K[\MNSoast]\oast & \K[\MNSthinstar]\thinstar \\ \K[\MNSfilledmedsquare]\filledmedsquare & \K[\MNSobackslash]\obackslash & \K[\MNSupslice]\upslice \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ defines \cmdI[\MNSfilledmedsquare]{\blacksquare} as a synonym for \cmdI[\MNSfilledmedsquare]{\filledmedsquare}; \cmdI[\MNSmedsquare]{\square} and \cmdI[\MNSmedsquare]{\Box} as synonyms for \cmdI[\MNSmedsquare]{\medsquare}; \cmdI[\MNSsmalldiamond]{\diamond} as a synonym for \cmdI[\MNSsmalldiamond]{\smalldiamond}; \cmdI[\MNSmeddiamond]{\Diamond} as a synonym for \cmdI[\MNSmeddiamond]{\meddiamond}; \cmdI[\MNSthinstar]{\star} as a synonym for \cmdI[\MNSthinstar]{\thinstar}; \cmdI[\MNSoast]{\circledast} as a synonym for \cmdI[\MNSoast]{\oast}; \cmdI[\MNSocirc]{\circledcirc} as a synonym for \cmdI[\MNSocirc]{\ocirc}; and, \cmdI[\MNSominus]{\circleddash} as a synonym for \cmdI[\MNSominus]{\ominus}. \end{tablenote} \end{symtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Geometric Binary Operators} \ltidxboth{binary}{operators} \ltidxboth{boxed}{symbols} \ltindex{circles} \ltindex{squares} \ltindex{triangles} \ltindex{rhombuses} \ltindex{stars} \ltindex{asterisks} \ltindex{asterisks>circled} \label{fdsym-geometric-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMboxbackslash]\boxbackslash & \K[\FDSYMmedblacktriangledown]\medblacktriangledown & \K[\FDSYMoplus]\oplus \\ \K[\FDSYMboxbox]\boxbox & \K[\FDSYMmedblacktriangleleft]\medblacktriangleleft & \K[\FDSYMoslash]\oslash \\ \K[\FDSYMboxdot]\boxdot & \K[\FDSYMmedblacktriangleright]\medblacktriangleright & \K[\FDSYMotimes]\otimes \\ \K[\FDSYMboxminus]\boxminus & \K[\FDSYMmedblacktriangleup]\medblacktriangleup & \K[\FDSYMovert]\overt \\ \K[\FDSYMboxplus]\boxplus & \K[\FDSYMmedcircle]\medcircle & \K[\FDSYMsmallblackcircle]\smallblackcircle \\ \K[\FDSYMboxslash]\boxslash & \K[\FDSYMmeddiamond]\meddiamond & \K[\FDSYMsmallblackdiamond]\smallblackdiamond \\ \K[\FDSYMboxtimes]\boxtimes & \K[\FDSYMmedslash]\medslash & \K[\FDSYMsmallblacksquare]\smallblacksquare \\ \K[\FDSYMboxvert]\boxvert & \K[\FDSYMmedsquare]\medsquare & \K[\FDSYMsmallblackstar]\smallblackstar \\ \K[\FDSYMdiamondbackslash]\diamondbackslash & \K[\FDSYMmedtriangledown]\medtriangledown & \K[\FDSYMsmallblacktriangledown]\smallblacktriangledown \\ \K[\FDSYMdiamonddiamond]\diamonddiamond & \K[\FDSYMmedtriangleleft]\medtriangleleft & \K[\FDSYMsmallblacktriangleleft]\smallblacktriangleleft \\ \K[\FDSYMdiamonddot]\diamonddot & \K[\FDSYMmedtriangleright]\medtriangleright & \K[\FDSYMsmallblacktriangleright]\smallblacktriangleright \\ \K[\FDSYMdiamondminus]\diamondminus & \K[\FDSYMmedtriangleup]\medtriangleup & \K[\FDSYMsmallblacktriangleup]\smallblacktriangleup \\ \K[\FDSYMdiamondplus]\diamondplus & \K[\FDSYMmedwhitestar]\medwhitestar & \K[\FDSYMsmallcircle]\smallcircle \\ \K[\FDSYMdiamondslash]\diamondslash & \K[\FDSYMoast]\oast & \K[\FDSYMsmalldiamond]\smalldiamond \\ \K[\FDSYMdiamondtimes]\diamondtimes & \K[\FDSYMobackslash]\obackslash & \K[\FDSYMsmallsquare]\smallsquare \\ \K[\FDSYMdiamondvert]\diamondvert & \K[\FDSYMocirc]\ocirc & \K[\FDSYMsmalltriangledown]\smalltriangledown \\ \K[\FDSYMmedblackcircle]\medblackcircle & \K[\FDSYModash]\odash & \K[\FDSYMsmalltriangleleft]\smalltriangleleft \\ \K[\FDSYMmedblackdiamond]\medblackdiamond & \K[\FDSYModot]\odot & \K[\FDSYMsmalltriangleright]\smalltriangleright \\ \K[\FDSYMmedblacksquare]\medblacksquare & \K[\FDSYMoequal]\oequal & \K[\FDSYMsmalltriangleup]\smalltriangleup \\ \K[\FDSYMmedblackstar]\medblackstar & \K[\FDSYMominus]\ominus & \K[\FDSYMsmallwhitestar]\smallwhitestar \\ \end{longtable} \FDSYM\ defines synonyms for most of the preceding symbols: \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMblackdiamond]{\blackdiamond} & \K[\FDSYMdiamond]{\diamond} & \K[\FDSYMsmblkcircle]{\smblkcircle} \\ \K[\FDSYMblacktriangle]{\blacktriangle} & \K[\FDSYMDiamond]{\Diamond} & \K[\FDSYMsmblkdiamond]{\smblkdiamond} \\ \K[\FDSYMblacktriangledown]{\blacktriangledown} & \K[\FDSYMdiamondbslash]{\diamondbslash} & \K[\FDSYMsmblksquare]{\smblksquare} \\ \K[\FDSYMblacktriangleleft]{\blacktriangleleft} & \K[\FDSYMdiamondcdot]{\diamondcdot} & \K[\FDSYMsmwhitestar]{\smwhitestar} \\ \K[\FDSYMblacktriangleright]{\blacktriangleright} & \K[\FDSYMmdblkdiamond]{\mdblkdiamond} & \K[\FDSYMsmwhtcircle]{\smwhtcircle} \\ \K[\FDSYMBox]{\Box} & \K[\FDSYMmdblksquare]{\mdblksquare} & \K[\FDSYMsmwhtdiamond]{\smwhtdiamond} \\ \K[\FDSYMboxbar]{\boxbar} & \K[\FDSYMmdlgblkcircle]{\mdlgblkcircle} & \K[\FDSYMsmwhtsquare]{\smwhtsquare} \\ \K[\FDSYMboxbslash]{\boxbslash} & \K[\FDSYMmdlgblkdiamond]{\mdlgblkdiamond} & \K[\FDSYMsquare]{\square} \\ \K[\FDSYMboxdiag]{\boxdiag} & \K[\FDSYMmdlgblksquare]{\mdlgblksquare} & \K[\FDSYMstar]{\star} \\ \K[\FDSYMbullet]{\bullet} & \K[\FDSYMmdlgwhtcircle]{\mdlgwhtcircle} & \K[\FDSYMtriangle]{\triangle} \\ \K[\FDSYMcirc]{\circ} & \K[\FDSYMmdlgwhtdiamond]{\mdlgwhtdiamond} & \K[\FDSYMtriangledown]{\triangledown} \\ \K[\FDSYMcircledast]{\circledast} & \K[\FDSYMmdlgwhtsquare]{\mdlgwhtsquare} & \K[\FDSYMtriangleleft]{\triangleleft} \\ \K[\FDSYMcircledcirc]{\circledcirc} & \K[\FDSYMmdwhtdiamond]{\mdwhtdiamond} & \K[\FDSYMtriangleright]{\triangleright} \\ \K[\FDSYMcircleddash]{\circleddash} & \K[\FDSYMmdwhtsquare]{\mdwhtsquare} & \K[\FDSYMvartriangle]{\vartriangle} \\ \K[\FDSYMcircledequal]{\circledequal} & \K[\FDSYMmedstar]{\medstar} & \\ \K[\FDSYMcircledvert]{\circledvert} & \K[\FDSYMobslash]{\obslash} & \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[BSK]{\BSK\ Geometric Binary Operators} \ltidxboth{binary}{operators} \ltidxboth{boxed}{symbols} \ltindex{rhombuses} \ltindex{squares} \ltindex{circles} \ltindex{triangles} \ltindex{stars} \label{bsk-geometric-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\BSKblacklozenge]\blacklozenge & \K[\BSKboxright]\boxright & \K[\BSKoblong]\oblong \\ \K[\BSKblacksquare]\blacksquare & \K[\BSKboxslash]\boxslash & \K[\BSKobot]\obot \\ \K[\BSKblacktriangle]\blacktriangle & \K[\BSKboxtimes]\boxtimes & \K[\BSKobslash]\obslash \\ \K[\BSKblacktriangledown]\blacktriangledown & \K[\BSKboxtop]\boxtop & \K[\BSKogreaterthan]\ogreaterthan \\ \K[\BSKblacktriangleleft]\blacktriangleleft & \K[\BSKboxtriangle]\boxtriangle & \K[\BSKoleft]\oleft \\ \K[\BSKblacktriangleright]\blacktriangleright & \K[\BSKcircledast]\circledast & \K[\BSKolessthan]\olessthan \\ \K[\BSKboxast]\boxast & \K[\BSKcircledcirc]\circledcirc & \K[\BSKominus]\ominus \\ \K[\BSKboxbar]\boxbar & \K[\BSKcircleddash]\circleddash & \K[\BSKoplus]\oplus \\ \K[\BSKboxbot]\boxbot & \K[\BSKdiamond]\diamond & \K[\BSKoright]\oright \\ \K[\BSKboxbox]\boxbox & \K[\BSKdiamondbar]\diamondbar & \K[\BSKoslash]\oslash \\ \K[\BSKboxbslash]\boxbslash & \K[\BSKdiamondcircle]\diamondcircle & \K[\BSKotimes]\otimes \\ \K[\BSKboxcircle]\boxcircle & \K[\BSKdiamondminus]\diamondminus & \K[\BSKotop]\otop \\ \K[\BSKboxdivision]\boxdivision & \K[\BSKdiamondop]\diamondop & \K[\BSKotriangle]\otriangle \\ \K[\BSKboxdot]\boxdot & \K[\BSKdiamondplus]\diamondplus & \K[\BSKovee]\ovee \\ \K[\BSKboxleft]\boxleft & \K[\BSKdiamondtimes]\diamondtimes & \K[\BSKowedge]\owedge \\ \K[\BSKboxminus]\boxminus & \K[\BSKdiamondtriangle]\diamondtriangle & \K[\BSKstar]\star \\ \K[\BSKboxplus]\boxplus & \K[\BSKobar]\obar & \K[\BSKtalloblong]\talloblong \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[STIX]{\STIX\ Geometric Binary Operators} \ltidxboth{binary}{operators} \ltindex{rhombuses} \ltindex{squares} \ltindex{circles} \ltindex{triangles} \ltindex{stars} \ltindex{crosses} \label{stix-geometric-bin} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXblackhourglass]\blackhourglass & \K[\STIXconcavediamondtickleft]\concavediamondtickleft & \K[\STIXoplus]\oplus \\ \K[\STIXboxast]\boxast & \K[\STIXconcavediamondtickright]\concavediamondtickright & \K[\STIXoslash]\oslash \\ \K[\STIXboxbar]\boxbar & \K[\STIXdiamond]\diamond & \K[\STIXotimes]\otimes \\ \K[\STIXboxbox]\boxbox & \K[\STIXdsub]\dsub & \K[\STIXOtimes]\Otimes \\ \K[\STIXboxbslash]\boxbslash & \K[\STIXhourglass]\hourglass & \K[\STIXotimeshat]\otimeshat \\ \K[\STIXboxcircle]\boxcircle & \K[\STIXlozengeminus]\lozengeminus & \K[\STIXrsub]\rsub \\ \K[\STIXboxdiag]\boxdiag & \K[\STIXmdlgblklozenge]\mdlgblklozenge & \K[\STIXsmblkcircle]\smblkcircle \\ \K[\STIXboxdot]\boxdot & \K[\STIXmdlgwhtcircle]\mdlgwhtcircle & \K[\STIXstar]\star \\ \K[\STIXboxminus]\boxminus & \K[\STIXobar]\obar & \K[\STIXtalloblong]\talloblong \\ \K[\STIXboxplus]\boxplus & \K[\STIXobot]\obot$^*$ & \K[\STIXtriangle]\triangle \\ \K[\STIXboxtimes]\boxtimes & \K[\STIXobslash]\obslash & \K[\STIXtriangleminus]\triangleminus \\ \K[\STIXcircledast]\circledast & \K[\STIXodiv]\odiv & \K[\STIXtriangleplus]\triangleplus \\ \K[\STIXcircledcirc]\circledcirc & \K[\STIXodot]\odot & \K[\STIXtriangleserifs]\triangleserifs \\ \K[\STIXcircleddash]\circleddash & \K[\STIXodotslashdot]\odotslashdot$^*$ & \K[\STIXtriangletimes]\triangletimes \\ \K[\STIXcircledequal]\circledequal & \K[\STIXogreaterthan]\ogreaterthan & \K[\STIXvysmblkcircle]\vysmblkcircle$^\dag$ \\ \K[\STIXcircledparallel]\circledparallel & \K[\STIXolcross]\olcross$^*$ & \K[\STIXvysmwhtcircle]\vysmwhtcircle \\ \K[\STIXcircledvert]\circledvert & \K[\STIXolessthan]\olessthan & \K[\STIXwhitesquaretickleft]\whitesquaretickleft \\ \K[\STIXcirclehbar]\circlehbar & \K[\STIXominus]\ominus & \K[\STIXwhitesquaretickright]\whitesquaretickright \\ \K[\STIXconcavediamond]\concavediamond & \K[\STIXoperp]\operp & \\ \end{longtable} \begin{tablenote}[*] Defined as an ordinary character, not as a binary relation. However, these symbols more closely resemble the other symbols in this table than they do the geometric shapes presented in \ref{stix-geometrical}, which is why they are included here. \end{tablenote} \bigskip \begin{tablenote}[\dag] \STIX\ defines \cmdI[\string\STIXbullet]{\bullet} as a synonym for \cmdI[\string\STIXvysmblkcircle]{\vysmblkcircle}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[LOGIX]{\LOGIX\ Geometric Binary Operators} \ltidxboth{binary}{operators} \ltindex{rhombuses} \ltindex{circles} \ltindex{triangles} \ltindex{squares} \ltindex{polygons} \ltindex{arrowheads} \ltindex{geometric shapes} \label{logix-geometric-bin} \begin{longtable}{*2{ll}} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K\BlackCircle & \K\LogPast \\ \K\BlackCircleA & \K\LogPos \\ \K\BlackCircleB & \K\LWhiteCircle \\ \K\BlackCircleC & \K\LWhiteCurvedDiamond \\ \K\BlackCircleD & \K\LWhiteDiamond \\ \K\BlackCircleE & \K\LWhiteDownTriangle \\ \K\BlackCircleF & \K\LWhiteLeftArrowHead \\ \K\BlackCircleG & \K\LWhiteLeftTriangle \\ \K\BlackCircleH & \K\LWhiteLozenge \\ \K\BlackCircleI & \K\LWhiteRightArrowHead \\ \K\BlackCurvedDiamond & \K\LWhiteRightCurvedArrowHead \\ \K\BlackDiamond & \K\LWhiteRightTriangle \\ \K\BlackDiamondA & \K\LWhiteSmallCircle \\ \K\BlackDiamondB & \K\LWhiteSquare \\ \K\BlackDiamondC & \K\LWhiteSquareRoundCorners \\ \K\BlackDiamondD & \K\LWhiteUpTriangle \\ \K\BlackDiamondE & \K\LWhiteVerySmallCircle \\ \K\BlackDiamondF & \K\LWhiteVerySmallSquare \\ \K\BlackDiamondG & \K\Nec \\ \K\BlackDiamondH & \K\Next \\ \K\BlackDiamondI & \K\NonCont \\ \K\BlackDownTriangle & \K\OutlineCircle \\ \K\BlackDownTriangleA & \K\OutlineCurvedDiamond \\ \K\BlackDownTriangleB & \K\OutlineDiamond \\ \K\BlackDownTriangleC & \K\OutlineDownTriangle \\ \K\BlackDownTriangleD & \K\OutlineLeftArrowHead \\ \K\BlackDownTriangleE & \K\OutlineLeftTriangle \\ \K\BlackDownTriangleF & \K\OutlineLozenge \\ \K\BlackDownTriangleG & \K\OutlineRightArrowHead \\ \K\BlackDownTriangleH & \K\OutlineRightCurvedArrowHead \\ \K\BlackDownTriangleI & \K\OutlineRightTriangle \\ \K\BlackLeftArrowHead & \K\OutlineSmallCircle \\ \K\BlackLeftTriangle & \K\OutlineSquare \\ \K\BlackLeftTriangleA & \K\OutlineSquareRoundCorners \\ \K\BlackLeftTriangleB & \K\OutlineUpTriangle \\ \K\BlackLeftTriangleC & \K\OutlineVerySmallCircle \\ \K\BlackLeftTriangleD & \K\OutlineVerySmallSquare \\ \K\BlackLeftTriangleE & \K\Past \\ \K\BlackLeftTriangleF & \K\Pos \\ \K\BlackLeftTriangleG & \K\QuartedLozenge \\ \K\BlackLeftTriangleH & \K\QuarteredCircle \\ \K\BlackLeftTriangleI & \K\QuarteredCurvedDiamond \\ \K\BlackLozenge & \K\QuarteredDiamond \\ \K\BlackReallySmallCircle & \K\QuarteredDownTriangle \\ \K\BlackReallySmallDiamond & \K\QuarteredLeftTriangle \\ \K\BlackReallySmallSquare & \K\QuarteredRightTriangle \\ \K\BlackRightArrowHead & \K\QuarteredSmallCircle \\ \K\BlackRightCurvedArrowHead & \K\QuarteredSquare \\ \K\BlackRightTriangle & \K\QuarteredSquareRoundCorners \\ \K\BlackRightTriangleA & \K\QuarteredUpTriangle \\ \K\BlackRightTriangleB & \K\QuarteredVerySmallCircle \\ \K\BlackRightTriangleC & \K\QuarteredVerySmallSquare \\ \K\BlackRightTriangleD & \K\TmpCont \\ \K\BlackRightTriangleE & \K\TmpFutr \\ \K\BlackRightTriangleF & \K\TmpNec \\ \K\BlackRightTriangleG & \K\TmpNext \\ \K\BlackRightTriangleH & \K\TmpNonCont \\ \K\BlackRightTriangleI & \K\TmpPast \\ \K\BlackSmallCircle & \K\TmpPos \\ \K\BlackSquare & \K\UpSlahsedSquareRoundCorners \\ \K\BlackSquareA & \K\UpSlashedCircle \\ \K\BlackSquareB & \K\UpSlashedCurvedDiamond \\ \K\BlackSquareC & \K\UpSlashedDiamond \\ \K\BlackSquareD & \K\UpSlashedDownTriangle \\ \K\BlackSquareE & \K\UpSlashedLeftTriangle \\ \K\BlackSquareF & \K\UpSlashedLozenge \\ \K\BlackSquareG & \K\UpSlashedRightTriangle \\ \K\BlackSquareH & \K\UpSlashedSmallCircle \\ \K\BlackSquareI & \K\UpSlashedSquare \\ \K\BlackSquareRoundCorners & \K\UpSlashedUpTriangle \\ \K\BlackUpTriangle & \K\UpSlashedVerySmallCircle \\ \K\BlackUpTriangleA & \K\UpSlashedVerySmallSquare \\ \K\BlackUpTriangleB & \K\VerticallyDividedCircle \\ \K\BlackUpTriangleC & \K\VerticallyDividedCurvedDiamond \\ \K\BlackUpTriangleD & \K\VerticallyDividedDiamond \\ \K\BlackUpTriangleE & \K\VerticallyDividedDownTriangle \\ \K\BlackUpTriangleF & \K\VerticallyDividedLeftTriangle \\ \K\BlackUpTriangleG & \K\VerticallyDividedLozenge \\ \K\BlackUpTriangleH & \K\VerticallyDividedRightTriangle \\ \K\BlackUpTriangleI & \K\VerticallyDividedSmallCircle \\ \K\BlackVerySmallCircle & \K\VerticallyDividedSquare \\ \K\BlackVerySmallSquare & \K\VerticallyDividedSquareRoundCorners \\ \K\Cont & \K\VerticallyDividedUpTriangle \\ \K\CrossedCircle & \K\VerticallyDividedVerySmallCircle \\ \K\CrossedCurvedDiamond & \K\VerticallyDividedVerySmallSquare \\ \K\CrossedDiamond & \K\WhiteCircle \\ \K\CrossedDownTriangle & \K\WhiteCircleA \\ \K\CrossedLeftTriangle & \K\WhiteCircleB \\ \K\CrossedLozenge & \K\WhiteCircleC \\ \K\CrossedRightTriangle & \K\WhiteCircleContainingBlackCircle \\ \K\CrossedSmallCircle & \K\WhiteCircleD \\ \K\CrossedSquare & \K\WhiteCircleE \\ \K\CrossedSquareRoundCorners & \K\WhiteCircleF \\ \K\CrossedUpTriangle & \K\WhiteCircleG \\ \K\CrossedVerySmallCircle & \K\WhiteCircleH \\ \K\CrossedVerySmallSquare & \K\WhiteCircleI \\ \K\DeoCont & \K\WhiteCurvedDiamond \\ \K\DeoFutr & \K\WhiteCurvedDiamondContainingBlackDiamond \\ \K\DeoNec & \K\WhiteDiamond \\ \K\DeoNext & \K\WhiteDiamondA \\ \K\DeoNonCont & \K\WhiteDiamondB \\ \K\DeoPast & \K\WhiteDiamondC \\ \K\DeoPos & \K\WhiteDiamondContainingBlackDiamond \\ \K\DottedCircl & \K\WhiteDiamondD \\ \K\DottedCurvedDiamond & \K\WhiteDiamondE \\ \K\DottedDiamond & \K\WhiteDiamondF \\ \K\DottedDownTriangle & \K\WhiteDiamondG \\ \K\DottedLeftArrowHead & \K\WhiteDiamondH \\ \K\DottedLeftTriangle & \K\WhiteDiamondI \\ \K\DottedLozenge & \K\WhiteDownTriangle \\ \K\DottedRightArrowHead & \K\WhiteDownTriangleA \\ \K\DottedRightCurvedArrowHead & \K\WhiteDownTriangleB \\ \K\DottedRightTriangle & \K\WhiteDownTriangleC \\ \K\DottedSmallCircle & \K\WhiteDownTriangleContainingBlackDownTriangle \\ \K\DottedSquare & \K\WhiteDownTriangleD \\ \K\DottedSquareRoundCorners & \K\WhiteDownTriangleE \\ \K\DottedUpTriangle & \K\WhiteDownTriangleF \\ \K\DottedVerySmallCircle & \K\WhiteDownTriangleG \\ \K\DottedVerySmallSquare & \K\WhiteDownTriangleH \\ \K\DownSlashedCircle & \K\WhiteDownTriangleI \\ \K\DownSlashedCurvedDiamond & \K\WhiteLeftArrowHead \\ \K\DownSlashedDiamond & \K\WhiteLeftTriangle \\ \K\DownSlashedDownTriangle & \K\WhiteLeftTriangleA \\ \K\DownSlashedLeftTriangle & \K\WhiteLeftTriangleB \\ \K\DownSlashedLozenge & \K\WhiteLeftTriangleC \\ \K\DownSlashedRightTriangle & \K\WhiteLeftTriangleContainingBlackLeftTriangle \\ \K\DownSlashedSmallCircle & \K\WhiteLeftTriangleD \\ \K\DownSlashedSquare & \K\WhiteLeftTriangleE \\ \K\DownSlashedSquareRoundCorners & \K\WhiteLeftTriangleF \\ \K\DownSlashedUpTriangle & \K\WhiteLeftTriangleG \\ \K\DownSlashedVerySmallCircle & \K\WhiteLeftTriangleH \\ \K\DownSlashedVerySmallSquare & \K\WhiteLeftTriangleI \\ \K\DoxCont & \K\WhiteLozenge \\ \K\DoxFutr & \K\WhiteLozengeContainingBlackLozenge \\ \K\DoxNec & \K\WhiteReallySmallCircle \\ \K\DoxNext & \K\WhiteReallySmallDiamond \\ \K\DoxNonCont & \K\WhiteReallySmallSquare \\ \K\DoxPast & \K\WhiteRightArrowHead \\ \K\DoxPos & \K\WhiteRightCurvedArrowHead \\ \K\FacCont & \K\WhiteRightTriangle \\ \K\FacFutr & \K\WhiteRightTriangleA \\ \K\FacNec & \K\WhiteRightTriangleB \\ \K\FacNext & \K\WhiteRightTriangleC \\ \K\FacNonCont & \K\WhiteRightTriangleContainingBlackRightTriangle \\ \K\FacPast & \K\WhiteRightTriangleD \\ \K\FacPos & \K\WhiteRightTriangleE \\ \K\Futr & \K\WhiteRightTriangleF \\ \K\HorizontallyDividedCircle & \K\WhiteRightTriangleG \\ \K\HorizontallyDividedCurvedDiamond & \K\WhiteRightTriangleH \\ \K\HorizontallyDividedDiamond & \K\WhiteRightTriangleI \\ \K\HorizontallyDividedDownTriangle & \K\WhiteSmallCircle \\ \K\HorizontallyDividedLeftTriangle & \K\WhiteSmallCircleContainingBlackCircle \\ \K\HorizontallyDividedLozenge & \K\WhiteSquare \\ \K\HorizontallyDividedRightTriangle & \K\WhiteSquareA \\ \K\HorizontallyDividedSmallCircle & \K\WhiteSquareB \\ \K\HorizontallyDividedSquare & \K\WhiteSquareC \\ \K\HorizontallyDividedSquareRoundCorners & \K\WhiteSquareContainingBlackSquare \\ \K\HorizontallyDividedUpTriangle & \K\WhiteSquareD \\ \K\HorizontallyDividedVerySmallCircle & \K\WhiteSquareE \\ \K\HorizontallyDividedVerySmallSquare & \K\WhiteSquareF \\ \K\LBlackCircle & \K\WhiteSquareG \\ \K\LBlackCurvedDiamond & \K\WhiteSquareH \\ \K\LBlackDiamond & \K\WhiteSquareI \\ \K\LBlackDownTriangle & \K\WhiteSquareRoundCorners \\ \K\LBlackLeftArrowHead & \K\WhiteSquareRoundCornersContainingBlackSquare \\ \K\LBlackLeftTriangle & \K\WhiteUpTriangle \\ \K\LBlackLozenge & \K\WhiteUpTriangleA \\ \K\LBlackRightArrowHead & \K\WhiteUpTriangleB \\ \K\LBlackRightCurvedArrowHead & \K\WhiteUpTriangleC \\ \K\LBlackRightTriangle & \K\WhiteUpTriangleContainingBlackUpTriangle \\ \K\LBlackSmallCircle & \K\WhiteUpTriangleD \\ \K\LBlackSquare & \K\WhiteUpTriangleE \\ \K\LBlackSquareRoundCorners & \K\WhiteUpTriangleF \\ \K\LBlackUpTriangle & \K\WhiteUpTriangleG \\ \K\LBlackVerySmallCircle & \K\WhiteUpTriangleH \\ \K\LBlackVerySmallSquare & \K\WhiteUpTriangleI \\ \K\LogCont & \K\WhiteVerySmallCircle \\ \K\LogFutr & \K\WhiteVerySmallCircleContainingBlackCircle \\ \K\LogNec & \K\WhiteVerySmallSquare \\ \K\LogNext & \K\WhiteVerySmallSquareContainingBlackSquare \\ \K\LogNonCont & \\ \end{longtable} \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{longsymtable} \begin{symtable}[HWMATH]{\HWMATH\ Halloween-Themed Math Operators} \index{pumpkins} \index{witches} \index{ghosts} \index{clouds} \index{skulls} \index{bats} \idxboth{Halloween}{symbols} \label{hwmath-binops} \renewcommand{\arraystretch}{1.25} % Keep high and low accents from touching. \begin{tabular}{ll*2{@{\qquad}ll}} \X\bigpumpkin$^\ddag$ & \X\mathleftghost & \X\reversemathcloud \\ \X\bigskull & \X\mathrightbat & \X\reversemathwitch$^\dag$ \\ \X\mathbat & \X\mathrightghost & \Xstar\reversemathwitch$^\dag$ \\ \X\mathcloud & \Xstar\mathwitch$^\dag$ & \X\skull \\ \X\mathghost & \X\mathwitch$^\dag$ & \\ \X\mathleftbat & \X\pumpkin & \\ \end{tabular} \bigskip \begin{tablenote}[\dag] These symbols accept limits. For example, \verb|\mathwitch*_{i=0}^{\infty} f(x)| produces ``$\mathwitch*_{i=0}^{\infty} f(x)$'' in text mode and \[ \mathwitch*_{i=0}^{\infty} f(x) \] in display mode. \end{tablenote} \bigskip \begin{tablenote}[\ddag] \cmdX{\greatpumpkin} is a synonym for \cmdX{\bigpumpkin}. \end{tablenote} \end{symtable} \begin{symtable}[STIX]{\STIX\ Small Integrals} \index{integrals} \label{stix-smint} \begin{tabular}{*3{ll}} \K[\STIXsmallawint]\smallawint & \K[\STIXsmallintcap]\smallintcap & \K[\STIXsmalloint]\smalloint \\ \K[\STIXsmallcirfnint]\smallcirfnint & \K[\STIXsmallintclockwise]\smallintclockwise & \K[\STIXsmallointctrclockwise]\smallointctrclockwise \\ \K[\STIXsmallfint]\smallfint & \K[\STIXsmallintcup]\smallintcup & \K[\STIXsmallpointint]\smallpointint \\ \K[\STIXsmalliiiint]\smalliiiint & \K[\STIXsmallintlarhk]\smallintlarhk & \K[\STIXsmallrppolint]\smallrppolint \\ \K[\STIXsmalliiint]\smalliiint & \K[\STIXsmallintx]\smallintx & \K[\STIXsmallscpolint]\smallscpolint \\ \K[\STIXsmalliint]\smalliint & \K[\STIXsmalllowint]\smalllowint & \K[\STIXsmallsqint]\smallsqint \\ \K[\STIXsmallint]\smallint & \K[\STIXsmallnpolint]\smallnpolint & \K[\STIXsmallsumint]\smallsumint \\ \K[\STIXsmallintbar]\smallintbar & \K[\STIXsmalloiiint]\smalloiiint & \K[\STIXsmallupint]\smallupint \\ \K[\STIXsmallintBar]\smallintBar & \K[\STIXsmalloiint]\smalloiint & \K[\STIXsmallvarointclockwise]\smallvarointclockwise \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{STIX}{stix}. \end{tablenote} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Small Integrals with Explicit Slant} \ltindex{integrals} \label{stix-smint-all} \begin{longtable}{ll@{\qquad}ll} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXsmallawintsl]\smallawintsl & \K[\STIXsmallawintup]\smallawintup \\ \K[\STIXsmallcirfnintsl]\smallcirfnintsl & \K[\STIXsmallcirfnintup]\smallcirfnintup \\ \K[\STIXsmallfintsl]\smallfintsl & \K[\STIXsmallfintup]\smallfintup \\ \K[\STIXsmalliiiintsl]\smalliiiintsl & \K[\STIXsmalliiiintup]\smalliiiintup \\ \K[\STIXsmalliiintsl]\smalliiintsl & \K[\STIXsmalliiintup]\smalliiintup \\ \K[\STIXsmalliintsl]\smalliintsl & \K[\STIXsmalliintup]\smalliintup \\ \K[\STIXsmallintbarsl]\smallintbarsl & \K[\STIXsmallintBarup]\smallintBarup \\ \K[\STIXsmallintBarsl]\smallintBarsl & \K[\STIXsmallintbarup]\smallintbarup \\ \K[\STIXsmallintcapsl]\smallintcapsl & \K[\STIXsmallintcapup]\smallintcapup \\ \K[\STIXsmallintclockwisesl]\smallintclockwisesl & \K[\STIXsmallintclockwiseup]\smallintclockwiseup \\ \K[\STIXsmallintcupsl]\smallintcupsl & \K[\STIXsmallintcupup]\smallintcupup \\ \K[\STIXsmallintlarhksl]\smallintlarhksl & \K[\STIXsmallintlarhkup]\smallintlarhkup \\ \K[\STIXsmallintsl]\smallintsl & \K[\STIXsmallintup]\smallintup \\ \K[\STIXsmallintxsl]\smallintxsl & \K[\STIXsmallintxup]\smallintxup \\ \K[\STIXsmalllowintsl]\smalllowintsl & \K[\STIXsmalllowintup]\smalllowintup \\ \K[\STIXsmallnpolintsl]\smallnpolintsl & \K[\STIXsmallnpolintup]\smallnpolintup \\ \K[\STIXsmalloiiintsl]\smalloiiintsl & \K[\STIXsmalloiiintup]\smalloiiintup \\ \K[\STIXsmalloiintsl]\smalloiintsl & \K[\STIXsmalloiintup]\smalloiintup \\ \K[\STIXsmallointctrclockwisesl]\smallointctrclockwisesl & \K[\STIXsmallointctrclockwiseup]\smallointctrclockwiseup \\ \K[\STIXsmallointsl]\smallointsl & \K[\STIXsmallointup]\smallointup \\ \K[\STIXsmallpointintsl]\smallpointintsl & \K[\STIXsmallpointintup]\smallpointintup \\ \K[\STIXsmallrppolintsl]\smallrppolintsl & \K[\STIXsmallrppolintup]\smallrppolintup \\ \K[\STIXsmallscpolintsl]\smallscpolintsl & \K[\STIXsmallscpolintup]\smallscpolintup \\ \K[\STIXsmallsqintsl]\smallsqintsl & \K[\STIXsmallsqintup]\smallsqintup \\ \K[\STIXsmallsumintsl]\smallsumintsl & \K[\STIXsmallsumintup]\smallsumintup \\ \K[\STIXsmallupintsl]\smallupintsl & \K[\STIXsmallupintup]\smallupintup \\ \K[\STIXsmallvarointclockwisesl]\smallvarointclockwisesl & \K[\STIXsmallvarointclockwiseup]\smallvarointclockwiseup \\ \end{longtable} \begin{tablenote} \seepackagenote{STIX}{stix}. \end{tablenote} \end{longsymtable} \begin{symtable}{Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \idxboth{logic}{symbols} \index{integrals>circular ($\oint$)} \label{op} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{tabular}{*3{l@{$\:$}ll@{\qquad}}l@{$\:$}ll} \R\bigcap & \R\bigotimes & \R\bigwedge & \R\prod \\ \R\bigcup & \R\bigsqcup & \R\coprod & \R\sum \\ \R\bigodot & \R\biguplus & \R\int \\ \R\bigoplus & \R\bigvee & \R\oint \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \subindex{integrals}{contour} \index{integrals>dotted} \label{ams-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{l@{$\:$}ll@{\qquad}l@{$\:$}ll} \R[\AMSiint]\iint & \R[\AMSiiint]\iiint \\ \R[\AMSiiiint]\iiiint & \R[\AMSidotsint]\idotsint \\ \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \label{st-large} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{tabular}{*2{l@{$\:$}ll@{\qquad}}l@{$\:$}ll} \R\bigbox & \R\biginterleave & \R\bigsqcap \\ \R\bigcurlyvee & \R\bignplus & \R[\STbigtriangledown]\bigtriangledown \\ \R\bigcurlywedge & \R\bigparallel & \R[\STbigtriangleup]\bigtriangleup \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{\WASY\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \subindex{integrals}{contour} \label{wasy-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{*2{l@{$\:$}ll@{\qquad}}l@{$\:$}ll} \R[\WASYint]\int & \R[\WASYiint]\iint & \R[\WASYiiint]\iiint \\ \R[\WASYoint]\oint & \R[\WASYoiint]\oiint & \\ \end{tabular} \bigskip \begin{tablenote} If \WASY\ is loaded without package options then none of the preceding symbols are defined. However, \cmdI[$\WASYint$]{\varint} produces \WASY's \cmdI[$\WASYint$]{\int} glyph, and \cmdI[$\WASYoint$]{\varoint} produces \WASY's \cmdI[$\WASYoint$]{\oint} glyph. If \WASY\ is loaded with the \optname{wasysym}{integrals} option then all of the preceding symbols are defined, but \cmdI[$\WASYint$]{\varint} and \cmdI[$\WASYoint$]{\varoint} are left undefined. If \WASY\ is loaded with the \optname{wasysym}{nointegrals} option then none of the preceding symbols, \cmdI[$\WASYint$]{\varint}, or \cmdI[$\WASYoint$]{\varoint} are defined. \end{tablenote} \end{symtable} \begin{longsymtable}[ABX]{\ABX\ Variable-sized Math Operators} \ltidxboth{variable-sized}{symbols} \ltidxboth{boxed}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \ltindex{asterisks} \ltindex{asterisks>boxed} \ltindex{asterisks>circled} \label{abx-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{longtable}{*2{l@{$\:$}ll@{\qquad}}l@{$\:$}ll} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \R[\ABXbigcurlyvee]\bigcurlyvee & \R[\ABXbigboxslash]\bigboxslash & \R[\ABXbigoright]\bigoright \\ \R[\ABXbigsqcap]\bigsqcap & \R[\ABXbigboxtimes]\bigboxtimes & \R[\ABXbigoslash]\bigoslash \\ \R[\ABXbigcurlywedge]\bigcurlywedge & \R[\ABXbigboxtop]\bigboxtop & \R[\ABXbigotop]\bigotop \\ \R[\ABXbigboxasterisk]\bigboxasterisk & \R[\ABXbigboxtriangleup]\bigboxtriangleup & \R[\ABXbigotriangleup]\bigotriangleup \\ \R[\ABXbigboxbackslash]\bigboxbackslash & \R[\ABXbigboxvoid]\bigboxvoid & \R[\ABXbigovoid]\bigovoid \\ \R[\ABXbigboxbot]\bigboxbot & \R[\ABXbigcomplementop]\bigcomplementop & \R[\ABXbigplus]\bigplus \\ \R[\ABXbigboxcirc]\bigboxcirc & \R[\ABXbigoasterisk]\bigoasterisk & \R[\ABXbigsquplus]\bigsquplus \\ \R[\ABXbigboxcoasterisk]\bigboxcoasterisk & \R[\ABXbigobackslash]\bigobackslash & \R[\ABXbigtimes]\bigtimes \\ \R[\ABXbigboxdiv]\bigboxdiv & \R[\ABXbigobot]\bigobot & \R[\ABXiiintop]\iiint \\ \R[\ABXbigboxdot]\bigboxdot & \R[\ABXbigocirc]\bigocirc & \R[\ABXiintop]\iint \\ \R[\ABXbigboxleft]\bigboxleft & \R[\ABXbigocoasterisk]\bigocoasterisk & \R[\ABXintop]\int \\ \R[\ABXbigboxminus]\bigboxminus & \R[\ABXbigodiv]\bigodiv & \R[\ABXoiintop]\oiint \\ \R[\ABXbigboxplus]\bigboxplus & \R[\ABXbigoleft]\bigoleft & \R[\ABXointop]\oint \\ \R[\ABXbigboxright]\bigboxright & \R[\ABXbigominus]\bigominus \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[TX]{\TXPX\ Variable-sized Math Operators} \ltidxboth{variable-sized}{symbols} \ltsubindex{integrals}{contour} \label{txpx-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{longtable}{l@{$\:$}ll@{\hspace{4em}}l@{$\:$}ll} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \R\bigsqcapplus & \R\ointclockwise \\ \R\bigsqcupplus & \R\ointctrclockwise \\ \R\fint & \R\sqiiint \\ \R\idotsint & \R\sqiint \\ \R\iiiint & \R\sqint \\ \R\iiint & \R\varoiiintclockwise \\ \R\iint & \R\varoiiintctrclockwise \\ \R\oiiintclockwise & \R\varoiintclockwise \\ \R\oiiintctrclockwise & \R\varoiintctrclockwise \\ \R\oiiint & \R\varointclockwise \\ \R\oiintclockwise & \R\varointctrclockwise \\ \R\oiintctrclockwise & \R\varprod \\ \R\oiint \\ \end{longtable} \end{longsymtable} \begin{symtable}[ES]{\ES\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \index{integrals} \label{es-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{*2{l@{\quad}ll@{\hspace{4em}}}l@{\quad}ll} \E{dotsint} & \E{ointclockwise} \\ \E{fint} & \E{ointctrclockwise} \\ \E{iiiint} & \E{sqiint} \\ \E{iiint} & \E{sqint} \\ \E{iint} & \E{varoiint} \\ \E{landdownint} & \E{varointclockwise} \\ \E{landupint} & \E{varointctrclockwise} \\ \E{oiint} \\ \end{tabular} \end{symtable} \begin{symtable}[BIGINTS]{\BIGINTS\ Variable-sized Math Operators} \label{bigints} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \R\bigint & \R\bigoint \\ \R\bigints & \R\bigoints \\ \R\bigintss & \R\bigointss \\ \R\bigintsss & \R\bigointsss \\ \R\bigintssss & \R\bigointssss \\ \end{tabular} \end{symtable} \begin{longsymtable}[MNS]{\MNS\ Variable-sized Math Operators} \ltidxboth{variable-sized}{symbols} \ltidxboth{logic}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \label{mns-large} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{longtable}{*2{c@{\quad}cl@{\qquad}}c@{\quad}cl} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KN[\MNStbigcap][\MNSdbigcap]\bigcap & \KN[\MNStbigominus][\MNSdbigominus]\bigominus & \KN[\MNStcomplement][\MNSdcomplement]\complement \\ \KN[\MNStbigcapdot][\MNSdbigcapdot]\bigcapdot & \KN[\MNStbigoplus][\MNSdbigoplus]\bigoplus & \KN[\MNStcoprod][\MNSdcoprod]\coprod \\ \KN[\MNStbigcapplus][\MNSdbigcapplus]\bigcapplus & \KN[\MNStbigoslash][\MNSdbigoslash]\bigoslash & \KN[\MNStidotsint][\MNSdidotsint]\idotsint \\ \KN[\MNStbigcircle][\MNSdbigcircle]\bigcircle & \KN[\MNStbigostar][\MNSdbigostar]\bigostar & \KN[\MNStiiiint][\MNSdiiiint]\iiiint \\ \KN[\MNStbigcup][\MNSdbigcup]\bigcup & \KN[\MNStbigotimes][\MNSdbigotimes]\bigotimes & \KN[\MNStiiint][\MNSdiiint]\iiint \\ \KN[\MNStbigcupdot][\MNSdbigcupdot]\bigcupdot & \KN[\MNStbigotriangle][\MNSdbigotriangle]\bigotriangle & \KN[\MNStiint][\MNSdiint]\iint \\ \KN[\MNStbigcupplus][\MNSdbigcupplus]\bigcupplus$^*$ & \KN[\MNStbigovert][\MNSdbigovert]\bigovert & \KN[\MNStint][\MNSdint]\int \\ \KN[\MNStbigcurlyvee][\MNSdbigcurlyvee]\bigcurlyvee & \KN[\MNStbigplus][\MNSdbigplus]\bigplus & \KN[\MNStlanddownint][\MNSdlanddownint]\landdownint \\ \KN[\MNStbigcurlyveedot][\MNSdbigcurlyveedot]\bigcurlyveedot & \KN[\MNStbigsqcap][\MNSdbigsqcap]\bigsqcap & \KN[\MNStlandupint][\MNSdlandupint]\landupint \\ \KN[\MNStbigcurlywedge][\MNSdbigcurlywedge]\bigcurlywedge & \KN[\MNStbigsqcapdot][\MNSdbigsqcapdot]\bigsqcapdot & \KN[\MNStlcircleleftint][\MNSdlcircleleftint]\lcircleleftint \\ \KN[\MNStbigcurlywedgedot][\MNSdbigcurlywedgedot]\bigcurlywedgedot & \KN[\MNStbigsqcapplus][\MNSdbigsqcapplus]\bigsqcapplus & \KN[\MNStlcirclerightint][\MNSdlcirclerightint]\lcirclerightint \\ \KN[\MNStbigdoublecurlyvee][\MNSdbigdoublecurlyvee]\bigdoublecurlyvee & \KN[\MNStbigsqcup][\MNSdbigsqcup]\bigsqcup & \KN[\MNStoiint][\MNSdoiint]\oiint \\ \KN[\MNStbigdoublecurlywedge][\MNSdbigdoublecurlywedge]\bigdoublecurlywedge & \KN[\MNStbigsqcupdot][\MNSdbigsqcupdot]\bigsqcupdot & \KN[\MNStoint][\MNSdoint]\oint \\ \KN[\MNStbigdoublevee][\MNSdbigdoublevee]\bigdoublevee & \KN[\MNStbigsqcupplus][\MNSdbigsqcupplus]\bigsqcupplus & \KN[\MNStprod][\MNSdprod]\prod \\ \KN[\MNStbigdoublewedge][\MNSdbigdoublewedge]\bigdoublewedge & \KN[\MNStbigtimes][\MNSdbigtimes]\bigtimes & \KN[\MNStrcircleleftint][\MNSdrcircleleftint]\rcircleleftint \\ \KN[\MNStbigoast][\MNSdbigoast]\bigoast & \KN[\MNStbigvee][\MNSdbigvee]\bigvee & \KN[\MNStrcirclerightint][\MNSdrcirclerightint]\rcirclerightint \\ \KN[\MNStbigobackslash][\MNSdbigobackslash]\bigobackslash & \KN[\MNStbigveedot][\MNSdbigveedot]\bigveedot & \KN[\MNStstrokedint][\MNSdstrokedint]\strokedint \\ \KN[\MNStbigocirc][\MNSdbigocirc]\bigocirc & \KN[\MNStbigwedge][\MNSdbigwedge]\bigwedge & \KN[\MNStsum][\MNSdsum]\sum \\ \KN[\MNStbigodot][\MNSdbigodot]\bigodot & \KN[\MNStbigwedgedot][\MNSdbigwedgedot]\bigwedgedot & \KN[\MNStsumint][\MNSdsumint]\sumint \\ \end{longtable} \bigskip \begin{tablenote}[*] \MNS\ defines \cmdI[\MNStbigcupplus]{\biguplus} as a synonym for \cmdI[\MNStbigcupplus]{\bigcupplus}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Variable-sized Math Operators} \ltidxboth{variable-sized}{symbols} \ltidxboth{logic}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \label{fdsym-large} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{longtable}{*2{c@{\quad}cl@{\qquad}}c@{\quad}cl} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KN[\FDSYMtbigcap][\FDSYMdbigcap]\bigcap & \KN[\FDSYMtbigsqcup][\FDSYMdbigsqcup]\bigsqcup & \KN[\FDSYMtlandupint][\FDSYMdlandupint]\landupint \\ \KN[\FDSYMtbigcapdot][\FDSYMdbigcapdot]\bigcapdot & \KN[\FDSYMtbigsqcupdot][\FDSYMdbigsqcupdot]\bigsqcupdot & \KN[\FDSYMtlcircleleftint][\FDSYMdlcircleleftint]\lcircleleftint \\ \KN[\FDSYMtbigcapplus][\FDSYMdbigcapplus]\bigcapplus & \KN[\FDSYMtbigsqcupplus][\FDSYMdbigsqcupplus]\bigsqcupplus & \KN[\FDSYMtlcirclerightint][\FDSYMdlcirclerightint]\lcirclerightint \\ \KN[\FDSYMtbigcup][\FDSYMdbigcup]\bigcup & \KN[\FDSYMtbigtimes][\FDSYMdbigtimes]\bigtimes & \KN[\FDSYMtoiiint][\FDSYMdoiiint]\oiiint \\ \KN[\FDSYMtbigcupdot][\FDSYMdbigcupdot]\bigcupdot & \KN[\FDSYMtbigvee][\FDSYMdbigvee]\bigvee & \KN[\FDSYMtoiint][\FDSYMdoiint]\oiint \\ \KN[\FDSYMtbigcupplus][\FDSYMdbigcupplus]\bigcupplus & \KN[\FDSYMtbigveedot][\FDSYMdbigveedot]\bigveedot & \KN[\FDSYMtoint][\FDSYMdoint]\oint \\ \KN[\FDSYMtbigcurlyvee][\FDSYMdbigcurlyvee]\bigcurlyvee & \KN[\FDSYMtbigwedge][\FDSYMdbigwedge]\bigwedge & \KN[\FDSYMtosum][\FDSYMdosum]\osum \\ \KN[\FDSYMtbigcurlywedge][\FDSYMdbigcurlywedge]\bigcurlywedge & \KN[\FDSYMtbigwedgedot][\FDSYMdbigwedgedot]\bigwedgedot & \KN[\FDSYMtprod][\FDSYMdprod]\prod \\ \KN[\FDSYMtbigdoublevee][\FDSYMdbigdoublevee]\bigdoublevee & \KN[\FDSYMtcoprod][\FDSYMdcoprod]\coprod & \KN[\FDSYMtrcircleleftint][\FDSYMdrcircleleftint]\rcircleleftint \\ \KN[\FDSYMtbigdoublewedge][\FDSYMdbigdoublewedge]\bigdoublewedge & \KN[\FDSYMtfint][\FDSYMdfint]\fint & \KN[\FDSYMtrcirclerightint][\FDSYMdrcirclerightint]\rcirclerightint \\ \KN[\FDSYMtbigoast][\FDSYMdbigoast]\bigoast & \KN[\FDSYMtidotsint][\FDSYMdidotsint]\idotsint & \KN[\FDSYMtsum][\FDSYMdsum]\sum \\ \KN[\FDSYMtbigodot][\FDSYMdbigodot]\bigodot & \KN[\FDSYMtiiiint][\FDSYMdiiiint]\iiiint & \KN[\FDSYMtsumint][\FDSYMdsumint]\sumint \\ \KN[\FDSYMtbigoplus][\FDSYMdbigoplus]\bigoplus & \KN[\FDSYMtiiint][\FDSYMdiiint]\iiint & \KN[\FDSYMtvarcoprod][\FDSYMdvarcoprod]\varcoprod \\ \KN[\FDSYMtbigotimes][\FDSYMdbigotimes]\bigotimes & \KN[\FDSYMtiint][\FDSYMdiint]\iint & \KN[\FDSYMtvarosum][\FDSYMdvarosum]\varosum \\ \KN[\FDSYMtbigplus][\FDSYMdbigplus]\bigplus & \KN[\FDSYMtint][\FDSYMdint]\int & \KN[\FDSYMtvarprod][\FDSYMdvarprod]\varprod \\ \KN[\FDSYMtbigsqcap][\FDSYMdbigsqcap]\bigsqcap & \KN[\FDSYMtintbar][\FDSYMdintbar]\intbar & \KN[\FDSYMtvarsum][\FDSYMdvarsum]\varsum \\ \KN[\FDSYMtbigsqcapdot][\FDSYMdbigsqcapdot]\bigsqcapdot & \KN[\FDSYMtintBar][\FDSYMdintBar]\intBar & \KN[\FDSYMtvarsumint][\FDSYMdvarsumint]\varsumint \\ \KN[\FDSYMtbigsqcapplus][\FDSYMdbigsqcapplus]\bigsqcapplus & \KN[\FDSYMtlanddownint][\FDSYMdlanddownint]\landdownint & \\ \end{longtable} \bigskip \begin{tablenote}[*] \FDSYM\ defines \cmdI[\string\FDSYMtawint]{\awint} as a synonym for \cmdI[\string\FDSYMtlanddownint]{\landdownint}, \cmdI[\string\FDSYMtbiguplus]{\biguplus} as a synonym for \cmdI[\string\FDSYMtbigcupplus]{\bigcupplus}, \cmdI[\string\FDSYMtconjquant]{\conjquant} as a synonym for \cmdI[\string\FDSYMtbigdoublewedge]{\bigdoublewedge}, \cmdI[\string\FDSYMtdisjquant]{\disjquant} as a synonym for \cmdI[\string\FDSYMtbigdoublevee]{\bigdoublevee}, \cmdI[\string\FDSYMtdotsint]{\dotsint} as a synonym for \cmdI[\string\FDSYMtidotsint]{\idotsint}, \cmdI[\string\FDSYMtintclockwise]{\intclockwise} as a synonym for \cmdI[\string\FDSYMtlandupint]{\landupint}, \cmdI[\string\FDSYMtintctrclockwise]{\intctrclockwise} as a synonym for \cmdI[\string\FDSYMtlanddownint]{\landdownint}, \cmdI[\string\FDSYMtmodtwosum]{\modtwosum} as a synonym for \cmdI[\string\FDSYMtosum]{\osum}, \cmdI[\string\FDSYMtointclockwise]{\ointclockwise} as a synonym for \cmdI[\string\FDSYMtlcircleleftint]{\lcircleleftint}, \cmdI[\string\FDSYMtointctrclockwise]{\ointctrclockwise} as a synonym for \cmdI[\string\FDSYMtrcirclerightint]{\rcirclerightint}, \cmdI[\string\FDSYMtvarmodtwosum]{\varmodtwosum} as a synonym for \cmdI[\string\FDSYMtvarosum]{\varosum}, \cmdI[\string\FDSYMtvarointclockwise]{\varointclockwise} as a synonym for \cmdI[\string\FDSYMtlcirclerightint]{\lcirclerightint}, and \cmdI[\string\FDSYMtvarointctrclockwise]{\varointctrclockwise} as a synonym for \cmdI[\string\FDSYMtrcircleleftint]{\rcircleleftint}. \end{tablenote} \end{longsymtable} \begin{symtable}[BSK]{\BSK\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \index{integrals} \label{bsk-large} \begin{tabular}{ccl} \KN[\BSKtintup][\BSKdintup]\intup \\ \end{tabular} \bigskip \begin{tablenote} \BSK\ additionally provides all of the symbols in \ref{op}. \end{tablenote} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Variable-sized Math Operators} \ltidxboth{variable-sized}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \label{stix-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{longtable}{*2{c@{\quad}cl@{\qquad}}c@{\quad}cl} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KN[\STIXtawintslop][\STIXdawintslop]\awint & \KN[\STIXtcoprodop][\STIXdcoprodop]\coprod & \KN[\STIXtoiiintslop][\STIXdoiiintslop]\oiiint \\ \KN[\STIXtBbbsumop][\STIXdBbbsumop]\Bbbsum & \KN[\STIXtdisjquantop][\STIXddisjquantop]\disjquant & \KN[\STIXtoiintslop][\STIXdoiintslop]\oiint \\ \KN[\STIXtbigcapop][\STIXdbigcapop]\bigcap & \KN[\STIXtfintslop][\STIXdfintslop]\fint & \KN[\STIXtointslop][\STIXdointslop]\oint \\ \KN[\STIXtbigcupop][\STIXdbigcupop]\bigcup & \KN[\STIXtiiiintslop][\STIXdiiiintslop]\iiiint & \KN[\STIXtointctrclockwiseslop][\STIXdointctrclockwiseslop]\ointctrclockwise \\ \KN[\STIXtbigcupdotop][\STIXdbigcupdotop]\bigcupdot & \KN[\STIXtiiintslop][\STIXdiiintslop]\iiint & \KN[\STIXtpointintslop][\STIXdpointintslop]\pointint \\ \KN[\STIXtbigodotop][\STIXdbigodotop]\bigodot & \KN[\STIXtiintslop][\STIXdiintslop]\iint & \KN[\STIXtprodop][\STIXdprodop]\prod \\ \KN[\STIXtbigoplusop][\STIXdbigoplusop]\bigoplus & \KN[\STIXtintslop][\STIXdintslop]\int & \KN[\STIXtrppolintslop][\STIXdrppolintslop]\rppolint \\ \KN[\STIXtbigotimesop][\STIXdbigotimesop]\bigotimes & \KN[\STIXtintbarslop][\STIXdintbarslop]\intbar & \KN[\STIXtscpolintslop][\STIXdscpolintslop]\scpolint \\ \KN[\STIXtbigsqcapop][\STIXdbigsqcapop]\bigsqcap & \KN[\STIXtintBarslop][\STIXdintBarslop]\intBar & \KN[\STIXtsqintslop][\STIXdsqintslop]\sqint \\ \KN[\STIXtbigsqcupop][\STIXdbigsqcupop]\bigsqcup & \KN[\STIXtintcapslop][\STIXdintcapslop]\intcap & \KN[\STIXtsumop][\STIXdsumop]\sum \\ \KN[\STIXtbigtalloblongop][\STIXdbigtalloblongop]\bigtalloblong & \KN[\STIXtintclockwiseslop][\STIXdintclockwiseslop]\intclockwise & \KN[\STIXtsumintslop][\STIXdsumintslop]\sumint \\ \KN[\STIXtbigtimesop][\STIXdbigtimesop]\bigtimes & \KN[\STIXtintcupslop][\STIXdintcupslop]\intcup & \KN[\STIXtupintslop][\STIXdupintslop]\upint \\ \KN[\STIXtbiguplusop][\STIXdbiguplusop]\biguplus & \KN[\STIXtintlarhkslop][\STIXdintlarhkslop]\intlarhk & \KN[\STIXtvarointclockwiseslop][\STIXdvarointclockwiseslop]\varointclockwise \\ \KN[\STIXtbigveeop][\STIXdbigveeop]\bigvee & \KN[\STIXtintxslop][\STIXdintxslop]\intx & \KN[\STIXtxbsolop][\STIXdxbsolop]\xbsol \\ \KN[\STIXtbigwedgeop][\STIXdbigwedgeop]\bigwedge & \KN[\STIXtlowintslop][\STIXdlowintslop]\lowint & \KN[\STIXtxsolop][\STIXdxsolop]\xsol \\ \KN[\STIXtcirfnintslop][\STIXdcirfnintslop]\cirfnint & \KN[\STIXtmodtwosumop][\STIXdmodtwosumop]\modtwosum & \\ \KN[\STIXtconjquantop][\STIXdconjquantop]\conjquant & \KN[\STIXtnpolintslop][\STIXdnpolintslop]\npolint & \\ \end{longtable} \begin{tablenote} \seepackagenote{STIX}{stix}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[STIX]{\STIX\ Integrals with Explicit Slant} \ltidxboth{variable-sized}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \label{stix-large-all} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{longtable}{c@{\quad}cl @{\qquad} c@{\quad}cl} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KN[\STIXtintslop][\STIXdintslop]\intsl & \KN[\STIXtintupop][\STIXdintupop]\intup \\ \KN[\STIXtiintslop][\STIXdiintslop]\iintsl & \KN[\STIXtiintupop][\STIXdiintupop]\iintup \\ \KN[\STIXtiiintslop][\STIXdiiintslop]\iiintsl & \KN[\STIXtiiintupop][\STIXdiiintupop]\iiintup \\ \KN[\STIXtointslop][\STIXdointslop]\ointsl & \KN[\STIXtointupop][\STIXdointupop]\ointup \\ \KN[\STIXtoiintslop][\STIXdoiintslop]\oiintsl & \KN[\STIXtoiintupop][\STIXdoiintupop]\oiintup \\ \KN[\STIXtoiiintslop][\STIXdoiiintslop]\oiiintsl & \KN[\STIXtoiiintupop][\STIXdoiiintupop]\oiiintup \\ \KN[\STIXtintclockwiseslop][\STIXdintclockwiseslop]\intclockwisesl & \KN[\STIXtintclockwiseupop][\STIXdintclockwiseupop]\intclockwiseup \\ \KN[\STIXtvarointclockwiseslop][\STIXdvarointclockwiseslop]\varointclockwisesl & \KN[\STIXtvarointclockwiseupop][\STIXdvarointclockwiseupop]\varointclockwiseup \\ \KN[\STIXtointctrclockwiseslop][\STIXdointctrclockwiseslop]\ointctrclockwisesl & \KN[\STIXtointctrclockwiseupop][\STIXdointctrclockwiseupop]\ointctrclockwiseup \\ \KN[\STIXtsumintslop][\STIXdsumintslop]\sumintsl & \KN[\STIXtsumintupop][\STIXdsumintupop]\sumintup \\ \KN[\STIXtiiiintslop][\STIXdiiiintslop]\iiiintsl & \KN[\STIXtiiiintupop][\STIXdiiiintupop]\iiiintup \\ \KN[\STIXtintbarslop][\STIXdintbarslop]\intbarsl & \KN[\STIXtintbarupop][\STIXdintbarupop]\intbarup \\ \KN[\STIXtintBarslop][\STIXdintBarslop]\intBarsl & \KN[\STIXtintBarupop][\STIXdintBarupop]\intBarup \\ \KN[\STIXtfintslop][\STIXdfintslop]\fintsl & \KN[\STIXtfintupop][\STIXdfintupop]\fintup \\ \KN[\STIXtcirfnintslop][\STIXdcirfnintslop]\cirfnintsl & \KN[\STIXtcirfnintupop][\STIXdcirfnintupop]\cirfnintup \\ \KN[\STIXtawintslop][\STIXdawintslop]\awintsl & \KN[\STIXtawintupop][\STIXdawintupop]\awintup \\ \KN[\STIXtrppolintslop][\STIXdrppolintslop]\rppolintsl & \KN[\STIXtrppolintupop][\STIXdrppolintupop]\rppolintup \\ \KN[\STIXtscpolintslop][\STIXdscpolintslop]\scpolintsl & \KN[\STIXtscpolintupop][\STIXdscpolintupop]\scpolintup \\ \KN[\STIXtnpolintslop][\STIXdnpolintslop]\npolintsl & \KN[\STIXtnpolintupop][\STIXdnpolintupop]\npolintup \\ \KN[\STIXtpointintslop][\STIXdpointintslop]\pointintsl & \KN[\STIXtpointintupop][\STIXdpointintupop]\pointintup \\ \KN[\STIXtsqintslop][\STIXdsqintslop]\sqintsl & \KN[\STIXtsqintupop][\STIXdsqintupop]\sqintup \\ \KN[\STIXtintlarhkslop][\STIXdintlarhkslop]\intlarhksl & \KN[\STIXtintlarhkupop][\STIXdintlarhkupop]\intlarhkup \\ \KN[\STIXtintxslop][\STIXdintxslop]\intxsl & \KN[\STIXtintxupop][\STIXdintxupop]\intxup \\ \KN[\STIXtintcapslop][\STIXdintcapslop]\intcapsl & \KN[\STIXtintcapupop][\STIXdintcapupop]\intcapup \\ \KN[\STIXtintcupslop][\STIXdintcupslop]\intcupsl & \KN[\STIXtintcupupop][\STIXdintcupupop]\intcupup \\ \KN[\STIXtupintslop][\STIXdupintslop]\upintsl & \KN[\STIXtupintupop][\STIXdupintupop]\upintup \\ \KN[\STIXtlowintslop][\STIXdlowintslop]\lowintsl & \KN[\STIXtlowintupop][\STIXdlowintupop]\lowintup \\ \end{longtable} \begin{tablenote} \seepackagenote{STIX}{stix}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[CMUPINT]{\CMUPINT\ Variable-sized Upright Integrals} \ltidxboth{variable-sized}{symbols} \ltindex{integrals} \ltsubindex{integrals}{contour} \label{cmupint} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{longtable}{*2{c@{\quad}cl@{\hspace{4em}}}c@{\quad}cl} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KN[\CMUPawintT][\CMUPawintD]\awint & \KN[\CMUPnpolintT][\CMUPnpolintD]\npolint \\ \KN[\CMUPbarintT][\CMUPbarintD]\barint & \KN[\CMUPoiiintT][\CMUPoiiintD]\oiiint \\ \KN[\CMUPcirfnintT][\CMUPcirfnintD]\cirfnint & \KN[\CMUPoiintT][\CMUPoiintD]\oiint \\ \KN[\CMUPdoublebarintT][\CMUPdoublebarintD]\doublebarint & \KN[\CMUPointT][\CMUPointD]\oint \\ \KN[\CMUPdownintT][\CMUPdownintD]\downint & \KN[\CMUPointclockwiseT][\CMUPointclockwiseD]\ointclockwise \\ \KN[\CMUPfintT][\CMUPfintD]\fint & \KN[\CMUPointctrclockwiseT][\CMUPointctrclockwiseD]\ointctrclockwise \\ \KN[\CMUPidotsintT][\CMUPidotsintD]\idotsint$^*$ & \KN[\CMUPpointintT][\CMUPpointintD]\pointint \\ \KN[\CMUPiiiintT][\CMUPiiiintD]\iiiint & \KN[\CMUPrppolintT][\CMUPrppolintD]\rppolint \\ \KN[\CMUPiiintT][\CMUPiiintD]\iiint & \KN[\CMUPscpolintT][\CMUPscpolintD]\scpolint \\ \KN[\CMUPiintT][\CMUPiintD]\iint & \KN[\CMUPsqiintT][\CMUPsqiintD]\sqiint \\ \KN[\CMUPintT][\CMUPintD]\int & \KN[\CMUPsqintT][\CMUPsqintD]\sqint \\ \KN[\CMUPintcapT][\CMUPintcapD]\intcap & \KN[\CMUPsumintT][\CMUPsumintD]\sumint \\ \KN[\CMUPintclockwiseT][\CMUPintclockwiseD]\intclockwise & \KN[\CMUPupintT][\CMUPupintD]\upint \\ \KN[\CMUPintcupT][\CMUPintcupD]\intcup & \KN[\CMUPvaridotsintT][\CMUPvaridotsintD]\varidotsint$^*$ \\ \KN[\CMUPintlarhkT][\CMUPintlarhkD]\intlarhk & \KN[\CMUPvarointclockwiseT][\CMUPvarointclockwiseD]\varointclockwise \\ \KN[\CMUPlanddownintT][\CMUPlanddownintD]\landdownint & \KN[\CMUPvarointctrclockwiseT][\CMUPvarointctrclockwiseD]\varointctrclockwise \\ \KN[\CMUPlandupintT][\CMUPlandupintD]\landupint & \KN[\CMUPxintT][\CMUPxintD]\xint \\ \end{longtable} \begin{tablenote} \seepackagenote{CMUPINT}{cmupint}. \end{tablenote} \bigskip \begin{tablenote}[*] \cmdI[\CMUPvaridotsintT]{\varidotsint} is always drawn as is. \cmdI[\CMUPvaridotsintT]{\idotsint} is drawn identically to \cmdI[\CMUPvaridotsintT]{\varidotsint} when \pkgname{amsmath} is not loaded or with more space surrounding each dot when \pkgname{amsmath} is loaded. \end{tablenote} \end{longsymtable} \begin{symtable}[MDES]{\MDES\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \index{integrals} \subindex{integrals}{contour} \label{mdes-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{*2{c@{\quad}cl@{\hspace{4em}}}c@{\quad}cl} \KN[\MDESintclockwisesm][\MDESintclockwise]\intclockwise & \KN[\MDESointclockwisesm][\MDESointclockwise]\ointclockwise \\ \KN[\MDESoiiintsm][\MDESoiiint]\oiiint & \KN[\MDESointctrclockwisesm][\MDESointctrclockwise]\ointctrclockwise \\ \KN[\MDESoiintsm][\MDESoiint]\oiint & \\ \end{tabular} \bigskip \begin{tablenote} The \MDES\ package provides three versions of each integral---in fact, of every symbol---to accompany different text fonts: \PSfont{Utopia}~(\raisebox{2ex}{\usefont{OMX}{mdput}{m}{n}\char"52}), \PSfont{Garamond}~(\raisebox{2ex}{\usefont{OMX}{mdugm}{m}{n}\char"52}), and \PSfont{Charter}~(\raisebox{2ex}{\usefont{OMX}{mdbch}{m}{n}\char"52}). \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \label{pdfmsym-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \R\aint & \R\bigforall \\ \R\bigcircwedge & \R[\biNint{5}]\biNint\verb|{5}|$^*$ \\ \R\bigdcup & \R[\iNint{5}]\iNint\verb|{5}|$^*$ \\ \R\bigdwedge & \R[\oiNint{5}]\oiNint\verb|{5}|$^*$ \\ \R\bigexists & \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \bigskip \begin{tablenote}[*] These commands have a required argument, which specifies the number of integrals. For example, \verb|\oiNint{7}| produces the symbol \[ \oiNint{7} \quad. \] \end{tablenote} \end{symtable} \begin{symtable}[NEWCM]{\NEWCM\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \label{newcm-large} \begin{tabular}{ccl} \KN[\NCMtconvolution][\NCMdconvolution]\convolution \\ \end{tabular} \bigskip \begin{tablenote} \NEWCM\ additionally provides many of the other operators appearing in this chapter. \seepackagenote{NEWCM}{newcomputermodern}. \end{tablenote} \end{symtable} \begin{symtable}[PRODINT]{\PRODINT\ Variable-sized Math Operators} \idxboth{variable-sized}{symbols} \index{product integrals} \subindex{integrals}{product} \label{prodint} \begin{tabular}{*3{ll}} \K\prodi & \K\Prodi & \K\PRODI \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{PRODINT}{prodint}. \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Extensible Math Operators} \label{pdfmsym-ext-ops} \begin{tabular}{ll@{\qquad}ll} \X\prood & \X\suum \\ \end{tabular} \bigskip \begin{tablenote} These symbols extend horizontally to fit their lower and upper limits. Hence, \begin{verbatim} \suum_{i=\lfloor\sqrt{a^2 + b^2 + c^2}\rfloor}^{\max(5N-3, 11N-8)} \end{verbatim} produces \[ \suum_{i=\lfloor\sqrt{a^2 + b^2 + c^2}\rfloor}^{\max(5N-3, 11N-8)} \quad. \] \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[CMLL]{\CMLL\ Large Math Operators} \idxboth{logic}{symbols} \label{cmll-large} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{ll@{\qquad}ll} \K[\CMLLbigparr]\bigparr$^*$ & \K[\CMLLbigwith]\bigwith \\ \end{tabular} \bigskip \begin{tablenote}[*] \CMLL\ defines \cmdI[\CMLLbigparr]{\biginvamp} as a synonym for \cmdI[\CMLLbigparr]{\bigparr}. \end{tablenote} \end{symtable} \begin{symtable}{Binary Relations} \idxboth{relational}{symbols} \idxboth{frown}{symbols} \idxboth{smile}{symbols} \idxboth{database}{symbols} \index{tacks} \label{rel} \begin{tabular}{*4{ll}} \X\approx & \X\equiv & \X\perp & \X\smile \\ \X\asymp & \X\frown & \X\prec & \X\succ \\ \X\bowtie & \X\Join$^*$ & \X\preceq & \X\succeq \\ \X\cong & \X\mid$^\dag$ & \X\propto & \X\vdash \\ \X\dashv & \X\models & \X\sim \\ \X\doteq & \X\parallel & \X\simeq \\ \end{tabular} \bigskip \notpredefinedmessage \bigskip \begin{tablenote}[\dag] The difference between \cmdX{\mid} and \verb+|+\index{_magicvertname=\magicvertname{} ($\vert$)} is that the former is a binary relation while the latter is a math ordinal. Consequently, \latex\ typesets the two with different surrounding spacing. Contrast ``\verb+P(A | B)+''~$\mapsto$ \mbox{``$P(A | B)$''} with ``\verb+P(A \mid B)+''~$\mapsto$ \mbox{``$P(A \mid B)$''}. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \index{pitchforks} \idxboth{frown}{symbols} \idxboth{smile}{symbols} \label{ams-rel} \begin{tabular}{*3{ll}} \X\approxeq & \X\eqcirc & \X\succapprox \\ \X\backepsilon & \X\fallingdotseq & \X\succcurlyeq \\ \X\backsim & \X\multimap & \X\succsim \\ \X\backsimeq & \X\pitchfork & \X\therefore \\ \X\because & \X\precapprox & \X\thickapprox \\ \X\between & \X\preccurlyeq & \X\thicksim \\ \X\Bumpeq & \X\precsim & \X\varpropto \\ \X\bumpeq & \X\risingdotseq & \X\Vdash \\ \X\circeq & \X\shortmid & \X\vDash \\ \X\curlyeqprec & \X\shortparallel & \X\Vvdash \\ \X\curlyeqsucc & \X\smallfrown & \\ \X\doteqdot & \X\smallsmile & \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Negated Binary Relations} \index{binary relations>negated} \index{relational symbols>negated binary} \label{ams-nrel} \begin{tabular}{*3{ll}} \X\ncong & \X\nshortparallel & \X\nVDash \\ \X\nmid & \X\nsim & \X\precnapprox \\ \X\nparallel & \X\nsucc & \X\precnsim \\ \X\nprec & \X\nsucceq & \X\succnapprox \\ \X\npreceq & \X\nvDash & \X\succnsim \\ \X\nshortmid & \X\nvdash \\ \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{st-rel} \begin{tabular}{*2{ll}} \X\inplus & \X\niplus \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{\WASY\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \idxboth{database}{symbols} \label{wasy-rel} \begin{tabular}{*3{ll}} \X\invneg & \X\leadsto & \X\wasypropto \\ \X\Join & \X\logof \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \idxboth{database}{symbols} \label{txpx-rel} \begin{tabular}{*3{ll}} \X\circledgtr & \X\lJoin & \X\opentimes \\ \X\circledless & \X\lrtimes & \X[\TXPerp]\Perp \\ \X\colonapprox & \X\multimap & \X\preceqq \\ \X\Colonapprox & \X\multimapboth & \X\precneqq \\ \X\coloneq & \X\multimapbothvert & \X\rJoin \\ \X\Coloneq & \X\multimapdot & \X\strictfi \\ \X\Coloneqq & \X\multimapdotboth & \X\strictif \\ \X\coloneqq$^*$ & \X\multimapdotbothA & \X\strictiff \\ \X\Colonsim & \X\multimapdotbothAvert & \X\succeqq \\ \X\colonsim & \X\multimapdotbothB & \X\succneqq \\ \X\Eqcolon & \X\multimapdotbothBvert & \X\varparallel \\ \X\eqcolon & \X\multimapdotbothvert & \X\varparallelinv \\ \X\eqqcolon & \X\multimapdotinv & \X\VvDash \\ \X\Eqqcolon & \X\multimapinv \\ \X\eqsim & \X\openJoin \\ \end{tabular} \bigskip \begin{tablenote}[*] As an alternative to using \TXPX, a ``$\mathrel{\mathop:}=$'' symbol can be constructed with ``\verb|\mathrel{\mathop:}=|''. \end{tablenote} \end{symtable} \begin{symtable}[TX]{\TXPX\ Negated Binary Relations} \index{binary relations>negated} \index{relational symbols>negated binary} \label{txpx-nrel} \begin{tabular}{*3{ll}} \X\napproxeq & \X\npreccurlyeq & \X\nthickapprox \\ \X\nasymp & \X\npreceqq & \X\ntwoheadleftarrow \\ \X\nbacksim & \X\nprecsim & \X\ntwoheadrightarrow \\ \X\nbacksimeq & \X\nsimeq & \X\nvarparallel \\ \X\nbumpeq & \X\nsuccapprox & \X\nvarparallelinv \\ \X\nBumpeq & \X\nsucccurlyeq & \X\nVdash \\ \X\nequiv & \X\nsucceqq \\ \X\nprecapprox & \X\nsuccsim \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{abx-rel} \begin{tabular}{*3{ll}} \X[\ABXbetween]\between & \X[\ABXdivides]\divides & \X[\ABXrisingdotseq]\risingdotseq \\ \X[\ABXbotdoteq]\botdoteq & \X[\ABXdotseq]\dotseq & \X[\ABXsuccapprox]\succapprox \\ \X[\ABXBumpedeq]\Bumpedeq & \X[\ABXeqbumped]\eqbumped & \X[\ABXsucccurlyeq]\succcurlyeq \\ \X[\ABXbumpedeq]\bumpedeq & \X[\ABXeqcirc]\eqcirc & \X[\ABXsuccdot]\succdot \\ \X[\ABXcirceq]\circeq & \X[\ABXeqcolon]\eqcolon & \X[\ABXsuccsim]\succsim \\ \X[\ABXcoloneq]\coloneq & \X[\ABXfallingdotseq]\fallingdotseq & \X[\ABXtherefore]\therefore \\ \X[\ABXcorresponds]\corresponds & \X[\ABXggcurly]\ggcurly & \X[\ABXtopdoteq]\topdoteq \\ \X[\ABXcurlyeqprec]\curlyeqprec & \X[\ABXllcurly]\llcurly & \X[\ABXvDash]\vDash \\ \X[\ABXcurlyeqsucc]\curlyeqsucc & \X[\ABXprecapprox]\precapprox & \X[\ABXVdash]\Vdash \\ \X[\ABXDashV]\DashV & \X[\ABXpreccurlyeq]\preccurlyeq & \X[\ABXVDash]\VDash \\ \X[\ABXDashv]\Dashv & \X[\ABXprecdot]\precdot & \X[\ABXVvdash]\Vvdash \\ \X[\ABXdashVv]\dashVv & \X[\ABXprecsim]\precsim \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Negated Binary Relations} \index{binary relations>negated} \index{relational symbols>negated binary} \label{abx-nrel} \begin{tabular}{*3{ll}} \X[\ABXnapprox]\napprox & \X[\ABXnotperp]\notperp & \X[\ABXnvDash]\nvDash \\ \X[\ABXncong]\ncong & \X[\ABXnprec]\nprec & \X[\ABXnVDash]\nVDash \\ \X[\ABXncurlyeqprec]\ncurlyeqprec & \X[\ABXnprecapprox]\nprecapprox & \X[\ABXnVdash]\nVdash \\ \X[\ABXncurlyeqsucc]\ncurlyeqsucc & \X[\ABXnpreccurlyeq]\npreccurlyeq & \X[\ABXnvdash]\nvdash \\ \X[\ABXnDashv]\nDashv & \X[\ABXnpreceq]\npreceq & \X[\ABXnVvash]\nVvash \\ \X[\ABXndashV]\ndashV & \X[\ABXnprecsim]\nprecsim & \X[\ABXprecnapprox]\precnapprox \\ \X[\ABXndashv]\ndashv & \X[\ABXnsim]\nsim & \X[\ABXprecneq]\precneq \\ \X[\ABXnDashV]\nDashV & \X[\ABXnsimeq]\nsimeq & \X[\ABXprecnsim]\precnsim \\ \X[\ABXndashVv]\ndashVv & \X[\ABXnsucc]\nsucc & \X[\ABXsuccnapprox]\succnapprox \\ \X[\ABXneq]\neq & \X[\ABXnsuccapprox]\nsuccapprox & \X[\ABXsuccneq]\succneq \\ \X[\ABXnotasymp]\notasymp & \X[\ABXnsucccurlyeq]\nsucccurlyeq & \X[\ABXsuccnsim]\succnsim \\ \X[\ABXnotdivides]\notdivides & \X[\ABXnsucceq]\nsucceq \\ \X[\ABXnotequiv]\notequiv & \X[\ABXnsuccsim]\nsuccsim \\ \end{tabular} \bigskip \begin{tablenote} \index{not equal=not equal ($\ABXvarnotsign!=$ vs.\ $\ABXnotsign!=$)} The \cmd{\changenotsign} command toggles the behavior of \cmd{\not} to produce either a vertical or a diagonal slash through a binary operator. Thus, ``\verb|$a \not= b$|'' can be made to produce either ``$a \ABXnotsign= b$'' or ``$a \ABXvarnotsign= b$''. \end{tablenote} \end{symtable} \begin{longsymtable}[MNS]{\MNS\ Binary Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \label{mns-rel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\MNSapprox]\approx & \K[\MNShateq]\hateq & \K[\MNSrightpropto]\rightpropto \\ \K[\MNSapproxeq]\approxeq & \K[\MNShcrossing]\hcrossing & \K[\MNSrightslice]\rightslice \\ \K[\MNSbackapprox]\backapprox & \K[\MNSleftfootline]\leftfootline & \K[\MNSrightVdash]\rightVdash \\ \K[\MNSbackapproxeq]\backapproxeq & \K[\MNSleftfree]\leftfree & \K[\MNSrightvdash]\rightvdash \\ \K[\MNSbackcong]\backcong & \K[\MNSleftmodels]\leftmodels & \K[\MNSrisingdotseq]\risingdotseq \\ \K[\MNSbackeqsim]\backeqsim & \K[\MNSleftModels]\leftModels & \K[\MNSsefootline]\sefootline \\ \K[\MNSbacksim]\backsim & \K[\MNSleftpropto]\leftpropto & \K[\MNSsefree]\sefree \\ \K[\MNSbacksimeq]\backsimeq & \K[\MNSleftrightline]\leftrightline & \K[\MNSseModels]\seModels \\ \K[\MNSbacktriplesim]\backtriplesim & \K[\MNSLeftrightline]\Leftrightline & \K[\MNSsemodels]\semodels \\ \K[\MNSbetween]\between & \K[\MNSleftslice]\leftslice & \K[\MNSseparated]\separated \\ \K[\MNSbumpeq]\bumpeq & \K[\MNSleftVdash]\leftVdash & \K[\MNSseVdash]\seVdash \\ \K[\MNSBumpeq]\Bumpeq & \K[\MNSleftvdash]\leftvdash & \K[\MNSsevdash]\sevdash \\ \K[\MNScirceq]\circeq & \K[\MNSnefootline]\nefootline & \K[\MNSshortparallel]\shortparallel \\ \K[\MNSclosedequal]\closedequal & \K[\MNSnefree]\nefree & \K[\MNSsim]\sim \\ \K[\MNSclosedprec]\closedprec & \K[\MNSneModels]\neModels & \K[\MNSsimeq]\simeq \\ \K[\MNSclosedsucc]\closedsucc & \K[\MNSnemodels]\nemodels & \K[\MNSsucc]\succ \\ \K[\MNScoloneq]\coloneq & \K[\MNSneswline]\neswline & \K[\MNSsuccapprox]\succapprox \\ \K[\MNScong]\cong & \K[\MNSNeswline]\Neswline & \K[\MNSsucccurlyeq]\succcurlyeq \\ \K[\MNScurlyeqprec]\curlyeqprec & \K[\MNSneVdash]\neVdash & \K[\MNSsucceq]\succeq \\ \K[\MNScurlyeqsucc]\curlyeqsucc & \K[\MNSnevdash]\nevdash & \K[\MNSsuccsim]\succsim \\ \K[\MNSDoteq]\Doteq & \K[\MNSnwfootline]\nwfootline & \K[\MNSswfootline]\swfootline \\ \K[\MNSdoteq]\doteq & \K[\MNSnwfree]\nwfree & \K[\MNSswfree]\swfree \\ \K[\MNSdownfootline]\downfootline & \K[\MNSnwmodels]\nwmodels & \K[\MNSswModels]\swModels \\ \K[\MNSdownfree]\downfree & \K[\MNSnwModels]\nwModels & \K[\MNSswmodels]\swmodels \\ \K[\MNSdownmodels]\downmodels & \K[\MNSnwsecrossing]\nwsecrossing & \K[\MNSswVdash]\swVdash \\ \K[\MNSdownModels]\downModels & \K[\MNSNwseline]\Nwseline & \K[\MNSswvdash]\swvdash \\ \K[\MNSdownpropto]\downpropto & \K[\MNSnwseline]\nwseline & \K[\MNStriplesim]\triplesim \\ \K[\MNSdownvdash]\downvdash & \K[\MNSnwvdash]\nwvdash & \K[\MNSupdownline]\updownline \\ \K[\MNSdownVdash]\downVdash & \K[\MNSnwVdash]\nwVdash & \K[\MNSUpdownline]\Updownline \\ \K[\MNSeqbump]\eqbump & \K[\MNSprec]\prec & \K[\MNSupfootline]\upfootline \\ \K[\MNSeqcirc]\eqcirc & \K[\MNSprecapprox]\precapprox & \K[\MNSupfree]\upfree \\ \K[\MNSeqdot]\eqdot & \K[\MNSpreccurlyeq]\preccurlyeq & \K[\MNSupModels]\upModels \\ \K[\MNSeqsim]\eqsim & \K[\MNSpreceq]\preceq & \K[\MNSupmodels]\upmodels \\ \K[\MNSequal]\equal & \K[\MNSprecsim]\precsim & \K[\MNSuppropto]\uppropto \\ \K[\MNSequalclosed]\equalclosed & \K[\MNSrightfootline]\rightfootline & \K[\MNSupvdash]\upvdash \\ \K[\MNSequiv]\equiv & \K[\MNSrightfree]\rightfree & \K[\MNSupVdash]\upVdash \\ \K[\MNSequivclosed]\equivclosed & \K[\MNSrightmodels]\rightmodels & \K[\MNSvcrossing]\vcrossing \\ \K[\MNSfallingdotseq]\fallingdotseq & \K[\MNSrightModels]\rightModels & \K[\MNSVvdash]\Vvdash \\ \end{longtable} \MNS\ additionally defines synonyms for some of the preceding symbols: \bigskip \newcommand*{\mnssyn}[1]{(same as \texttt{\string#1})} \begin{tabular}{ll@{\quad}l} \K[\MNSleftvdash]\dashv & \mnssyn\leftvdash \\ \K[\MNSnwseline]\diagdown & \mnssyn\nwseline \\ \K[\MNSneswline]\diagup & \mnssyn\neswline \\ \K[\MNSupdownline]\divides & \mnssyn\updownline \\ \K[\MNSDoteq]\doteqdot & \mnssyn\Doteq \\ \K[\MNSrightmodels]\models & \mnssyn\rightmodels \\ \K[\MNSUpdownline]\parallel & \mnssyn\Updownline \\ \K[\MNSupvdash]\perp & \mnssyn\upvdash \\ \K[\MNSleftpropto]\propto & \mnssyn\leftpropto \\ \K[\MNSleftrightline]\relbar & \mnssyn\leftrightline \\ \K[\MNSLeftrightline]\Relbar & \mnssyn\Leftrightline \\ \K[\MNSleftpropto]\varpropto & \mnssyn\leftpropto \\ \K[\MNSrightmodels]\vDash & \mnssyn\rightmodels \\ \K[\MNSrightModels]\VDash & \mnssyn\rightModels \\ \K[\MNSrightvdash]\vdash & \mnssyn\rightvdash \\ \K[\MNSrightVdash]\Vdash & \mnssyn\rightVdash \\ \end{tabular} \end{longsymtable} \begin{longsymtable}[MNS]{\MNS\ Negated Binary Relations} \ltindex{binary relations>negated} \ltindex{relational symbols>negated binary} \label{mns-nrel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\MNSnapprox]\napprox & \K[\MNSnleftfootline]\nleftfootline & \K[\MNSnrisingdotseq]\nrisingdotseq \\ \K[\MNSnapproxeq]\napproxeq & \K[\MNSnleftfree]\nleftfree & \K[\MNSnsefootline]\nsefootline \\ \K[\MNSnbackapprox]\nbackapprox & \K[\MNSnleftmodels]\nleftmodels & \K[\MNSnsefree]\nsefree \\ \K[\MNSnbackapproxeq]\nbackapproxeq & \K[\MNSnleftModels]\nleftModels & \K[\MNSnseModels]\nseModels \\ \K[\MNSnbackcong]\nbackcong & \K[\MNSnleftrightline]\nleftrightline & \K[\MNSnsemodels]\nsemodels \\ \K[\MNSnbackeqsim]\nbackeqsim & \K[\MNSnLeftrightline]\nLeftrightline & \K[\MNSnsevdash]\nsevdash \\ \K[\MNSnbacksim]\nbacksim & \K[\MNSnleftvdash]\nleftvdash & \K[\MNSnseVdash]\nseVdash \\ \K[\MNSnbacksimeq]\nbacksimeq & \K[\MNSnleftVdash]\nleftVdash & \K[\MNSnshortmid]\nshortmid \\ \K[\MNSnbacktriplesim]\nbacktriplesim & \K[\MNSnnefootline]\nnefootline & \K[\MNSnshortparallel]\nshortparallel \\ \K[\MNSnbumpeq]\nbumpeq & \K[\MNSnnefree]\nnefree & \K[\MNSnsim]\nsim \\ \K[\MNSnBumpeq]\nBumpeq & \K[\MNSnnemodels]\nnemodels & \K[\MNSnsimeq]\nsimeq \\ \K[\MNSncirceq]\ncirceq & \K[\MNSnneModels]\nneModels & \K[\MNSnsucc]\nsucc \\ \K[\MNSnclosedequal]\nclosedequal & \K[\MNSnneswline]\nneswline & \K[\MNSnsuccapprox]\nsuccapprox \\ \K[\MNSncong]\ncong & \K[\MNSnNeswline]\nNeswline & \K[\MNSnsucccurlyeq]\nsucccurlyeq \\ \K[\MNSncurlyeqprec]\ncurlyeqprec & \K[\MNSnneVdash]\nneVdash & \K[\MNSnsucceq]\nsucceq \\ \K[\MNSncurlyeqsucc]\ncurlyeqsucc & \K[\MNSnnevdash]\nnevdash & \K[\MNSnsuccsim]\nsuccsim \\ \K[\MNSndoteq]\ndoteq & \K[\MNSnnwfootline]\nnwfootline & \K[\MNSnswfootline]\nswfootline \\ \K[\MNSnDoteq]\nDoteq & \K[\MNSnnwfree]\nnwfree & \K[\MNSnswfree]\nswfree \\ \K[\MNSndownfootline]\ndownfootline & \K[\MNSnnwmodels]\nnwmodels & \K[\MNSnswModels]\nswModels \\ \K[\MNSndownfree]\ndownfree & \K[\MNSnnwModels]\nnwModels & \K[\MNSnswmodels]\nswmodels \\ \K[\MNSndownModels]\ndownModels & \K[\MNSnNwseline]\nNwseline & \K[\MNSnswvdash]\nswvdash \\ \K[\MNSndownmodels]\ndownmodels & \K[\MNSnnwseline]\nnwseline & \K[\MNSnswVdash]\nswVdash \\ \K[\MNSndownVdash]\ndownVdash & \K[\MNSnnwvdash]\nnwvdash & \K[\MNSntriplesim]\ntriplesim \\ \K[\MNSndownvdash]\ndownvdash & \K[\MNSnnwVdash]\nnwVdash & \K[\MNSnUpdownline]\nUpdownline \\ \K[\MNSneqbump]\neqbump & \K[\MNSnprec]\nprec & \K[\MNSnupdownline]\nupdownline \\ \K[\MNSneqcirc]\neqcirc & \K[\MNSnprecapprox]\nprecapprox & \K[\MNSnupfootline]\nupfootline \\ \K[\MNSneqdot]\neqdot & \K[\MNSnpreccurlyeq]\npreccurlyeq & \K[\MNSnupfree]\nupfree \\ \K[\MNSneqsim]\neqsim & \K[\MNSnpreceq]\npreceq & \K[\MNSnupModels]\nupModels \\ \K[\MNSnequal]\nequal & \K[\MNSnprecsim]\nprecsim & \K[\MNSnupmodels]\nupmodels \\ \K[\MNSnequalclosed]\nequalclosed & \K[\MNSnrightfootline]\nrightfootline & \K[\MNSnupVdash]\nupVdash \\ \K[\MNSnequiv]\nequiv & \K[\MNSnrightfree]\nrightfree & \K[\MNSnupvdash]\nupvdash \\ \K[\MNSnequivclosed]\nequivclosed & \K[\MNSnrightModels]\nrightModels & \K[\MNSprecnapprox]\precnapprox \\ \K[\MNSneswcrossing]\neswcrossing & \K[\MNSnrightmodels]\nrightmodels & \K[\MNSprecnsim]\precnsim \\ \K[\MNSnfallingdotseq]\nfallingdotseq & \K[\MNSnrightvdash]\nrightvdash & \K[\MNSsuccnapprox]\succnapprox \\ \K[\MNSnhateq]\nhateq & \K[\MNSnrightVdash]\nrightVdash & \K[\MNSsuccnsim]\succnsim \\ \end{longtable} \MNS\ additionally defines synonyms for some of the preceding symbols: \bigskip \newcommand*{\mnssyn}[1]{(same as \texttt{\string#1})} \begin{tabular}{ll@{\quad}l} \K[\MNSnleftvdash]\ndashv & \mnssyn\nleftvdash \\ \K[\MNSnnwseline]\ndiagdown & \mnssyn\nnwseline \\ \K[\MNSnneswline]\ndiagup & \mnssyn\nneswline \\ \K[\MNSnupdownline]\ndivides & \mnssyn\nupdownline \\ \K[\MNSnequal]\ne & \mnssyn\nequal \\ \K[\MNSnequal]\neq & \mnssyn\nequal \\ \K[\MNSnupdownline]\nmid & \mnssyn\nupdownline \\ \K[\MNSnrightmodels]\nmodels & \mnssyn\nrightmodels \\ \K[\MNSnUpdownline]\nparallel & \mnssyn\nUpdownline \\ \K[\MNSnupvdash]\nperp & \mnssyn\nupvdash \\ \K[\MNSnleftrightline]\nrelbar & \mnssyn\nleftrightline \\ \K[\MNSnLeftrightline]\nRelbar & \mnssyn\nLeftrightline \\ \K[\MNSnrightmodels]\nvDash & \mnssyn\nrightmodels \\ \K[\MNSnrightvdash]\nvdash & \mnssyn\nrightvdash \\ \K[\MNSnrightVdash]\nVdash & \mnssyn\nrightVdash \\ \K[\MNSnrightModels]\nVDash & \mnssyn\nrightModels \\ \end{tabular} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Binary Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltidxboth{frown}{symbols} \ltidxboth{smile}{symbols} \ltidxboth{database}{symbols} \label{fdsym-rel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMapprox]\approx & \K[\FDSYMequiv]\equiv & \K[\FDSYMrightmodels]\rightmodels \\ \K[\FDSYMapproxeq]\approxeq & \K[\FDSYMfallingdotseq]\fallingdotseq & \K[\FDSYMrightVdash]\rightVdash \\ \K[\FDSYMbackcong]\backcong & \K[\FDSYMfrown]\frown & \K[\FDSYMrightVDash]\rightVDash \\ \K[\FDSYMbackpropto]\backpropto & \K[\FDSYMfrowneq]\frowneq & \K[\FDSYMrightvdash]\rightvdash \\ \K[\FDSYMbacksim]\backsim & \K[\FDSYMfrownsmile]\frownsmile & \K[\FDSYMrightvDash]\rightvDash \\ \K[\FDSYMbacksimeq]\backsimeq & \K[\FDSYMin]\in & \K[\FDSYMrisingdotseq]\risingdotseq \\ \K[\FDSYMbetween]\between & \K[\FDSYMleftassert]\leftassert & \K[\FDSYMshortmid]\shortmid \\ \K[\FDSYMbowtie]\bowtie & \K[\FDSYMleftAssert]\leftAssert & \K[\FDSYMshortparallel]\shortparallel \\ \K[\FDSYMbumpeq]\bumpeq & \K[\FDSYMleftfootline]\leftfootline & \K[\FDSYMsim]\sim \\ \K[\FDSYMBumpeq]\Bumpeq & \K[\FDSYMleftmodels]\leftmodels & \K[\FDSYMsimeq]\simeq \\ \K[\FDSYMbumpeqq]\bumpeqq & \K[\FDSYMleftvdash]\leftvdash & \K[\FDSYMsmile]\smile \\ \K[\FDSYMcirceq]\circeq & \K[\FDSYMleftvDash]\leftvDash & \K[\FDSYMsmileeq]\smileeq \\ \K[\FDSYMcoloneq]\coloneq & \K[\FDSYMleftVdash]\leftVdash & \K[\FDSYMsmilefrown]\smilefrown \\ \K[\FDSYMcong]\cong & \K[\FDSYMleftVDash]\leftVDash & \K[\FDSYMstareq]\stareq \\ \K[\FDSYMcrossing]\crossing & \K[\FDSYMlongleftfootline]\longleftfootline & \K[\FDSYMsucc]\succ \\ \K[\FDSYMcurlyeqprec]\curlyeqprec & \K[\FDSYMLongmapsfrom]\Longmapsfrom & \K[\FDSYMsuccapprox]\succapprox \\ \K[\FDSYMcurlyeqsucc]\curlyeqsucc & \K[\FDSYMlongmapsfrom]\longmapsfrom & \K[\FDSYMsucccurlyeq]\succcurlyeq \\ \K[\FDSYMdashVv]\dashVv & \K[\FDSYMlongrightfootline]\longrightfootline & \K[\FDSYMsucceq]\succeq \\ \K[\FDSYMDdashv]\Ddashv & \K[\FDSYMmid]\mid & \K[\FDSYMsucceqq]\succeqq \\ \X[\FDSYMdotcong]\dotcong & \K[\FDSYMowns]\owns & \K[\FDSYMsuccsim]\succsim \\ \K[\FDSYMdoteq]\doteq & \K[\FDSYMparallel]\parallel & \K[\FDSYMthickapprox]\thickapprox \\ \K[\FDSYMDoteq]\Doteq & \K[\FDSYMprec]\prec & \K[\FDSYMthicksim]\thicksim \\ \K[\FDSYMdotsminusdots]\dotsminusdots & \K[\FDSYMprecapprox]\precapprox & \K[\FDSYMtriplesim]\triplesim \\ \K[\FDSYMdownAssert]\downAssert & \K[\FDSYMpreccurlyeq]\preccurlyeq & \K[\FDSYMupassert]\upassert \\ \K[\FDSYMdownassert]\downassert & \K[\FDSYMpreceq]\preceq & \K[\FDSYMupAssert]\upAssert \\ \K[\FDSYMdownmodels]\downmodels & \K[\FDSYMpreceqq]\preceqq & \K[\FDSYMupmodels]\upmodels \\ \K[\FDSYMdownvDash]\downvDash & \K[\FDSYMprecnapprox]\precnapprox & \K[\FDSYMupvdash]\upvdash \\ \K[\FDSYMdownVdash]\downVdash & \K[\FDSYMprecneq]\precneq & \K[\FDSYMupvDash]\upvDash \\ \K[\FDSYMdownvdash]\downvdash & \K[\FDSYMprecneqq]\precneqq & \K[\FDSYMupVdash]\upVdash \\ \K[\FDSYMdownVDash]\downVDash & \K[\FDSYMprecnsim]\precnsim & \K[\FDSYMupVDash]\upVDash \\ \K[\FDSYMeqcirc]\eqcirc & \K[\FDSYMprecsim]\precsim & \K[\FDSYMvDdash]\vDdash \\ \K[\FDSYMeqcolon]\eqcolon & \K[\FDSYMpropto]\propto & \K[\FDSYMveeeq]\veeeq \\ \K[\FDSYMeqdot]\eqdot & \K[\FDSYMrightassert]\rightassert & \K[\FDSYMVvdash]\Vvdash \\ \K[\FDSYMeqsim]\eqsim & \K[\FDSYMrightAssert]\rightAssert & \K[\FDSYMwedgeq]\wedgeq \\ \K[\FDSYMequal]\equal & \K[\FDSYMrightfootline]\rightfootline & \\ \end{longtable} \FDSYM\ defines synonyms for many of the preceding symbols: \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMapproxident]{\approxident} & \K[\FDSYMdashV]{\dashV} & \K[\FDSYMshortrighttack]{\shortrighttack} \\ \K[\FDSYMarceq]{\arceq} & \K[\FDSYMdoteqdot]{\doteqdot} & \K[\FDSYMshortuptack]{\shortuptack} \\ \K[\FDSYMAssert]{\Assert} & \K[\FDSYMeqqcolon]{\eqqcolon} & \K[\FDSYMsmallfrown]{\smallfrown} \\ \K[\FDSYMassert]{\assert} & \K[\FDSYMhateq]\hateq & \K[\FDSYMsmallsmile]{\smallsmile} \\ \K[\FDSYMasymp]{\asymp} & \K[\FDSYMJoin]{\Join} & \K[\FDSYMvarpropto]{\varpropto} \\ \K[\FDSYMBarv]{\Barv} & \K[\FDSYMlongdashv]{\longdashv} & \K[\FDSYMvBar]{\vBar} \\ \K[\FDSYMbarV]{\barV} & \K[\FDSYMmodels]{\models} & \K[\FDSYMVbar]{\Vbar} \\ \K[\FDSYMclosure]{\closure} & \K[\FDSYMni]{\ni} & \K[\FDSYMvDash]{\vDash} \\ \K[\FDSYMcoloneqq]{\coloneqq} & \K[\FDSYMperp]{\perp} & \K[\FDSYMVDash]{\VDash} \\ \K[\FDSYMdashv]{\dashv} & \K[\FDSYMpropfrom]{\propfrom} & \K[\FDSYMVdash]{\Vdash} \\ \K[\FDSYMDashV]{\DashV} & \K[\FDSYMshortdowntack]{\shortdowntack} & \K[\FDSYMvdash]{\vdash} \\ \K[\FDSYMDashv]{\Dashv} & \K[\FDSYMshortlefttack]{\shortlefttack} & \K[\FDSYMvlongdash]{\vlongdash} \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Negated Binary Relations} \ltindex{binary relations>negated} \ltindex{relational symbols>negated binary} \ltidxboth{frown}{symbols} \ltidxboth{smile}{symbols} \label{fdsym-nrel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMbacksimneqq]\backsimneqq & \K[\FDSYMnin]\nin & \K[\FDSYMnsim]\nsim \\ \K[\FDSYMnapprox]\napprox & \K[\FDSYMnleftAssert]\nleftAssert & \K[\FDSYMnsimeq]\nsimeq \\ \K[\FDSYMnapproxeq]\napproxeq & \K[\FDSYMnleftassert]\nleftassert & \K[\FDSYMnsmile]\nsmile \\ \K[\FDSYMnbackcong]\nbackcong & \K[\FDSYMnleftfootline]\nleftfootline & \K[\FDSYMnsmileeq]\nsmileeq \\ \K[\FDSYMnbacksim]\nbacksim & \K[\FDSYMnleftmodels]\nleftmodels & \K[\FDSYMnsmilefrown]\nsmilefrown \\ \K[\FDSYMnbacksimeq]\nbacksimeq & \K[\FDSYMnleftvDash]\nleftvDash & \K[\FDSYMnstareq]\nstareq \\ \K[\FDSYMnbumpeq]\nbumpeq & \K[\FDSYMnleftvdash]\nleftvdash & \K[\FDSYMnsucc]\nsucc \\ \K[\FDSYMnBumpeq]\nBumpeq & \K[\FDSYMnleftVdash]\nleftVdash & \K[\FDSYMnsuccapprox]\nsuccapprox \\ \K[\FDSYMnbumpeqq]\nbumpeqq & \K[\FDSYMnleftVDash]\nleftVDash & \K[\FDSYMnsucccurlyeq]\nsucccurlyeq \\ \K[\FDSYMncirceq]\ncirceq & \K[\FDSYMnlongleftfootline]\nlongleftfootline & \K[\FDSYMnsucceq]\nsucceq \\ \K[\FDSYMncong]\ncong & \K[\FDSYMnLongmapsfrom]\nLongmapsfrom & \K[\FDSYMnsucceqq]\nsucceqq \\ \K[\FDSYMncurlyeqprec]\ncurlyeqprec & \K[\FDSYMnlongmapsfrom]\nlongmapsfrom & \K[\FDSYMnsuccsim]\nsuccsim \\ \K[\FDSYMncurlyeqsucc]\ncurlyeqsucc & \K[\FDSYMnlongrightfootline]\nlongrightfootline & \K[\FDSYMntriplesim]\ntriplesim \\ \K[\FDSYMndashVv]\ndashVv & \K[\FDSYMnmid]\nmid & \K[\FDSYMnupassert]\nupassert \\ \K[\FDSYMnDdashv]\nDdashv & \K[\FDSYMnowns]\nowns & \K[\FDSYMnupAssert]\nupAssert \\ \K[\FDSYMndoteq]\ndoteq & \K[\FDSYMnparallel]\nparallel & \K[\FDSYMnupmodels]\nupmodels \\ \K[\FDSYMnDoteq]\nDoteq & \K[\FDSYMnprec]\nprec & \K[\FDSYMnupVDash]\nupVDash \\ \K[\FDSYMndownassert]\ndownassert & \K[\FDSYMnprecapprox]\nprecapprox & \K[\FDSYMnupvDash]\nupvDash \\ \K[\FDSYMndownAssert]\ndownAssert & \K[\FDSYMnpreccurlyeq]\npreccurlyeq & \K[\FDSYMnupVdash]\nupVdash \\ \K[\FDSYMndownmodels]\ndownmodels & \K[\FDSYMnpreceq]\npreceq & \K[\FDSYMnupvdash]\nupvdash \\ \K[\FDSYMndownvdash]\ndownvdash & \K[\FDSYMnpreceqq]\npreceqq & \K[\FDSYMnvDdash]\nvDdash \\ \K[\FDSYMndownVdash]\ndownVdash & \K[\FDSYMnprecsim]\nprecsim & \K[\FDSYMnveeeq]\nveeeq \\ \K[\FDSYMndownVDash]\ndownVDash & \K[\FDSYMnrightassert]\nrightassert & \K[\FDSYMnVvdash]\nVvdash \\ \K[\FDSYMndownvDash]\ndownvDash & \K[\FDSYMnrightAssert]\nrightAssert & \K[\FDSYMnwedgeq]\nwedgeq \\ \K[\FDSYMneqcirc]\neqcirc & \K[\FDSYMnrightfootline]\nrightfootline & \K[\FDSYMprecneq]\precneq \\ \K[\FDSYMneqdot]\neqdot & \K[\FDSYMnrightmodels]\nrightmodels & \K[\FDSYMprecneqq]\precneqq \\ \K[\FDSYMneqsim]\neqsim & \K[\FDSYMnrightvdash]\nrightvdash & \K[\FDSYMsimneqq]\simneqq \\ \K[\FDSYMnequal]\nequal & \K[\FDSYMnrightVdash]\nrightVdash & \K[\FDSYMsuccnapprox]\succnapprox \\ \K[\FDSYMnequiv]\nequiv & \K[\FDSYMnrightvDash]\nrightvDash & \K[\FDSYMsuccneq]\succneq \\ \K[\FDSYMnfallingdotseq]\nfallingdotseq & \K[\FDSYMnrightVDash]\nrightVDash & \K[\FDSYMsuccneqq]\succneqq \\ \K[\FDSYMnfrown]\nfrown & \K[\FDSYMnrisingdotseq]\nrisingdotseq & \K[\FDSYMsuccnsim]\succnsim \\ \K[\FDSYMnfrowneq]\nfrowneq & \K[\FDSYMnshortmid]\nshortmid & \\ \K[\FDSYMnfrownsmile]\nfrownsmile & \K[\FDSYMnshortparallel]\nshortparallel & \\ \end{longtable} \FDSYM\ defines synonyms for many of the preceding symbols: \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMnapproxident]{\napproxident} & \K[\FDSYMndashV]{\ndashV} & \K[\FDSYMnshortrighttack]{\nshortrighttack} \\ \K[\FDSYMnarceq]{\narceq} & \K[\FDSYMne]{\ne} & \K[\FDSYMnshortuptack]{\nshortuptack} \\ \K[\FDSYMnAssert]{\nAssert} & \K[\FDSYMneq]{\neq} & \K[\FDSYMnsime]{\nsime} \\ \K[\FDSYMnassert]{\nassert} & \K[\FDSYMnhateq]{\nhateq} & \K[\FDSYMnvBar]{\nvBar} \\ \K[\FDSYMnasymp]{\nasymp} & \K[\FDSYMnlongdashv]{\nlongdashv} & \K[\FDSYMnVbar]{\nVbar} \\ \K[\FDSYMnBarv]{\nBarv} & \K[\FDSYMnmodels]{\nmodels} & \K[\FDSYMnVdash]{\nVdash} \\ \K[\FDSYMnbarV]{\nbarV} & \K[\FDSYMnni]{\nni} & \K[\FDSYMnvDash]{\nvDash} \\ \K[\FDSYMnclosure]{\nclosure} & \K[\FDSYMnotin]{\notin} & \K[\FDSYMnVDash]{\nVDash} \\ \K[\FDSYMnDashV]{\nDashV} & \K[\FDSYMnperp]{\nperp} & \K[\FDSYMnvdash]{\nvdash} \\ \K[\FDSYMnDashv]{\nDashv} & \K[\FDSYMnshortdowntack]{\nshortdowntack} & \K[\FDSYMnvlongdash]{\nvlongdash} \\ \K[\FDSYMndashv]{\ndashv} & \K[\FDSYMnshortlefttack]{\nshortlefttack} & \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[BSK]{\BSK\ Binary Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltidxboth{frown}{symbols} \ltidxboth{smile}{symbols} \label{bsk-rel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\BSKac]\ac & \K[\BSKfatslash]\fatslash & \K[\BSKscurel]\scurel \\ \K[\BSKapproxeq]\approxeq & \K[\BSKforkv]\forkv & \K[\BSKshortmid]\shortmid \\ \K[\BSKarceq]\arceq & \K[\BSKfrown]\frown & \K[\BSKshortparallel]\shortparallel \\ \K[\BSKbacksim]\backsim & \K[\BSKggcurly]\ggcurly & \K[\BSKsimrdots]\simrdots \\ \K[\BSKbacksimeq]\backsimeq & \K[\BSKhash]\hash & \K[\BSKsmallfrown]\smallfrown \\ \K[\BSKbagmember]\bagmember & \K[\BSKinplus]\inplus & \K[\BSKsmallsmile]\smallsmile \\ \K[\BSKbecause]\because & \K[\BSKkernelcontraction]\kernelcontraction & \K[\BSKsmile]\smile \\ \K[\BSKbetween]\between & \K[\BSKllcurly]\llcurly & \K[\BSKstrictfi]\strictfi \\ \K[\BSKbumpeq]\bumpeq & \K[\BSKmultimap]\multimap & \K[\BSKstrictif]\strictif \\ \K[\BSKBumpeq]\Bumpeq & \K[\BSKmultimapboth]\multimapboth & \K[\BSKsuccapprox]\succapprox \\ \K[\BSKcirceq]\circeq & \K[\BSKmultimapbothvert]\multimapbothvert & \K[\BSKsucccurlyeq]\succcurlyeq \\ \K[\BSKCircledEq]\CircledEq & \K[\BSKmultimapdot]\multimapdot & \K[\BSKsuccnapprox]\succnapprox \\ \K[\BSKcong]\cong & \K[\BSKmultimapdotboth]\multimapdotboth & \K[\BSKsuccneqq]\succneqq \\ \K[\BSKcorresponds]\corresponds & \K[\BSKmultimapdotbothA]\multimapdotbothA & \K[\BSKsuccnsim]\succnsim \\ \K[\BSKcurlyeqprec]\curlyeqprec & \K[\BSKmultimapdotbothAvert]\multimapdotbothAvert & \K[\BSKsuccsim]\succsim \\ \K[\BSKcurlyeqsucc]\curlyeqsucc & \K[\BSKmultimapdotbothB]\multimapdotbothB & \K[\BSKtherefore]\therefore \\ \K[\BSKdashV]\dashV & \K[\BSKmultimapdotbothBvert]\multimapdotbothBvert & \K[\BSKthickapprox]\thickapprox \\ \K[\BSKDashV]\DashV & \K[\BSKmultimapdotbothvert]\multimapdotbothvert & \K[\BSKthicksim]\thicksim \\ \K[\BSKdashVv]\dashVv & \K[\BSKmultimapdotinv]\multimapdotinv & \K[\BSKtopfork]\topfork \\ \K[\BSKdfourier]\dfourier & \K[\BSKmultimapinv]\multimapinv & \K[\BSKtriangleq]\triangleq \\ \K[\BSKDfourier]\Dfourier & \K[\BSKniplus]\niplus & \K[\BSKvarhash]\varhash \\ \K[\BSKdisin]\disin & \K[\BSKnisd]\nisd & \K[\BSKvarisins]\varisins \\ \K[\BSKdoteq]\doteq & \K[\BSKPerp]\Perp & \K[\BSKvarnis]\varnis \\ \K[\BSKdoteqdot]\doteqdot & \K[\BSKpitchfork]\pitchfork & \K[\BSKvarpropto]\varpropto \\ \K[\BSKdotminus]\dotminus & \K[\BSKprecapprox]\precapprox & \K[\BSKVdash]\Vdash \\ \K[\BSKdotsim]\dotsim & \K[\BSKpreccurlyeq]\preccurlyeq & \K[\BSKvDash]\vDash \\ \K[\BSKeqbumped]\eqbumped & \K[\BSKprecnapprox]\precnapprox & \K[\BSKVDash]\VDash \\ \K[\BSKeqcirc]\eqcirc & \K[\BSKprecneqq]\precneqq & \K[\BSKveeeq]\veeeq \\ \K[\BSKeqsim]\eqsim & \K[\BSKprecnsim]\precnsim & \K[\BSKVvdash]\Vvdash \\ \K[\BSKequalparallel]\equalparallel & \K[\BSKprecsim]\precsim & \K[\BSKztransf]\ztransf \\ \K[\BSKfallingdotseq]\fallingdotseq & \K[\BSKprurel]\prurel & \K[\BSKZtransf]\Ztransf \\ \K[\BSKfatbslash]\fatbslash & \K[\BSKrisingdotseq]\risingdotseq & \\ \end{longtable} \end{longsymtable} \begin{symtable}[BSK]{\BSK\ Negated Binary Relations} \index{binary relations>negated} \index{relational symbols>negated binary} \label{bsk-nrel} \begin{tabular}{*3{ll}} \K[\BSKncong]\ncong & \K[\BSKnpreceq]\npreceq & \K[\BSKnVDash]\nVDash \\ \K[\BSKneq]\neq & \K[\BSKnshortmid]\nshortmid & \K[\BSKnVdash]\nVdash \\ \K[\BSKnequiv]\nequiv & \K[\BSKnshortparallel]\nshortparallel & \K[\BSKnvdash]\nvdash \\ \K[\BSKnmid]\nmid & \K[\BSKnsim]\nsim & \K[\BSKnvDash]\nvDash \\ \K[\BSKnparallel]\nparallel & \K[\BSKnsucc]\nsucc & \\ \K[\BSKnprec]\nprec & \K[\BSKnsucceq]\nsucceq & \\ \end{tabular} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Binary Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltidxboth{APL}{symbols} \ltidxboth{frown}{symbols} \label{stix-rel} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXapprox]\approx & \K[\STIXeqvparsl]\eqvparsl & \K[\STIXrightfishtail]\rightfishtail \\ \K[\STIXapproxeq]\approxeq & \K[\STIXfallingdotseq]\fallingdotseq & \K[\STIXrightimply]\rightimply \\ \K[\STIXapproxeqq]\approxeqq & \K[\STIXfbowtie]\fbowtie & \K[\STIXrighttail]\righttail \\ \K[\STIXapproxident]\approxident & \K[\STIXforksnot]\forksnot & \K[\STIXrisingdotseq]\risingdotseq \\ \K[\STIXarceq]\arceq & \K[\STIXforkv]\forkv & \K[\STIXrsqhook]\rsqhook \\ \K[\STIXassert]\assert & \K[\STIXfrown]\frown & \K[\STIXruledelayed]\ruledelayed \\ \K[\STIXasteq]\asteq & \K[\STIXgleichstark]\gleichstark & \K[\STIXscurel]\scurel \\ \K[\STIXasymp]\asymp & \K[\STIXhatapprox]\hatapprox & \K[\STIXshortdowntack]\shortdowntack \\ \K[\STIXbackcong]\backcong & \K[\STIXimageof]\imageof & \K[\STIXshortlefttack]\shortlefttack \\ \K[\STIXbacksim]\backsim & \K[\STIXin]\in & \K[\STIXshortmid]\shortmid \\ \K[\STIXbacksimeq]\backsimeq & \K[\STIXisindot]\isindot & \K[\STIXshortparallel]\shortparallel \\ \K[\STIXbagmember]\bagmember & \K[\STIXisinE]\isinE & \K[\STIXshortuptack]\shortuptack \\ \K[\STIXBarv]\Barv & \K[\STIXisinobar]\isinobar & \K[\STIXsim]\sim \\ \K[\STIXbarV]\barV & \K[\STIXisins]\isins & \K[\STIXsimeq]\simeq \\ \K[\STIXbetween]\between & \K[\STIXisinvb]\isinvb & \K[\STIXsimminussim]\simminussim \\ \K[\STIXbNot]\bNot & \K[\STIXkernelcontraction]\kernelcontraction & \K[\STIXsimneqq]\simneqq \\ \K[\STIXbowtie]\bowtie & \K[\STIXleftdbltail]\leftdbltail & \K[\STIXsimrdots]\simrdots \\ \K[\STIXBumpeq]\Bumpeq & \K[\STIXleftfishtail]\leftfishtail & \K[\STIXsmallfrown]\smallfrown \\ \K[\STIXbumpeq]\bumpeq & \K[\STIXlefttail]\lefttail & \K[\STIXsmallin]\smallin \\ \K[\STIXbumpeqq]\bumpeqq & \K[\STIXlfbowtie]\lfbowtie & \K[\STIXsmallni]\smallni \\ \K[\STIXcirbot]\cirbot & \K[\STIXlftimes]\lftimes & \K[\STIXsmallsmile]\smallsmile \\ \K[\STIXcirceq]\circeq & \K[\STIXlongdashv]\longdashv & \K[\STIXsmeparsl]\smeparsl \\ \K[\STIXcirmid]\cirmid & \K[\STIXlsqhook]\lsqhook & \K[\STIXsmile]\smile \\ \K[\STIXclosure]\closure & \K[\STIXmeaseq]\measeq & \K[\STIXstareq]\stareq \\ \K[\STIXColoneq]\Coloneq & \K[\STIXmid]\mid & \K[\STIXsucc]\succ \\ \K[\STIXcoloneq]\coloneq & \K[\STIXmidcir]\midcir & \K[\STIXSucc]\Succ \\ \K[\STIXcong]\cong & \K[\STIXmlcp]\mlcp & \K[\STIXsuccapprox]\succapprox \\ \K[\STIXcongdot]\congdot & \K[\STIXmodels]\models & \K[\STIXsucccurlyeq]\succcurlyeq \\ \K[\STIXcurlyeqprec]\curlyeqprec & \K[\STIXmultimap]\multimap & \K[\STIXsucceq]\succeq \\ \K[\STIXcurlyeqsucc]\curlyeqsucc & \K[\STIXmultimapinv]\multimapinv & \K[\STIXsucceqq]\succeqq \\ \K[\STIXdashcolon]\dashcolon & \K[\STIXni]\ni & \K[\STIXsuccnapprox]\succnapprox \\ \K[\STIXdashv]\dashv & \K[\STIXniobar]\niobar & \K[\STIXsuccneq]\succneq \\ \K[\STIXdashV]\dashV & \K[\STIXnis]\nis & \K[\STIXsuccneqq]\succneqq \\ \K[\STIXDashv]\Dashv & \K[\STIXnisd]\nisd & \K[\STIXsuccnsim]\succnsim \\ \K[\STIXDashV]\DashV & \K[\STIXNot]\Not & \K[\STIXsuccsim]\succsim \\ \K[\STIXDashVDash]\DashVDash & \K[\STIXnotchar]\notchar & \K[\STIXthickapprox]\thickapprox \\ \K[\STIXdashVdash]\dashVdash & \K[\STIXorigof]\origof & \K[\STIXthicksim]\thicksim \\ \K[\STIXddotseq]\ddotseq & \K[\STIXparallel]\parallel & \K[\STIXtopfork]\topfork \\ \K[\STIXdisin]\disin & \K[\STIXparsim]\parsim & \K[\STIXupfishtail]\upfishtail \\ \K[\STIXDoteq]\Doteq & \K[\STIXperp]\perp & \K[\STIXupin]\upin \\ \K[\STIXdoteq]\doteq & \K[\STIXpitchfork]\pitchfork & \K[\STIXvarisinobar]\varisinobar \\ \K[\STIXdotequiv]\dotequiv & \K[\STIXprec]\prec & \K[\STIXvarisins]\varisins \\ \K[\STIXdotsim]\dotsim & \K[\STIXPrec]\Prec & \K[\STIXvarniobar]\varniobar \\ \K[\STIXdotsminusdots]\dotsminusdots & \K[\STIXprecapprox]\precapprox & \K[\STIXvarnis]\varnis \\ \K[\STIXdownfishtail]\downfishtail & \K[\STIXpreccurlyeq]\preccurlyeq & \K[\STIXvarpropto]\varpropto \\ \K[\STIXdualmap]\dualmap & \K[\STIXpreceq]\preceq & \K[\STIXvarVdash]\varVdash \\ \K[\STIXeparsl]\eparsl & \K[\STIXpreceqq]\preceqq & \K[\STIXvBar]\vBar \\ \K[\STIXeqcirc]\eqcirc & \K[\STIXprecnapprox]\precnapprox & \K[\STIXVbar]\Vbar \\ \K[\STIXeqcolon]\eqcolon & \K[\STIXprecneq]\precneq & \K[\STIXvBarv]\vBarv \\ \K[\STIXeqdef]\eqdef & \K[\STIXprecneqq]\precneqq & \K[\STIXVdash]\Vdash \\ \K[\STIXeqdot]\eqdot & \K[\STIXprecnsim]\precnsim & \K[\STIXvdash]\vdash \\ \K[\STIXeqeq]\eqeq & \K[\STIXprecsim]\precsim & \K[\STIXvDash]\vDash \\ \K[\STIXeqeqeq]\eqeqeq & \K[\STIXpropto]\propto & \K[\STIXVDash]\VDash \\ \K[\STIXeqqsim]\eqqsim & \K[\STIXprurel]\prurel & \K[\STIXvDdash]\vDdash \\ \K[\STIXeqsim]\eqsim & \K[\STIXpullback]\pullback & \K[\STIXvdots]\vdots \\ \K[\STIXequalparallel]\equalparallel & \K[\STIXpushout]\pushout & \K[\STIXveeeq]\veeeq \\ \K[\STIXequiv]\equiv & \K[\STIXquesteq]\questeq & \K[\STIXveeonwedge]\veeonwedge \\ \K[\STIXEquiv]\Equiv & \K[\STIXrevnmid]\revnmid & \K[\STIXvertoverlay]\vertoverlay \\ \K[\STIXequivDD]\equivDD & \K[\STIXrfbowtie]\rfbowtie & \K[\STIXvlongdash]\vlongdash \\ \K[\STIXequivVert]\equivVert & \K[\STIXrftimes]\rftimes & \K[\STIXVvdash]\Vvdash \\ \K[\STIXequivVvert]\equivVvert & \K[\STIXrightdbltail]\rightdbltail & \K[\STIXwedgeq]\wedgeq \\ \end{longtable} \begin{tablenote} \STIX\ defines \cmdI[\string\STIXowns]{\owns} as a synonym for \cmdI[\string\STIXni]{\ni} and \cmdI[\string\STIXdoteqdot]{\doteqdot} as a synonym for \cmdI[\string\STIXDoteq]{\Doteq}. \end{tablenote} \end{longsymtable} \begin{symtable}[STIX]{\STIX\ Negated Binary Relations} \index{binary relations>negated} \index{relational symbols>negated binary} \label{stix-nrel} \begin{tabular}{*3{ll}} \K[\STIXforks]\forks & \K[\STIXnhpar]\nhpar & \K[\STIXnsime]\nsime \\ \K[\STIXnapprox]\napprox & \K[\STIXnmid]\nmid & \K[\STIXnsucc]\nsucc \\ \K[\STIXnapproxeqq]\napproxeqq & \K[\STIXnni]\nni & \K[\STIXnsucccurlyeq]\nsucccurlyeq \\ \K[\STIXnasymp]\nasymp & \K[\STIXnotin]\notin & \K[\STIXnsucceq]\nsucceq \\ \K[\STIXnBumpeq]\nBumpeq & \K[\STIXnparallel]\nparallel & \K[\STIXnvarisinobar]\nvarisinobar \\ \K[\STIXnbumpeq]\nbumpeq & \K[\STIXnprec]\nprec & \K[\STIXnvarniobar]\nvarniobar \\ \K[\STIXncong]\ncong & \K[\STIXnpreccurlyeq]\npreccurlyeq & \K[\STIXnvDash]\nvDash \\ \K[\STIXncongdot]\ncongdot & \K[\STIXnpreceq]\npreceq & \K[\STIXnvdash]\nvdash \\ \K[\STIXne]\ne & \K[\STIXnshortmid]\nshortmid & \K[\STIXnVDash]\nVDash \\ \K[\STIXneqsim]\neqsim & \K[\STIXnshortparallel]\nshortparallel & \K[\STIXnVdash]\nVdash \\ \K[\STIXnequiv]\nequiv & \K[\STIXnsim]\nsim & \\ \end{tabular} \bigskip \begin{tablenote} \STIX\ defines \cmdI[\string\STIXneq]{\neq} as a synonym for \cmdI[\string\STIXne]{\ne}, \cmdI[\string\STIXnsimeq]{\nsimeq} as a synonym for \cmdI[\string\STIXnsime]{\nsime}, and \cmdI[\string\STIXnforksnot]{\nforksnot} as a synonym for \cmdI[\string\STIXforks]{\forks}. \end{tablenote} \end{symtable} \begin{symtable}[MTOOLS]{\MTOOLS\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{mtools-rel} \begin{tabular}{ll@{\qquad}ll@{\qquad}ll} \X[\MTOOLSColonapprox]\Colonapprox & \X[\MTOOLScoloneq]\coloneq & \X[\MTOOLSEqcolon]\Eqcolon \\ \X[\MTOOLScolonapprox]\colonapprox & \X[\MTOOLScolonsim]\colonsim & \X[\MTOOLSeqqcolon]\eqqcolon \\ \X[\MTOOLScoloneqq]\coloneqq & \X[\MTOOLSColonsim]\Colonsim & \X[\MTOOLSEqqcolon]\Eqqcolon \\ \X[\MTOOLSColoneqq]\Coloneqq & \X[\MTOOLSdblcolon]\dblcolon & \\ \X[\MTOOLSColoneq]\Coloneq & \X[\MTOOLSeqcolon]\eqcolon & \\ \end{tabular} \bigskip \begin{tablenote} Similar symbols can be defined using \MTOOLS's \cmdX{\vcentcolon}, which produces a colon centered on the font's math axis: \begin{center} \begin{tabular}{ccc} \Huge $=:=$ & vs. & \Huge $=\vcentcolon=$ \\ ``\verb|=:=|'' & & ``\verb|=\vcentcolon=|'' \\ \end{tabular} \end{center} \end{tablenote} \end{symtable} \begin{longsymtable}[TURN]{\TURN\ Binary Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltindex{consequence relations} \label{turn-rel} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{longtable}{ll@{\hspace*{2em}}ll@{\hspace*{2em}}ll} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \Wul\dddtstile{abc}{def} & \Wul\nntstile{abc}{def} & \Wul\stdtstile{abc}{def} \\ \Wul\ddststile{abc}{def} & \Wul\nnttstile{abc}{def} & \Wul\stststile{abc}{def} \\ \Wul\ddtstile{abc}{def} & \Wul\nsdtstile{abc}{def} & \Wul\sttstile{abc}{def} \\ \Wul\ddttstile{abc}{def} & \Wul\nsststile{abc}{def} & \Wul\stttstile{abc}{def} \\ \Wul\dndtstile{abc}{def} & \Wul\nststile{abc}{def} & \Wul\tddtstile{abc}{def} \\ \Wul\dnststile{abc}{def} & \Wul\nsttstile{abc}{def} & \Wul\tdststile{abc}{def} \\ \Wul\dntstile{abc}{def} & \Wul\ntdtstile{abc}{def} & \Wul\tdtstile{abc}{def} \\ \Wul\dnttstile{abc}{def} & \Wul\ntststile{abc}{def} & \Wul\tdttstile{abc}{def} \\ \Wul\dsdtstile{abc}{def} & \Wul\nttstile{abc}{def} & \Wul\tndtstile{abc}{def} \\ \Wul\dsststile{abc}{def} & \Wul\ntttstile{abc}{def} & \Wul\tnststile{abc}{def} \\ \Wul\dststile{abc}{def} & \Wul\sddtstile{abc}{def} & \Wul\tntstile{abc}{def} \\ \Wul\dsttstile{abc}{def} & \Wul\sdststile{abc}{def} & \Wul\tnttstile{abc}{def} \\ \Wul\dtdtstile{abc}{def} & \Wul\sdtstile{abc}{def} & \Wul\tsdtstile{abc}{def} \\ \Wul\dtststile{abc}{def} & \Wul\sdttstile{abc}{def} & \Wul\tsststile{abc}{def} \\ \Wul\dttstile{abc}{def} & \Wul\sndtstile{abc}{def} & \Wul\tststile{abc}{def} \\ \Wul\dtttstile{abc}{def} & \Wul\snststile{abc}{def} & \Wul\tsttstile{abc}{def} \\ \Wul\nddtstile{abc}{def} & \Wul\sntstile{abc}{def} & \Wul\ttdtstile{abc}{def} \\ \Wul\ndststile{abc}{def} & \Wul\snttstile{abc}{def} & \Wul\ttststile{abc}{def} \\ \Wul\ndtstile{abc}{def} & \Wul\ssdtstile{abc}{def} & \Wul\tttstile{abc}{def} \\ \Wul\ndttstile{abc}{def} & \Wul\ssststile{abc}{def} & \Wul\ttttstile{abc}{def} \\ \Wul\nndtstile{abc}{def} & \Wul\sststile{abc}{def} & \\ \Wul\nnststile{abc}{def} & \Wul\ssttstile{abc}{def} & \\ \end{longtable} \begin{tablenote} \seepackagenote{TURN}{turnstile}. \end{tablenote} \end{longsymtable} \begin{symtable}[TRSYM]{\TRSYM\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \index{transforms} \label{trsym-rel} \begin{tabular}{ll@{\hspace*{2em}}ll} \K\InversTransformHoriz & \K\TransformHoriz \\ \K\InversTransformVert & \K\TransformVert \\ \end{tabular} \end{symtable} \begin{symtable}[TRF]{\TRF\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \index{transforms} \label{trf-rel} \begin{tabular}{ll@{\hspace*{2em}}ll} \X\dfourier & \X\Dfourier \\ \X\fourier & \X\Fourier \\ \X\laplace & \X\Laplace \\ \X\ztransf & \X\Ztransf \\ \end{tabular} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Binary Relations} \idxboth{relational}{symbols} \label{pdfmsym-rel} \begin{tabular}{*3{ll}} \X\leftPP & \X\longroundedarrow & \X\roundedarrow \\ \X\longleftPP & \X\longsquaredarrow & \X\squaredarrow \\ \X\longrightPP & \X\rightPP & \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[CMLL]{\CMLL\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \idxboth{logic}{symbols} \label{cmll-rel} \begin{tabular}{ll@{\hspace*{2em}}ll} \K[\CMLLcoh]\coh & \K[\CMLLscoh]\scoh \\ \K[\CMLLincoh]\incoh & \K[\CMLLsincoh]\sincoh \\ \K[\CMLLPerp]\Perp & \K[\CMLLsimperp]\simperp \\ \K[\CMLLmultimapboth]\multimapboth \\ \end{tabular} \end{symtable} \begin{symtable}[CEQ]{\CEQ\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{ceq-rel} \begin{tabular}{*3{ll}} \X\approxcolon & \X\coloncolonminus & \X\equalscoloncolon \\ \X\approxcoloncolon & \X\coloncolonsim & \X\minuscolon \\ \X[\CEQcolonapprox]\colonapprox & \X\colonequals & \X\minuscoloncolon \\ \X\coloncolon & \X\colonminus & \X\ratio \\ \X\coloncolonapprox & \X[\CEQcolonsim]\colonsim & \X\simcolon \\ \X\coloncolonequals & \X\equalscolon & \X\simcoloncolon \\ \end{tabular} \end{symtable} \begin{symtable}[FOUR]{\FOUR\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{fourier-rel} \begin{tabular}{ll@{\quad}ll} \K\nparallelslant & \K\parallelslant \\ \end{tabular} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Binary Relations} \index{binary relations} \index{relational symbols>binary} \label{logix-rel} \begin{tabular}{*4{ll}} \K\ClsEquv & \K\NotClsEquv & \K\NotPre & \K\Pre \\ \K\ClsImpl & \K\NotClsImpl & \K\NotPreq & \K\Preq \\ \K\Conseq & \K\NotConseq & \K\NotRule & \K\Rule \\ \K\DTrpTurn & \K\NotDTrpTurn & \K\NotSeq & \K\Seq \\ \K\DTurnDWavy & \K\NotDTurnDWavy & \K\NotSuc & \K\Suc \\ \K\DTurnWavy & \K\NotDTurnWavy & \K\NotSucq & \K\Sucq \\ \K\Model & \K\NotModel & \K\NotTrpTurn & \K\TrpTurn \\ \K\MulMap & \K\NotMulMap & \K\NotTurn & \K\Turn \\ \K\MulMapDual & \K\NotMulMapDual & \K\NotTurnDWavy & \K\TurnDWavy \\ \K\MulMapInv & \K\NotMulMapInv & \K\NotTurnWavy & \K\TurnWavy \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Set Symbols} \label{logix-set} \begin{tabular}{*4{ll}} \K\In & \K\NotOwns & \K\Of & \K\VoidBunch \\ \K\NotIn & \K\NullSet & \K\Owns & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}{Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{subsets} \begin{tabular}{*3{ll}} \X\sqsubset$^*$ & \X\sqsupseteq & \X\supset \\ \X\sqsubseteq & \X\subset & \X\supseteq \\ \X\sqsupset$^*$ & \X\subseteq \\ \end{tabular} \bigskip \notpredefinedmessage \end{symtable} \begin{symtable}[AMS]{\AMS\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{ams-subsets} \begin{tabular}{*3{ll}} \X\nsubseteq & \X\subseteqq & \X\supsetneqq \\ \X\nsupseteq & \X\subsetneq & \X\varsubsetneq \\ \X\nsupseteqq & \X\subsetneqq & \X\varsubsetneqq \\ \X\sqsubset & \X\Supset & \X\varsupsetneq \\ \X\sqsupset & \X\supseteqq & \X\varsupsetneqq \\ \X\Subset & \X\supsetneq \\ \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{st-subsets} \begin{tabular}{*2{ll}} \X\subsetplus & \X\supsetplus \\ \X\subsetpluseq & \X\supsetpluseq \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{\WASY\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{wasy-subset} \begin{tabular}{*2{ll}} \X\sqsubset & \X\sqsupset \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{txpx-subset} \begin{tabular}{*3{ll}} \X\nsqsubset & \X\nsqsupseteq & \X\nSupset \\ \X\nsqsubseteq & \X\nSubset \\ \X\nsqsupset & \X\nsubseteqq \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{abx-subsets} \begin{tabular}{*4{ll}} \X[\ABXnsqsubset]\nsqsubset & \X[\ABXnsupset]\nsupset & \X[\ABXsqsupseteq]\sqsupseteq & \X[\ABXsupseteq]\supseteq \\ \X[\ABXnsqSubset]\nsqSubset & \X[\ABXnSupset]\nSupset & \X[\ABXsqsupseteqq]\sqsupseteqq & \X[\ABXsupseteqq]\supseteqq \\ \X[\ABXnsqsubseteq]\nsqsubseteq & \X[\ABXnsupseteq]\nsupseteq & \X[\ABXsqsupsetneq]\sqsupsetneq & \X[\ABXsupsetneq]\supsetneq \\ \X[\ABXnsqsubseteqq]\nsqsubseteqq & \X[\ABXnsupseteqq]\nsupseteqq & \X[\ABXsqsupsetneqq]\sqsupsetneqq & \X[\ABXsupsetneqq]\supsetneqq \\ \X[\ABXnsqsupset]\nsqsupset & \X[\ABXsqsubset]\sqsubset & \X[\ABXsubset]\subset & \X[\ABXvarsqsubsetneq]\varsqsubsetneq \\ \X[\ABXnsqSupset]\nsqSupset & \X[\ABXsqSubset]\sqSubset & \X[\ABXSubset]\Subset & \X[\ABXvarsqsubsetneqq]\varsqsubsetneqq \\ \X[\ABXnsqsupseteq]\nsqsupseteq & \X[\ABXsqsubseteq]\sqsubseteq & \X[\ABXsubseteq]\subseteq & \X[\ABXvarsqsupsetneq]\varsqsupsetneq \\ \X[\ABXnsqsupseteqq]\nsqsupseteqq & \X[\ABXsqsubseteqq]\sqsubseteqq & \X[\ABXsubseteqq]\subseteqq & \X[\ABXvarsqsupsetneqq]\varsqsupsetneqq \\ \X[\ABXnsubset]\nsubset & \X[\ABXsqsubsetneq]\sqsubsetneq & \X[\ABXsubsetneq]\subsetneq & \X[\ABXvarsubsetneq]\varsubsetneq \\ \X[\ABXnSubset]\nSubset & \X[\ABXsqsubsetneqq]\sqsubsetneqq & \X[\ABXsubsetneqq]\subsetneqq & \X[\ABXvarsubsetneqq]\varsubsetneqq \\ \X[\ABXnsubseteq]\nsubseteq & \X[\ABXsqSupset]\sqSupset & \X[\ABXsupset]\supset & \X[\ABXvarsupsetneq]\varsupsetneq \\ \X[\ABXnsubseteqq]\nsubseteqq & \X[\ABXsqsupset]\sqsupset & \X[\ABXSupset]\Supset & \X[\ABXvarsupsetneqq]\varsupsetneqq \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{mns-subsets} \begin{tabular}{*4{ll}} \K[\MNSnSqsubset]\nSqsubset & \K[\MNSnsubseteq]\nsubseteq & \K[\MNSsqsubsetneq]\sqsubsetneq & \K[\MNSsubseteq]\subseteq \\ \K[\MNSnsqsubset]\nsqsubset & \K[\MNSnsubseteqq]\nsubseteqq & \K[\MNSsqsubsetneqq]\sqsubsetneqq & \K[\MNSsubseteqq]\subseteqq \\ \K[\MNSnsqsubseteq]\nsqsubseteq & \K[\MNSnSupset]\nSupset & \K[\MNSSqsupset]\Sqsupset & \K[\MNSsubsetneq]\subsetneq \\ \K[\MNSnsqsubseteqq]\nsqsubseteqq & \K[\MNSnsupset]\nsupset & \K[\MNSsqsupset]\sqsupset & \K[\MNSsubsetneqq]\subsetneqq \\ \K[\MNSnSqsupset]\nSqsupset & \K[\MNSnsupseteq]\nsupseteq & \K[\MNSsqsupseteq]\sqsupseteq & \K[\MNSSupset]\Supset \\ \K[\MNSnsqsupset]\nsqsupset & \K[\MNSnsupseteqq]\nsupseteqq & \K[\MNSsqsupseteqq]\sqsupseteqq & \K[\MNSsupset]\supset \\ \K[\MNSnsqsupseteq]\nsqsupseteq & \K[\MNSSqsubset]\Sqsubset & \K[\MNSsqsupsetneq]\sqsupsetneq & \K[\MNSsupseteq]\supseteq \\ \K[\MNSnsqsupseteqq]\nsqsupseteqq & \K[\MNSsqsubset]\sqsubset & \K[\MNSsqsupsetneqq]\sqsupsetneqq & \K[\MNSsupseteqq]\supseteqq \\ \K[\MNSnSubset]\nSubset & \K[\MNSsqsubseteq]\sqsubseteq & \K[\MNSSubset]\Subset & \K[\MNSsupsetneq]\supsetneq \\ \K[\MNSnsubset]\nsubset & \K[\MNSsqsubseteqq]\sqsubseteqq & \K[\MNSsubset]\subset & \K[\MNSsupsetneqq]\supsetneqq \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ additionally defines \cmdI[\MNSsubsetneq]{\varsubsetneq} as a synonym for \cmdI[\MNSsubsetneq]{\subsetneq}, \cmdI[\MNSsubsetneqq]{\varsubsetneqq} as a synonym for \cmdI[\MNSsubsetneqq]{\subsetneqq}, \cmdI[\MNSsupsetneq]{\varsupsetneq} as a synonym for \cmdI[\MNSsupsetneq]{\supsetneq}, and \cmdI[\MNSsupsetneqq]{\varsupsetneqq} as a synonym for \cmdI[\MNSsupsetneqq]{\supsetneqq}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{fdsym-subsets} \begin{tabular}{*4{ll}} \K[\FDSYMnsqsubset]\nsqsubset & \K[\FDSYMnsubseteq]\nsubseteq & \K[\FDSYMsqsubsetneq]\sqsubsetneq & \K[\FDSYMsubseteq]\subseteq \\ \K[\FDSYMnSqsubset]\nSqsubset & \K[\FDSYMnsubseteqq]\nsubseteqq & \K[\FDSYMsqsubsetneqq]\sqsubsetneqq & \K[\FDSYMsubseteqq]\subseteqq \\ \K[\FDSYMnsqsubseteq]\nsqsubseteq & \K[\FDSYMnsupset]\nsupset & \K[\FDSYMsqsupset]\sqsupset & \K[\FDSYMsubsetneq]\subsetneq \\ \K[\FDSYMnsqsubseteqq]\nsqsubseteqq & \K[\FDSYMnSupset]\nSupset & \K[\FDSYMSqsupset]\Sqsupset & \K[\FDSYMsubsetneqq]\subsetneqq \\ \K[\FDSYMnsqsupset]\nsqsupset & \K[\FDSYMnsupseteq]\nsupseteq & \K[\FDSYMsqsupseteq]\sqsupseteq & \K[\FDSYMsupset]\supset \\ \K[\FDSYMnSqsupset]\nSqsupset & \K[\FDSYMnsupseteqq]\nsupseteqq & \K[\FDSYMsqsupseteqq]\sqsupseteqq & \K[\FDSYMSupset]\Supset \\ \K[\FDSYMnsqsupseteq]\nsqsupseteq & \K[\FDSYMsqsubset]\sqsubset & \K[\FDSYMsqsupsetneq]\sqsupsetneq & \K[\FDSYMsupseteq]\supseteq \\ \K[\FDSYMnsqsupseteqq]\nsqsupseteqq & \K[\FDSYMSqsubset]\Sqsubset & \K[\FDSYMsqsupsetneqq]\sqsupsetneqq & \K[\FDSYMsupseteqq]\supseteqq \\ \K[\FDSYMnsubset]\nsubset & \K[\FDSYMsqsubseteq]\sqsubseteq & \K[\FDSYMsubset]\subset & \K[\FDSYMsupsetneq]\supsetneq \\ \K[\FDSYMnSubset]\nSubset & \K[\FDSYMsqsubseteqq]\sqsubseteqq & \K[\FDSYMSubset]\Subset & \K[\FDSYMsupsetneqq]\supsetneqq \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ additionally defines \cmdI[\string\FDSYMvarsubsetneqq]{\varsubsetneqq} as a synonym for \cmdI[\string\FDSYMsubsetneqq]{\subsetneqq}, \cmdI[\string\FDSYMvarsubsetneq]{\varsubsetneq} as a synonym for \cmdI[\string\FDSYMsubsetneq]{\subsetneq}, \cmdI[\string\FDSYMvarsupsetneqq]{\varsupsetneqq} as a synonym for \cmdI[\string\FDSYMsupsetneqq]{\supsetneqq}, and \cmdI[\string\FDSYMvarsupsetneq]{\varsupsetneq} as a synonym for \cmdI[\string\FDSYMsupsetneq]{\supsetneq}. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{bsk-subsets} \begin{tabular}{*4{ll}} \K[\BSKnsubset]\nsubset & \K[\BSKsqSubset]\sqSubset & \K[\BSKsubsetplus]\subsetplus & \K[\BSKsupsetpluseq]\supsetpluseq \\ \K[\BSKnsubseteq]\nsubseteq & \K[\BSKsqSupset]\sqSupset & \K[\BSKsubsetpluseq]\subsetpluseq & \K[\BSKvarsubsetneq]\varsubsetneq \\ \K[\BSKnsubseteqq]\nsubseteqq & \K[\BSKsqsupset]\sqsupset & \K[\BSKSupset]\Supset & \K[\BSKvarsubsetneqq]\varsubsetneqq \\ \K[\BSKnsupset]\nsupset & \K[\BSKSubset]\Subset & \K[\BSKsupseteqq]\supseteqq & \K[\BSKvarsupsetneq]\varsupsetneq \\ \K[\BSKnsupseteq]\nsupseteq & \K[\BSKsubseteqq]\subseteqq & \K[\BSKsupsetneq]\supsetneq & \K[\BSKvarsupsetneqq]\varsupsetneqq \\ \K[\BSKnsupseteqq]\nsupseteqq & \K[\BSKsubsetneq]\subsetneq & \K[\BSKsupsetneqq]\supsetneqq & \\ \K[\BSKsqsubset]\sqsubset & \K[\BSKsubsetneqq]\subsetneqq & \K[\BSKsupsetplus]\supsetplus & \\ \end{tabular} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Subset and Superset Relations} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltindex{subsets} \ltindex{supersets} \ltindex{symbols>subset and superset} \label{stix-subsets} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXbsolhsub]\bsolhsub & \K[\STIXsqsupseteq]\sqsupseteq & \K[\STIXsuphsub]\suphsub \\ \K[\STIXcsub]\csub & \K[\STIXsqsupsetneq]\sqsupsetneq & \K[\STIXsuplarr]\suplarr \\ \K[\STIXcsube]\csube & \K[\STIXsubedot]\subedot & \K[\STIXsupmult]\supmult \\ \K[\STIXcsup]\csup & \K[\STIXsubmult]\submult & \K[\STIXSupset]\Supset \\ \K[\STIXcsupe]\csupe & \K[\STIXsubrarr]\subrarr & \K[\STIXsupset]\supset \\ \K[\STIXleftarrowsubset]\leftarrowsubset & \K[\STIXSubset]\Subset & \K[\STIXsupsetapprox]\supsetapprox \\ \K[\STIXnsqsubset]\nsqsubset & \K[\STIXsubset]\subset & \K[\STIXsupsetcirc]\supsetcirc$^*$ \\ \K[\STIXnsqsubseteq]\nsqsubseteq & \K[\STIXsubsetapprox]\subsetapprox & \K[\STIXsupsetdot]\supsetdot \\ \K[\STIXnsqsupset]\nsqsupset & \K[\STIXsubsetcirc]\subsetcirc$^*$ & \K[\STIXsupseteq]\supseteq \\ \K[\STIXnsqsupseteq]\nsqsupseteq & \K[\STIXsubsetdot]\subsetdot & \K[\STIXsupseteqq]\supseteqq \\ \K[\STIXnsubset]\nsubset & \K[\STIXsubseteq]\subseteq & \K[\STIXsupsetneq]\supsetneq \\ \K[\STIXnsubseteq]\nsubseteq & \K[\STIXsubseteqq]\subseteqq & \K[\STIXsupsetneqq]\supsetneqq \\ \K[\STIXnsubseteqq]\nsubseteqq & \K[\STIXsubsetneq]\subsetneq & \K[\STIXsupsetplus]\supsetplus \\ \K[\STIXnsupset]\nsupset & \K[\STIXsubsetneqq]\subsetneqq & \K[\STIXsupsim]\supsim \\ \K[\STIXnsupseteq]\nsupseteq & \K[\STIXsubsetplus]\subsetplus & \K[\STIXsupsub]\supsub \\ \K[\STIXnsupseteqq]\nsupseteqq & \K[\STIXsubsim]\subsim & \K[\STIXsupsup]\supsup \\ \K[\STIXrightarrowsupset]\rightarrowsupset & \K[\STIXsubsub]\subsub & \K[\STIXvarsubsetneq]\varsubsetneq \\ \K[\STIXsqsubset]\sqsubset & \K[\STIXsubsup]\subsup & \K[\STIXvarsubsetneqq]\varsubsetneqq \\ \K[\STIXsqsubseteq]\sqsubseteq & \K[\STIXsupdsub]\supdsub & \K[\STIXvarsupsetneq]\varsupsetneq \\ \K[\STIXsqsubsetneq]\sqsubsetneq & \K[\STIXsupedot]\supedot & \K[\STIXvarsupsetneqq]\varsupsetneqq \\ \K[\STIXsqsupset]\sqsupset & \K[\STIXsuphsol]\suphsol & \\ \end{longtable} \begin{tablenote}[*] Defined as an ordinary character, not as a binary relation. \end{tablenote} \end{longsymtable} \begin{symtable}[LOGIX]{\LOGIX\ Subset and Superset Relations} \index{binary relations} \index{relational symbols>binary} \index{subsets} \index{supersets} \index{symbols>subset and superset} \label{logix-subsets} \begin{tabular}{*4{ll}} \K\FntSbset & \K\NotStrctFntSbset & \K\NotWkSbnch & \K\StrctSbmap \\ \K\NotFntSbset & \K\NotStrctSbmap & \K\Sbmap & \K\StrctSbnch \\ \K\NotSbmap & \K\NotStrctSbnch & \K\Sbnch & \K\StrctSbset \\ \K\NotSbnch & \K\NotStrctSbset & \K\Sbset & \K\StrctWkSbnch \\ \K\NotSbset & \K\NotStrctWkSbnch & \K\StrctFntSbset & \K\WkSbnch \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}{Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{inequal-rel} \begin{tabular}{*5{ll}} \X\geq & \X\gg & \X\leq & \X\ll & \X\neq \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{ams-inequal-rel} \renewcommand{\arraystretch}{1.5} % Keep visually similar symbols from touching. \begin{tabular}{*4{ll}} \X\eqslantgtr & \X\gtrdot & \X\lesseqgtr & \X\ngeq \\ \X\eqslantless & \X\gtreqless & \X\lesseqqgtr & \X\ngeqq \\ \X\geqq & \X\gtreqqless & \X\lessgtr & \X\ngeqslant \\ \X\geqslant & \X\gtrless & \X\lesssim & \X\ngtr \\ \X\ggg & \X\gtrsim & \X\lll & \X\nleq \\ \X\gnapprox & \X\gvertneqq & \X\lnapprox & \X\nleqq \\ \X\gneq & \X\leqq & \X\lneq & \X\nleqslant \\ \X\gneqq & \X\leqslant & \X\lneqq & \X\nless \\ \X\gnsim & \X\lessapprox & \X\lnsim & \\ \X\gtrapprox & \X\lessdot & \X\lvertneqq & \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{\WASY\ Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{wasy-inequal-rel} \begin{tabular}{*2{ll}} \X\apprge & \X\apprle \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{txpx-inequal-rel} \begin{tabular}{*3{ll}} \X\ngg & \X\ngtrsim & \X\nlesssim \\ \X\ngtrapprox & \X\nlessapprox & \X\nll \\ \X\ngtrless & \X\nlessgtr \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{abx-inequal-rel} \renewcommand{\arraystretch}{1.5} % Keep visually similar symbols from touching. \begin{tabular}{*4{ll}} \X[\ABXeqslantgtr]\eqslantgtr & \X[\ABXgtreqless]\gtreqless & \X[\ABXlesssim]\lesssim & \X[\ABXngtr]\ngtr \\ \X[\ABXeqslantless]\eqslantless & \X[\ABXgtreqqless]\gtreqqless & \X[\ABXll]\ll & \X[\ABXngtrapprox]\ngtrapprox \\ \X[\ABXgeq]\geq & \X[\ABXgtrless]\gtrless & \X[\ABXlll]\lll & \X[\ABXngtrsim]\ngtrsim \\ \X[\ABXgeqq]\geqq & \X[\ABXgtrsim]\gtrsim & \X[\ABXlnapprox]\lnapprox & \X[\ABXnleq]\nleq \\ \X[\ABXgg]\gg & \X[\ABXgvertneqq]\gvertneqq & \X[\ABXlneq]\lneq & \X[\ABXnleqq]\nleqq \\ \X[\ABXggg]\ggg & \X[\ABXleq]\leq & \X[\ABXlneqq]\lneqq & \X[\ABXnless]\nless \\ \X[\ABXgnapprox]\gnapprox & \X[\ABXleqq]\leqq & \X[\ABXlnsim]\lnsim & \X[\ABXnlessapprox]\nlessapprox \\ \X[\ABXgneq]\gneq & \X[\ABXlessapprox]\lessapprox & \X[\ABXlvertneqq]\lvertneqq & \X[\ABXnlesssim]\nlesssim \\ \X[\ABXgneqq]\gneqq & \X[\ABXlessdot]\lessdot & \X[\ABXneqslantgtr]\neqslantgtr & \X[\ABXnvargeq]\nvargeq \\ \X[\ABXgnsim]\gnsim & \X[\ABXlesseqgtr]\lesseqgtr & \X[\ABXneqslantless]\neqslantless & \X[\ABXnvarleq]\nvarleq \\ \X[\ABXgtrapprox]\gtrapprox & \X[\ABXlesseqqgtr]\lesseqqgtr & \X[\ABXngeq]\ngeq & \X[\ABXvargeq]\vargeq \\ \X[\ABXgtrdot]\gtrdot & \X[\ABXlessgtr]\lessgtr & \X[\ABXngeqq]\ngeqq & \X[\ABXvarleq]\varleq \\ \end{tabular} \bigskip \begin{tablenote} \ABX\ defines \verb|\leqslant| and \verb|\le| as synonyms for \cmdX{\leq}, \verb|\geqslant| and \verb|\ge| as synonyms for \cmdX{\geq}, \verb|\nleqslant| as a synonym for \cmdX{\nleq}, and \verb|\ngeqslant| as a synonym for \cmdX{\ngeq}. \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Inequalities} \index{binary relations}\index{relational symbols>binary} \index{inequalities} \label{mns-inequal-rel} \renewcommand{\arraystretch}{1.25} % Keep visually similar symbols from touching. \begin{tabular}{*4{ll}} \K[\MNSeqslantgtr]\eqslantgtr & \K[\MNSgtreqqless]\gtreqqless & \K[\MNSlesssim]\lesssim & \K[\MNSngtreqless]\ngtreqless \\ \K[\MNSeqslantless]\eqslantless & \K[\MNSgtrless]\gtrless & \K[\MNSll]\ll & \K[\MNSngtreqlessslant]\ngtreqlessslant \\ \K[\MNSgeq]\geq & \K[\MNSgtrneqqless]\gtrneqqless & \K[\MNSlll]\lll & \K[\MNSngtreqqless]\ngtreqqless \\ \K[\MNSgeqclosed]\geqclosed & \K[\MNSgtrsim]\gtrsim & \K[\MNSlnapprox]\lnapprox & \K[\MNSngtrless]\ngtrless \\ \K[\MNSgeqdot]\geqdot & \K[\MNSleq]\leq & \K[\MNSlneqq]\lneqq & \K[\MNSnleq]\nleq \\ \K[\MNSgeqq]\geqq & \K[\MNSleqclosed]\leqclosed & \K[\MNSlnsim]\lnsim & \K[\MNSnleqclosed]\nleqclosed \\ \K[\MNSgeqslant]\geqslant & \K[\MNSleqdot]\leqdot & \K[\MNSneqslantgtr]\neqslantgtr & \K[\MNSnleqdot]\nleqdot \\ \K[\MNSgeqslantdot]\geqslantdot & \K[\MNSleqq]\leqq & \K[\MNSneqslantless]\neqslantless & \K[\MNSnleqq]\nleqq \\ \K[\MNSgg]\gg & \K[\MNSleqslant]\leqslant & \K[\MNSngeq]\ngeq & \K[\MNSnleqslant]\nleqslant \\ \K[\MNSggg]\ggg & \K[\MNSleqslantdot]\leqslantdot & \K[\MNSngeqclosed]\ngeqclosed & \K[\MNSnleqslantdot]\nleqslantdot \\ \K[\MNSgnapprox]\gnapprox & \K[\MNSless]\less & \K[\MNSngeqdot]\ngeqdot & \K[\MNSnless]\nless \\ \K[\MNSgneqq]\gneqq & \K[\MNSlessapprox]\lessapprox & \K[\MNSngeqq]\ngeqq & \K[\MNSnlessclosed]\nlessclosed \\ \K[\MNSgnsim]\gnsim & \K[\MNSlessclosed]\lessclosed & \K[\MNSngeqslant]\ngeqslant & \K[\MNSnlessdot]\nlessdot \\ \K[\MNSgtr]\gtr & \K[\MNSlessdot]\lessdot & \K[\MNSngeqslantdot]\ngeqslantdot & \K[\MNSnlesseqgtr]\nlesseqgtr \\ \K[\MNSgtrapprox]\gtrapprox & \K[\MNSlesseqgtr]\lesseqgtr & \K[\MNSngg]\ngg & \K[\MNSnlesseqgtrslant]\nlesseqgtrslant \\ \K[\MNSgtrclosed]\gtrclosed & \K[\MNSlesseqgtrslant]\lesseqgtrslant & \K[\MNSnggg]\nggg & \K[\MNSnlesseqqgtr]\nlesseqqgtr \\ \K[\MNSgtrdot]\gtrdot & \K[\MNSlesseqqgtr]\lesseqqgtr & \K[\MNSngtr]\ngtr & \K[\MNSnlessgtr]\nlessgtr \\ \K[\MNSgtreqless]\gtreqless & \K[\MNSlessgtr]\lessgtr & \K[\MNSngtrclosed]\ngtrclosed & \K[\MNSnll]\nll \\ \K[\MNSgtreqlessslant]\gtreqlessslant & \K[\MNSlessneqqgtr]\lessneqqgtr & \K[\MNSngtrdot]\ngtrdot & \K[\MNSnlll]\nlll \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ additionally defines synonyms for some of the preceding symbols: \newcommand*{\mnssyn}[1]{(same as \texttt{\string#1})} \renewcommand{\arraystretch}{1} \begin{tabular}{ll@{\quad}l} \K[\MNSggg]\gggtr & \mnssyn\ggg \\ \K[\MNSgneqq]\gvertneqq & \mnssyn\gneqq \\ \K[\MNSlessclosed]\lhd & \mnssyn\lessclosed \\ \K[\MNSlll]\llless & \mnssyn\lll \\ \K[\MNSlneqq]\lvertneqq & \mnssyn\lneqq \\ \K[\MNSnleqclosed]\ntrianglelefteq & \mnssyn\nleqclosed \\ \K[\MNSnlessclosed]\ntriangleleft & \mnssyn\nlessclosed \\ \K[\MNSngeqclosed]\ntrianglerighteq & \mnssyn\ngeqclosed \\ \K[\MNSngtrclosed]\ntriangleright & \mnssyn\ngtrclosed \\ \K[\MNSgtrclosed]\rhd & \mnssyn\gtrclosed \\ \K[\MNSleqclosed]\trianglelefteq & \mnssyn\leqclosed \\ \K[\MNSgeqclosed]\trianglerighteq & \mnssyn\geqclosed \\ \K[\MNSleqclosed]\unlhd & \mnssyn\leqclosed \\ \K[\MNSgeqclosed]\unrhd & \mnssyn\geqclosed \\ \K[\MNSlessclosed]\vartriangleleft & \mnssyn\lessclosed \\ \K[\MNSgtrclosed]\vartriangleright & \mnssyn\gtrclosed \\ \end{tabular} \end{tablenote} \end{symtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Inequalities} \ltindex{binary relations}\index{relational symbols>binary} \ltindex{inequalities} \label{fdsym-inequal-rel} \renewcommand{\arraystretch}{1.25} % Keep visually similar symbols from touching. \begin{longtable}{ll*2{@{\hspace*{2em}}ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMeqslantgtr]\eqslantgtr & \K[\FDSYMleqslantdot]\leqslantdot & \K[\FDSYMngtrapprox]\ngtrapprox \\ \K[\FDSYMeqslantless]\eqslantless & \K[\FDSYMleqslcc]\leqslcc & \K[\FDSYMngtrcc]\ngtrcc \\ \K[\FDSYMgeq]\geq & \K[\FDSYMless]\less & \K[\FDSYMngtrclosed]\ngtrclosed \\ \K[\FDSYMgeqclosed]\geqclosed & \K[\FDSYMlessapprox]\lessapprox & \K[\FDSYMngtrdot]\ngtrdot \\ \K[\FDSYMgeqdot]\geqdot & \K[\FDSYMlesscc]\lesscc & \K[\FDSYMngtreqless]\ngtreqless \\ \K[\FDSYMgeqq]\geqq & \K[\FDSYMlessclosed]\lessclosed & \K[\FDSYMngtreqqless]\ngtreqqless \\ \K[\FDSYMgeqslant]\geqslant & \K[\FDSYMlessdot]\lessdot & \K[\FDSYMngtreqslantless]\ngtreqslantless \\ \K[\FDSYMgeqslantdot]\geqslantdot & \K[\FDSYMlesseqgtr]\lesseqgtr & \K[\FDSYMngtrless]\ngtrless \\ \K[\FDSYMgeqslcc]\geqslcc & \K[\FDSYMlesseqqgtr]\lesseqqgtr & \K[\FDSYMngtrsim]\ngtrsim \\ \K[\FDSYMgg]\gg & \K[\FDSYMlesseqslantgtr]\lesseqslantgtr & \K[\FDSYMnleq]\nleq \\ \K[\FDSYMggg]\ggg & \K[\FDSYMlessgtr]\lessgtr & \K[\FDSYMnleqclosed]\nleqclosed \\ \K[\FDSYMgnapprox]\gnapprox & \K[\FDSYMlesssim]\lesssim & \K[\FDSYMnleqdot]\nleqdot \\ \K[\FDSYMgneq]\gneq & \K[\FDSYMll]\ll & \K[\FDSYMnleqq]\nleqq \\ \K[\FDSYMgneqq]\gneqq & \K[\FDSYMlll]\lll & \K[\FDSYMnleqslant]\nleqslant \\ \K[\FDSYMgnsim]\gnsim & \K[\FDSYMlnapprox]\lnapprox & \K[\FDSYMnleqslantdot]\nleqslantdot \\ \K[\FDSYMgtr]\gtr & \K[\FDSYMlneq]\lneq & \K[\FDSYMnleqslcc]\nleqslcc \\ \K[\FDSYMgtrapprox]\gtrapprox & \K[\FDSYMlneqq]\lneqq & \K[\FDSYMnless]\nless \\ \K[\FDSYMgtrcc]\gtrcc & \K[\FDSYMlnsim]\lnsim & \K[\FDSYMnlessapprox]\nlessapprox \\ \K[\FDSYMgtrclosed]\gtrclosed & \K[\FDSYMneqslantgtr]\neqslantgtr & \K[\FDSYMnlesscc]\nlesscc \\ \K[\FDSYMgtrdot]\gtrdot & \K[\FDSYMneqslantless]\neqslantless & \K[\FDSYMnlessclosed]\nlessclosed \\ \K[\FDSYMgtreqless]\gtreqless & \K[\FDSYMngeq]\ngeq & \K[\FDSYMnlessdot]\nlessdot \\ \K[\FDSYMgtreqqless]\gtreqqless & \K[\FDSYMngeqclosed]\ngeqclosed & \K[\FDSYMnlesseqgtr]\nlesseqgtr \\ \K[\FDSYMgtreqslantless]\gtreqslantless & \K[\FDSYMngeqdot]\ngeqdot & \K[\FDSYMnlesseqqgtr]\nlesseqqgtr \\ \K[\FDSYMgtrless]\gtrless & \K[\FDSYMngeqq]\ngeqq & \K[\FDSYMnlesseqslantgtr]\nlesseqslantgtr \\ \K[\FDSYMgtrsim]\gtrsim & \K[\FDSYMngeqslant]\ngeqslant & \K[\FDSYMnlessgtr]\nlessgtr \\ \K[\FDSYMleq]\leq & \K[\FDSYMngeqslantdot]\ngeqslantdot & \K[\FDSYMnlesssim]\nlesssim \\ \K[\FDSYMleqclosed]\leqclosed & \K[\FDSYMngeqslcc]\ngeqslcc & \K[\FDSYMnll]\nll \\ \K[\FDSYMleqdot]\leqdot & \K[\FDSYMngg]\ngg & \K[\FDSYMnlll]\nlll \\ \K[\FDSYMleqq]\leqq & \K[\FDSYMnggg]\nggg & \\ \K[\FDSYMleqslant]\leqslant & \K[\FDSYMngtr]\ngtr & \\ \end{longtable} \FDSYM\ defines synonyms for some of the preceding symbols: \begin{longtable}{ll*2{@{\hspace*{2em}}ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMge]{\ge} & \K[\FDSYMlesdot]{\lesdot} & \K[\FDSYMngtcc]{\ngtcc} \\ \K[\FDSYMgescc]{\gescc} & \K[\FDSYMlesg]{\lesg} & \K[\FDSYMngtreqlessslant]{\ngtreqlessslant} \\ \K[\FDSYMgesdot]{\gesdot} & \K[\FDSYMlesseqgtrslant]{\lesseqgtrslant} & \K[\FDSYMnlescc]{\nlescc} \\ \K[\FDSYMgesl]{\gesl} & \K[\FDSYMlhd]{\lhd} & \K[\FDSYMnlesdot]{\nlesdot} \\ \K[\FDSYMgggtr]{\gggtr} & \K[\FDSYMllless]{\llless} & \K[\FDSYMnlesg]{\nlesg} \\ \K[\FDSYMgtcc]{\gtcc} & \K[\FDSYMltcc]{\ltcc} & \K[\FDSYMnlesseqgtrslant]{\nlesseqgtrslant} \\ \K[\FDSYMgtreqlessslant]{\gtreqlessslant} & \K[\FDSYMlvertneqq]{\lvertneqq} & \K[\FDSYMnltcc]{\nltcc} \\ \K[\FDSYMgvertneqq]{\gvertneqq} & \K[\FDSYMngescc]{\ngescc} & \K[\FDSYMrhd]{\rhd} \\ \K[\FDSYMle]{\le} & \K[\FDSYMngesdot]{\ngesdot} & \K[\FDSYMunlhd]{\unlhd} \\ \K[\FDSYMlescc]{\lescc} & \K[\FDSYMngesl]{\ngesl} & \K[\FDSYMunrhd]{\unrhd} \\ \end{longtable} \end{longsymtable} \begin{symtable}[BSK]{\BSK\ Inequalities} \index{binary relations} \index{relational symbols>binary} \index{inequalities} \label{bsk-inequal-rel} \renewcommand{\arraystretch}{1.25} % Keep visually similar symbols from touching. \begin{tabular}{ll*3{@{\hspace*{2em}}ll}} \K[\BSKeqslantgtr]\eqslantgtr & \K[\BSKgtcir]\gtcir & \K[\BSKlesseqqgtr]\lesseqqgtr & \K[\BSKngeq]\ngeq \\ \K[\BSKeqslantless]\eqslantless & \K[\BSKgtrapprox]\gtrapprox & \K[\BSKlessgtr]\lessgtr & \K[\BSKngeqq]\ngeqq \\ \K[\BSKgeqq]\geqq & \K[\BSKgtreqless]\gtreqless & \K[\BSKlesssim]\lesssim & \K[\BSKngeqslant]\ngeqslant \\ \K[\BSKgeqslant]\geqslant & \K[\BSKgtreqqless]\gtreqqless & \K[\BSKlll]\lll & \K[\BSKngtr]\ngtr \\ \K[\BSKggg]\ggg & \K[\BSKgtrless]\gtrless & \K[\BSKlnapprox]\lnapprox & \K[\BSKnleq]\nleq \\ \K[\BSKglj]\glj & \K[\BSKgtrsim]\gtrsim & \K[\BSKlneq]\lneq & \K[\BSKnleqq]\nleqq \\ \K[\BSKgnapprox]\gnapprox & \K[\BSKgvertneqq]\gvertneqq & \K[\BSKlneqq]\lneqq & \K[\BSKnleqslant]\nleqslant \\ \K[\BSKgneq]\gneq & \K[\BSKleqq]\leqq & \K[\BSKlnsim]\lnsim & \K[\BSKnless]\nless \\ \K[\BSKgneqq]\gneqq & \K[\BSKleqslant]\leqslant & \K[\BSKLt]\Lt & \\ \K[\BSKgnsim]\gnsim & \K[\BSKlessapprox]\lessapprox & \K[\BSKltcir]\ltcir & \\ \K[\BSKGt]\Gt & \K[\BSKlesseqgtr]\lesseqgtr & \K[\BSKlvertneqq]\lvertneqq & \\ \end{tabular} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Inequalities} \ltindex{binary relations} \ltindex{relational symbols>binary} \ltindex{inequalities} \label{stix-inequal-rel} \renewcommand{\arraystretch}{1.25} % Keep visually similar symbols from touching. \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXegsdot]\egsdot & \K[\STIXgtquest]\gtquest & \K[\STIXlnsim]\lnsim \\ \K[\STIXelsdot]\elsdot & \K[\STIXgtrapprox]\gtrapprox & \K[\STIXlsime]\lsime \\ \K[\STIXeqgtr]\eqgtr & \K[\STIXgtrarr]\gtrarr & \K[\STIXlsimg]\lsimg \\ \K[\STIXeqless]\eqless & \K[\STIXgtrdot]\gtrdot & \K[\STIXLt]\Lt \\ \K[\STIXeqqgtr]\eqqgtr & \K[\STIXgtreqless]\gtreqless & \K[\STIXltcc]\ltcc \\ \K[\STIXeqqless]\eqqless & \K[\STIXgtreqqless]\gtreqqless & \K[\STIXltcir]\ltcir \\ \K[\STIXeqqslantgtr]\eqqslantgtr & \K[\STIXgtrless]\gtrless & \K[\STIXltlarr]\ltlarr \\ \K[\STIXeqqslantless]\eqqslantless & \K[\STIXgtrsim]\gtrsim & \K[\STIXltquest]\ltquest \\ \K[\STIXeqslantgtr]\eqslantgtr & \K[\STIXgvertneqq]\gvertneqq & \K[\STIXlvertneqq]\lvertneqq \\ \K[\STIXeqslantless]\eqslantless & \K[\STIXlat]\lat & \K[\STIXneqslantgtr]\neqslantgtr \\ \K[\STIXgeq]\geq & \K[\STIXlate]\late & \K[\STIXneqslantless]\neqslantless \\ \K[\STIXgeqq]\geqq & \K[\STIXleftarrowless]\leftarrowless & \K[\STIXngeq]\ngeq \\ \K[\STIXgeqqslant]\geqqslant & \K[\STIXleq]\leq & \K[\STIXngeqq]\ngeqq \\ \K[\STIXgeqslant]\geqslant & \K[\STIXleqq]\leqq & \K[\STIXngeqslant]\ngeqslant \\ \K[\STIXgescc]\gescc & \K[\STIXleqqslant]\leqqslant & \K[\STIXngg]\ngg \\ \K[\STIXgesdot]\gesdot & \K[\STIXleqslant]\leqslant & \K[\STIXngtr]\ngtr \\ \K[\STIXgesdoto]\gesdoto & \K[\STIXlescc]\lescc & \K[\STIXngtrless]\ngtrless \\ \K[\STIXgesdotol]\gesdotol & \K[\STIXlesdot]\lesdot & \K[\STIXngtrsim]\ngtrsim \\ \K[\STIXgesles]\gesles & \K[\STIXlesdoto]\lesdoto & \K[\STIXnleq]\nleq \\ \K[\STIXgg]\gg & \K[\STIXlesdotor]\lesdotor & \K[\STIXnleqq]\nleqq \\ \K[\STIXggg]\ggg & \K[\STIXlesges]\lesges & \K[\STIXnleqslant]\nleqslant \\ \K[\STIXgggnest]\gggnest & \K[\STIXlessapprox]\lessapprox & \K[\STIXnless]\nless \\ \K[\STIXgla]\gla & \K[\STIXlessdot]\lessdot & \K[\STIXnlessgtr]\nlessgtr \\ \K[\STIXglE]\glE & \K[\STIXlesseqgtr]\lesseqgtr & \K[\STIXnlesssim]\nlesssim \\ \K[\STIXglj]\glj & \K[\STIXlesseqqgtr]\lesseqqgtr & \K[\STIXnll]\nll \\ \K[\STIXgnapprox]\gnapprox & \K[\STIXlessgtr]\lessgtr & \K[\STIXpartialmeetcontraction]\partialmeetcontraction \\ \K[\STIXgneq]\gneq & \K[\STIXlesssim]\lesssim & \K[\STIXrightarrowgtr]\rightarrowgtr \\ \K[\STIXgneqq]\gneqq & \K[\STIXlgE]\lgE & \K[\STIXsimgE]\simgE \\ \K[\STIXgnsim]\gnsim & \K[\STIXll]\ll & \K[\STIXsimgtr]\simgtr \\ \K[\STIXgsime]\gsime & \K[\STIXlll]\lll & \K[\STIXsimlE]\simlE \\ \K[\STIXgsiml]\gsiml & \K[\STIXlllnest]\lllnest & \K[\STIXsimless]\simless \\ \K[\STIXGt]\Gt & \K[\STIXlnapprox]\lnapprox & \K[\STIXsmt]\smt \\ \K[\STIXgtcc]\gtcc & \K[\STIXlneq]\lneq & \K[\STIXsmte]\smte \\ \K[\STIXgtcir]\gtcir & \K[\STIXlneqq]\lneqq & \\ \end{longtable} \begin{tablenote} \STIX\ defines \cmdI[\string\STIXle]{\le} as a synonym for \cmdI[\string\STIXleq]{\leq}, \cmdI[\string\STIXge]{\ge} as a synonym for \cmdI[\string\STIXgeq]{\geq}, \cmdI[\string\STIXllless]{\llless} as a synonym for \cmdI[\string\STIXlll]{\lll}, \cmdI[\string\STIXgggtr]{\gggtr} as a synonym for \cmdI[\string\STIXggg]{\ggg}, \cmdI[\string\STIXnle]{\nle} as a synonym for \cmdI[\string\STIXnleq]{\nleq}, and \cmdI[\string\STIXnge]{\nge} as a synonym for \cmdI[\string\STIXngeq]{\ngeq}. \end{tablenote} \end{longsymtable} \begin{symtable}[LOGIX]{\LOGIX\ Inequalities and Equalities} \index{binary relations} \index{relational symbols>binary} \index{inequalities} \label{logix-inequal-rel} \begin{tabular}{*4{ll}} \K\CircEq & \K\Gr & \K\NotLs & \K\SbGr \\ \K\CircGr & \K\Gre & \K\NotLse & \K\SbGre \\ \K\CircGre & \K\Ls & \K\NotSbGr & \K\SbLs \\ \K\CircLs & \K\Lse & \K\NotSbGre & \K\SbLse \\ \K\CircLse & \K\NotEq & \K\NotSbLs & \K\Sm \\ \K\CircSm & \K\NotGr & \K\NotSbLse & \\ \K\Eq & \K\NotGre & \K\NotSm & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Triangle Relations} \index{triangle relations} \index{relational symbols>triangle} \label{ams-triangle-rel} \begin{tabular}{*3{ll}} \X\blacktriangleleft & \X\ntriangleright & \X\trianglerighteq \\ \X\blacktriangleright & \X\ntrianglerighteq & \X\vartriangleleft \\ \X\ntriangleleft & \X\trianglelefteq & \X\vartriangleright \\ \X\ntrianglelefteq & \X\triangleq & \\ \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Triangle Relations} \index{triangle relations}\index{relational symbols>triangle} \label{st-triangle-rel} \begin{tabular}{*2{ll}} \X\trianglelefteqslant & \X\trianglerighteqslant \\ \X\ntrianglelefteqslant & \X\ntrianglerighteqslant \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Triangle Relations} \index{triangle relations}\index{relational symbols>triangle} \label{abx-triangle-rel} \begin{tabular}{*3{ll}} \X[\ABXntriangleleft]\ntriangleleft & \X[\ABXtriangleleft]\triangleleft & \X[\ABXvartriangleleft]\vartriangleleft \\ \X[\ABXntrianglelefteq]\ntrianglelefteq & \X[\ABXtrianglelefteq]\trianglelefteq & \X[\ABXvartriangleright]\vartriangleright \\ \X[\ABXntriangleright]\ntriangleright & \X[\ABXtriangleright]\triangleright & \\ \X[\ABXntrianglerighteq]\ntrianglerighteq & \X[\ABXtrianglerighteq]\trianglerighteq & \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Triangle Relations} \index{triangle relations}\index{relational symbols>triangle} \label{mns-triangle-rel} \begin{tabular}{*3{ll}} \K[\MNSfilledmedtriangledown]\filledmedtriangledown & \K[\MNSlargetriangleup]\largetriangleup & \K[\MNSsmalltriangledown]\smalltriangledown \\ \K[\MNSfilledmedtriangleleft]\filledmedtriangleleft & \K[\MNSmedtriangledown]\medtriangledown & \K[\MNSsmalltriangleleft]\smalltriangleleft \\ \K[\MNSfilledmedtriangleright]\filledmedtriangleright & \K[\MNSmedtriangleleft]\medtriangleleft & \K[\MNSsmalltriangleright]\smalltriangleright \\ \K[\MNSfilledmedtriangleup]\filledmedtriangleup & \K[\MNSmedtriangleright]\medtriangleright & \K[\MNSsmalltriangleup]\smalltriangleup \\ \K[\MNSfilledtriangledown]\filledtriangledown & \K[\MNSmedtriangleup]\medtriangleup & \K[\MNStriangleeq]\triangleeq \\ \K[\MNSfilledtriangleleft]\filledtriangleleft & \K[\MNSntriangleeq]\ntriangleeq & \K[\MNSleqclosed]\trianglelefteq \\ \K[\MNSfilledtriangleright]\filledtriangleright & \K[\MNSnlessclosed]\ntriangleleft & \K[\MNSgeqclosed]\trianglerighteq \\ \K[\MNSfilledtriangleup]\filledtriangleup & \K[\MNSnleqclosed]\ntrianglelefteq & \K[\MNSlessclosed]\vartriangleleft \\ \K[\MNSlargetriangledown]\largetriangledown & \K[\MNSngtrclosed]\ntriangleright & \K[\MNSgtrclosed]\vartriangleright \\ \K[\MNSlargetriangleleft]\largetriangleleft & \K[\MNSngeqclosed]\ntrianglerighteq & \\ \K[\MNSlargetriangleright]\largetriangleright & \K[\MNSotriangle]\otriangle & \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ additionally defines synonyms for many of the preceding symbols: \cmdI[\MNStriangleeq]{\triangleq} is a synonym for \cmdI[\MNStriangleeq]{\triangleeq}; \cmdI[\MNSlessclosed]{\lhd} and \cmdI[\MNSlessclosed]{\lessclosed} are synonyms for \cmdI[\MNSlessclosed]{\vartriangleleft}; \cmdI[\MNSgtrclosed]{\rhd} and \cmdI[\MNSgtrclosed]{\gtrclosed} are synonyms for \cmdI[\MNSgtrclosed]{\vartriangleright}; \cmdI[\MNSleqclosed]{\unlhd} and \cmdI[\MNSleqclosed]{\leqclosed} are synonyms for \cmdI[\MNSleqclosed]{\trianglelefteq}; \cmdI[\MNSgeqclosed]{\unrhd} and \cmdI[\MNSgeqclosed]{\geqclosed} are synonyms for \cmdI[\MNSgeqclosed]{\trianglerighteq}; \cmdI[\MNSfilledmedtriangledown]{\blacktriangledown}, \cmdI[\MNSfilledmedtriangleleft]{\blacktriangleleft}, \cmdI[\MNSfilledmedtriangleright]{\blacktriangleright}, and \cmdI[\MNSfilledmedtriangleup]{\blacktriangle} [\textit{sic}] are synonyms for, respectively, \cmdI[\MNSfilledmedtriangledown]{\filledmedtriangledown}, \cmdI[\MNSfilledmedtriangleleft]{\filledmedtriangleleft}, \cmdI[\MNSfilledmedtriangleright]{\filledmedtriangleright}, and \cmdI[\MNSfilledmedtriangleup]{\filledmedtriangleup}; \cmdI[\MNSmedtriangleright]{\triangleright} is a synonym for \cmdI[\MNSmedtriangleright]{\medtriangleright}; \cmdI[\MNSmedtriangleup]{\triangle}, \cmdI[\MNSmedtriangleup]{\vartriangle}, and \cmdI[\MNSmedtriangleup]{\bigtriangleup} are synonyms for \cmdI[\MNSmedtriangleup]{\medtriangleup}; \cmdI[\MNSmedtriangleleft]{\triangleleft} is a synonym for \cmdI[\MNSmedtriangleleft]{\medtriangleleft}; \cmdI[\MNSmedtriangledown]{\triangledown} and \cmdI[\MNSmedtriangledown]{\bigtriangledown} are synonyms for \cmdI[\MNSmedtriangledown]{\medtriangledown}; \cmdI[\MNSnlessclosed]{\nlessclosed} is a synonym for \cmdI[\MNSnlessclosed]{\ntriangleleft}; \cmdI[\MNSngtrclosed]{\ngtrclosed} is a synonym for \cmdI[\MNSngtrclosed]{\ntriangleright}; \cmdI[\MNSnleqclosed]{\nleqclosed} is a synonym for \cmdI[\MNSnleqclosed]{\ntrianglelefteq}; and \cmdI[\MNSngeqclosed]{\ngeqclosed} is a synonym for \cmdI[\MNSngeqclosed]{\ntrianglerighteq}. \end{tablenote} \bigskip \begin{tablenote} The title ``Triangle Relations'' is a bit of a misnomer here as only \cmdI[\MNStriangleeq]{\triangleeq} and \cmdI[\MNSntriangleeq]{\ntriangleeq} are defined as \tex\ relations (class~3 symbols). The \verb|\largetriangle|\rule{2em}{1pt} symbols are defined as \tex\ ``ordinary'' characters (class~0) and all of the remaining characters are defined as \tex\ binary operators (class~2). \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Triangle Relations} \index{triangle relations}\index{relational symbols>triangle} \label{fdsym-triangle-rel} \begin{tabular}{*3{ll}} \K[\FDSYMgeqclosed]\geqclosed & \K[\FDSYMmedtriangledown]\medtriangledown & \K[\FDSYMsmallblacktriangleleft]\smallblacktriangleleft \\ \K[\FDSYMgtrclosed]\gtrclosed & \K[\FDSYMmedtriangleleft]\medtriangleleft & \K[\FDSYMsmallblacktriangleright]\smallblacktriangleright \\ \K[\FDSYMlargetriangledown]\largetriangledown & \K[\FDSYMmedtriangleright]\medtriangleright & \K[\FDSYMsmallblacktriangleup]\smallblacktriangleup \\ \K[\FDSYMlargetriangleup]\largetriangleup & \K[\FDSYMmedtriangleup]\medtriangleup & \K[\FDSYMsmalltriangledown]\smalltriangledown \\ \K[\FDSYMleqclosed]\leqclosed & \K[\FDSYMngeqclosed]\ngeqclosed & \K[\FDSYMsmalltriangleleft]\smalltriangleleft \\ \K[\FDSYMlessclosed]\lessclosed & \K[\FDSYMngtrclosed]\ngtrclosed & \K[\FDSYMsmalltriangleright]\smalltriangleright \\ \K[\FDSYMmedblacktriangledown]\medblacktriangledown & \K[\FDSYMnleqclosed]\nleqclosed & \K[\FDSYMsmalltriangleup]\smalltriangleup \\ \K[\FDSYMmedblacktriangleleft]\medblacktriangleleft & \K[\FDSYMnlessclosed]\nlessclosed & \K[\FDSYMtriangleeq]\triangleeq \\ \K[\FDSYMmedblacktriangleright]\medblacktriangleright & \K[\FDSYMntriangleeq]\ntriangleeq & \\ \K[\FDSYMmedblacktriangleup]\medblacktriangleup & \K[\FDSYMsmallblacktriangledown]\smallblacktriangledown & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines synonyms for almost all of the preceding symbols: \begin{tabular}{*3{ll}} \K[\FDSYMbigtriangledown]{\bigtriangledown} & \K[\FDSYMntrianglelefteq]{\ntrianglelefteq} & \K[\FDSYMtriangleq]{\triangleq} \\ \K[\FDSYMbigtriangleup]{\bigtriangleup} & \K[\FDSYMntriangleright]{\ntriangleright} & \K[\FDSYMtriangleright]{\triangleright} \\ \K[\FDSYMblacktriangle]{\blacktriangle} & \K[\FDSYMntrianglerighteq]{\ntrianglerighteq} & \K[\FDSYMtrianglerighteq]{\trianglerighteq} \\ \K[\FDSYMblacktriangledown]{\blacktriangledown} & \K[\FDSYMtriangle]{\triangle} & \K[\FDSYMvartriangle]{\vartriangle} \\ \K[\FDSYMblacktriangleleft]{\blacktriangleleft} & \K[\FDSYMtriangledown]{\triangledown} & \K[\FDSYMvartriangleleft]{\vartriangleleft} \\ \K[\FDSYMblacktriangleright]{\blacktriangleright} & \K[\FDSYMtriangleleft]{\triangleleft} & \K[\FDSYMvartriangleright]{\vartriangleright} \\ \K[\FDSYMntriangleleft]{\ntriangleleft} & \K[\FDSYMtrianglelefteq]{\trianglelefteq} & \\ \end{tabular} \end{tablenote} \bigskip \begin{tablenote} The title ``Triangle Relations'' is a bit of a misnomer here as only \cmdI[\FDSYMtriangleeq]{\triangleeq} and \cmdI[\FDSYMntriangleeq]{\ntriangleeq} are defined as \tex\ relations (class~3 symbols). The \verb|\largetriangle|\rule{2em}{1pt} symbols are defined as \tex\ ``ordinary'' characters (class~0) and all of the remaining characters are defined as \tex\ binary operators (class~2). \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Triangle Relations} \index{triangle relations} \index{relational symbols>triangle} \label{bsk-triangle-rel} \begin{tabular}{*3{ll}} \K[\BSKntriangleleft]\ntriangleleft & \K[\BSKtrianglelefteq]\trianglelefteq & \K[\BSKvarlrttriangle]\varlrttriangle \\ \K[\BSKntrianglelefteq]\ntrianglelefteq & \K[\BSKtrianglelefteqslant]\trianglelefteqslant & \K[\BSKvartriangle]\vartriangle \\ \K[\BSKntriangleright]\ntriangleright & \K[\BSKtriangleright]\triangleright & \K[\BSKvartriangleleft]\vartriangleleft \\ \K[\BSKntrianglerighteq]\ntrianglerighteq & \K[\BSKtrianglerighteq]\trianglerighteq & \K[\BSKvartriangleright]\vartriangleright \\ \K[\BSKtriangleleft]\triangleleft & \K[\BSKtrianglerighteqslant]\trianglerighteqslant & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Triangle Relations} \index{triangle relations} \index{relational symbols>triangle} \label{stix-triangle-rel} \begin{tabular}{*3{ll}} \K[\STIXlrtriangleeq]\lrtriangleeq & \K[\STIXnvartriangleright]\nvartriangleright & \K[\STIXvartriangle]\vartriangle \\ \K[\STIXltrivb]\ltrivb & \K[\STIXrtriltri]\rtriltri & \K[\STIXvartriangleleft]\vartriangleleft \\ \K[\STIXntrianglelefteq]\ntrianglelefteq & \K[\STIXtrianglelefteq]\trianglelefteq & \K[\STIXvartriangleright]\vartriangleright \\ \K[\STIXntrianglerighteq]\ntrianglerighteq & \K[\STIXtriangleq]\triangleq & \K[\STIXvbrtri]\vbrtri \\ \K[\STIXnvartriangleleft]\nvartriangleleft & \K[\STIXtrianglerighteq]\trianglerighteq & \\ \end{tabular} \end{symtable} \begin{symtable}{Arrows} \index{arrows} \label{arrow} \begin{tabular}{*3{ll}} \X\Downarrow & \X\longleftarrow & \X\nwarrow \\ \X\downarrow & \X\Longleftarrow & \X\Rightarrow \\ \X\hookleftarrow & \X\longleftrightarrow & \X\rightarrow \\ \X\hookrightarrow & \X\Longleftrightarrow & \X\searrow \\ \X\leadsto$^*$ & \X\longmapsto & \X\swarrow \\ \X\leftarrow & \X\Longrightarrow & \X\uparrow \\ \X\Leftarrow & \X\longrightarrow & \X\Uparrow \\ \X\Leftrightarrow & \X\mapsto & \X\updownarrow \\ \X\leftrightarrow & \X\nearrow$^\dag$ & \X\Updownarrow \\ \end{tabular} \bigskip \notpredefinedmessage \bigskip \begin{tablenote}[\dag] See the note beneath \ref{extensible-accents} for information about how to put a diagonal arrow across a mathematical expression% \ifhavecancel ~(as in ``$\cancelto{0}{\nabla \cdot \vec{B}}\quad$'') \fi . \end{tablenote} \end{symtable} \begin{symtable}{Harpoons} \index{harpoons} \label{harpoons} \begin{tabular}{*3{ll}} \X\leftharpoondown & \X\rightharpoondown & \X\rightleftharpoons \\ \X\leftharpoonup & \X\rightharpoonup \\ \end{tabular} \end{symtable} \begin{symtable}{\TC\ Text-mode Arrows} \index{arrows} \label{tc-arrows} \begin{tabular}{*2{ll}} \K\textdownarrow & \K\textrightarrow \\ \K\textleftarrow & \K\textuparrow \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Arrows} \index{arrows} \label{ams-arrows} \begin{tabular}{*3{ll}} \X\circlearrowleft & \X\leftleftarrows & \X\rightleftarrows \\ \X\circlearrowright & \X\leftrightarrows & \X\rightrightarrows \\ \X\curvearrowleft & \X\leftrightsquigarrow & \X\rightsquigarrow \\ \X\curvearrowright & \X\Lleftarrow & \X\Rsh \\ \X\dashleftarrow & \X\looparrowleft & \X\twoheadleftarrow \\ \X\dashrightarrow & \X\looparrowright & \X\twoheadrightarrow \\ \X\downdownarrows & \X\Lsh & \X\upuparrows \\ \X\leftarrowtail & \X\rightarrowtail & \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Negated Arrows} \subindex{arrows}{negated} \label{ams-narrows} \begin{tabular}{*3{ll}} \X\nLeftarrow & \X\nLeftrightarrow & \X\nRightarrow \\ \X\nleftarrow & \X\nleftrightarrow & \X\nrightarrow \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Harpoons} \index{harpoons} \label{ams-harpoons} \begin{tabular}{*3{ll}} \X\downharpoonleft & \X\leftrightharpoons & \X\upharpoonleft \\ \X\downharpoonright & \X[\AMSrightleftharpoons]\rightleftharpoons & \X\upharpoonright \\ \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Arrows} \index{arrows} \index{lightning} \label{st-arrows} \begin{tabular}{*3{ll}} \X\leftarrowtriangle & \X\Mapsfrom & \X\shortleftarrow \\ \X\leftrightarroweq & \X\mapsfrom & \X\shortrightarrow \\ \X\leftrightarrowtriangle & \X\Mapsto & \X\shortuparrow \\ \X\lightning & \X\nnearrow & \X\ssearrow \\ \X\Longmapsfrom & \X\nnwarrow & \X\sswarrow \\ \X\longmapsfrom & \X\rightarrowtriangle \\ \X\Longmapsto & \X\shortdownarrow \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Arrows} \index{arrows} \index{rhombuses} \label{txpx-arrows} \begin{tabular}{*3{ll}} \X\boxdotLeft & \X\circleddotright & \X\Diamondleft \\ \X\boxdotleft & \X\circleleft & \X\Diamondright \\ \X\boxdotright & \X\circleright & \X\DiamondRight \\ \X\boxdotRight & \X\dashleftrightarrow & \X\leftsquigarrow \\ \X\boxLeft & \X\DiamonddotLeft & \X\Nearrow \\ \X\boxleft & \X\Diamonddotleft & \X\Nwarrow \\ \X\boxright & \X\Diamonddotright & \X\Rrightarrow \\ \X\boxRight & \X\DiamonddotRight & \X\Searrow \\ \X\circleddotleft & \X\DiamondLeft & \X\Swarrow \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Arrows} \index{arrows} \index{restrictions} \label{abx-arrows} \begin{tabular}{*3{ll}} \X[\ABXcirclearrowleft]\circlearrowleft & \X[\ABXleftarrow]\leftarrow & \X[\ABXnwarrow]\nwarrow \\ \X[\ABXcirclearrowright]\circlearrowright & \X[\ABXleftleftarrows]\leftleftarrows & \X[\ABXrestriction]\restriction \\ \X[\ABXcurvearrowbotleft]\curvearrowbotleft & \X[\ABXleftrightarrow]\leftrightarrow & \X[\ABXrightarrow]\rightarrow \\ \X[\ABXcurvearrowbotleftright]\curvearrowbotleftright & \X[\ABXleftrightarrows]\leftrightarrows & \X[\ABXrightleftarrows]\rightleftarrows \\ \X[\ABXcurvearrowbotright]\curvearrowbotright & \X[\ABXleftrightsquigarrow]\leftrightsquigarrow & \X[\ABXrightrightarrows]\rightrightarrows \\ \X[\ABXcurvearrowleft]\curvearrowleft & \X[\ABXleftsquigarrow]\leftsquigarrow & \X[\ABXrightsquigarrow]\rightsquigarrow \\ \X[\ABXcurvearrowleftright]\curvearrowleftright & \X[\ABXlefttorightarrow]\lefttorightarrow & \X[\ABXrighttoleftarrow]\righttoleftarrow \\ \X[\ABXcurvearrowright]\curvearrowright & \X[\ABXlooparrowdownleft]\looparrowdownleft & \X[\ABXRsh]\Rsh \\ \X[\ABXdlsh]\dlsh & \X[\ABXlooparrowdownright]\looparrowdownright & \X[\ABXsearrow]\searrow \\ \X[\ABXdowndownarrows]\downdownarrows & \X[\ABXlooparrowleft]\looparrowleft & \X[\ABXswarrow]\swarrow \\ \X[\ABXdowntouparrow]\downtouparrow & \X[\ABXlooparrowright]\looparrowright & \X[\ABXupdownarrows]\updownarrows \\ \X[\ABXdownuparrows]\downuparrows & \X[\ABXLsh]\Lsh & \X[\ABXuptodownarrow]\uptodownarrow \\ \X[\ABXdrsh]\drsh & \X[\ABXnearrow]\nearrow & \X[\ABXupuparrows]\upuparrows \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Negated Arrows} \subindex{arrows}{negated} \label{abx-narrows} \begin{tabular}{*3{ll}} \X[\ABXnLeftarrow]\nLeftarrow & \X[\ABXnleftrightarrow]\nleftrightarrow & \X[\ABXnrightarrow]\nrightarrow \\ \X[\ABXnleftarrow]\nleftarrow & \X[\ABXnLeftrightarrow]\nLeftrightarrow & \X[\ABXnRightarrow]\nRightarrow \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Harpoons} \index{harpoons} \label{abx-harpoons} \begin{tabular}{*3{ll}} \X[\ABXbarleftharpoon]\barleftharpoon & \X[\ABXleftharpoonup]\leftharpoonup & \X[\ABXrightleftharpoons]\rightleftharpoons \\ \X[\ABXbarrightharpoon]\barrightharpoon & \X[\ABXleftleftharpoons]\leftleftharpoons & \X[\ABXrightrightharpoons]\rightrightharpoons \\ \X[\ABXdowndownharpoons]\downdownharpoons & \X[\ABXleftrightharpoon]\leftrightharpoon & \X[\ABXupdownharpoons]\updownharpoons \\ \X[\ABXdownharpoonleft]\downharpoonleft & \X[\ABXleftrightharpoons]\leftrightharpoons & \X[\ABXupharpoonleft]\upharpoonleft \\ \X[\ABXdownharpoonright]\downharpoonright & \X[\ABXrightbarharpoon]\rightbarharpoon & \X[\ABXupharpoonright]\upharpoonright \\ \X[\ABXdownupharpoons]\downupharpoons & \X[\ABXrightharpoondown]\rightharpoondown & \X[\ABXupupharpoons]\upupharpoons \\ \X[\ABXleftbarharpoon]\leftbarharpoon & \X[\ABXrightharpoonup]\rightharpoonup \\ \X[\ABXleftharpoondown]\leftharpoondown & \X[\ABXrightleftharpoon]\rightleftharpoon \\ \end{tabular} \end{symtable} \begin{longsymtable}[MNS]{\MNS\ Arrows} \ltindex{arrows} \ltindex{lightning} \label{mns-arrows} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\MNScurvearrowdownup]\curvearrowdownup & \X[\MNSlongleftarrow]\longleftarrow & \K[\MNSrhookswarrow]\rhookswarrow \\ \K[\MNScurvearrowleftright]\curvearrowleftright & \X[\MNSLongleftarrow]\Longleftarrow & \K[\MNSrhookuparrow]\rhookuparrow \\ \K[\MNScurvearrownesw]\curvearrownesw & \X[\MNSlongleftrightarrow]\longleftrightarrow & \K[\MNSrightarrow]\rightarrow \\ \K[\MNScurvearrownwse]\curvearrownwse & \X[\MNSLongleftrightarrow]\Longleftrightarrow & \K[\MNSRightarrow]\Rightarrow \\ \K[\MNScurvearrowrightleft]\curvearrowrightleft & \X[\MNSlongmapsto]\longmapsto & \K[\MNSrightarrowtail]\rightarrowtail \\ \K[\MNScurvearrowsenw]\curvearrowsenw & \X[\MNSlongrightarrow]\longrightarrow & \K[\MNSrightleftarrows]\rightleftarrows \\ \K[\MNScurvearrowswne]\curvearrowswne & \X[\MNSLongrightarrow]\Longrightarrow & \K[\MNSrightlsquigarrow]\rightlsquigarrow \\ \K[\MNScurvearrowupdown]\curvearrowupdown & \K[\MNSlooparrowleft]\looparrowleft & \K[\MNSrightmapsto]\rightmapsto \\ \K[\MNSdasheddownarrow]\dasheddownarrow & \K[\MNSlooparrowright]\looparrowright & \K[\MNSrightrightarrows]\rightrightarrows \\ \K[\MNSdashedleftarrow]\dashedleftarrow & \K[\MNSLsh]\Lsh & \K[\MNSrightrsquigarrow]\rightrsquigarrow \\ \K[\MNSdashednearrow]\dashednearrow & \K[\MNSnearrow]\nearrow & \K[\MNSRrightarrow]\Rrightarrow \\ \K[\MNSdashednwarrow]\dashednwarrow & \K[\MNSNearrow]\Nearrow & \K[\MNSRsh]\Rsh \\ \K[\MNSdashedrightarrow]\dashedrightarrow & \K[\MNSnearrowtail]\nearrowtail & \K[\MNSsearrow]\searrow \\ \K[\MNSdashedsearrow]\dashedsearrow & \K[\MNSnelsquigarrow]\nelsquigarrow & \K[\MNSSearrow]\Searrow \\ \K[\MNSdashedswarrow]\dashedswarrow & \K[\MNSnemapsto]\nemapsto & \K[\MNSsearrowtail]\searrowtail \\ \K[\MNSdasheduparrow]\dasheduparrow & \K[\MNSnenearrows]\nenearrows & \K[\MNSselsquigarrow]\selsquigarrow \\ \K[\MNSDownarrow]\Downarrow & \K[\MNSnersquigarrow]\nersquigarrow & \K[\MNSsemapsto]\semapsto \\ \K[\MNSdownarrow]\downarrow & \K[\MNSneswarrow]\neswarrow & \K[\MNSsenwarrows]\senwarrows \\ \K[\MNSdownarrowtail]\downarrowtail & \K[\MNSNeswarrow]\Neswarrow & \K[\MNSsersquigarrow]\sersquigarrow \\ \K[\MNSdowndownarrows]\downdownarrows & \K[\MNSneswarrows]\neswarrows & \K[\MNSsesearrows]\sesearrows \\ \K[\MNSdownlsquigarrow]\downlsquigarrow & \K[\MNSnwarrow]\nwarrow & \K[\MNSsquigarrowdownup]\squigarrowdownup \\ \K[\MNSdownmapsto]\downmapsto & \K[\MNSNwarrow]\Nwarrow & \K[\MNSsquigarrowleftright]\squigarrowleftright \\ \K[\MNSdownrsquigarrow]\downrsquigarrow & \K[\MNSnwarrowtail]\nwarrowtail & \K[\MNSsquigarrownesw]\squigarrownesw \\ \K[\MNSdownuparrows]\downuparrows & \K[\MNSnwlsquigarrow]\nwlsquigarrow & \K[\MNSsquigarrownwse]\squigarrownwse \\ \K[\MNSlcirclearrowdown]\lcirclearrowdown & \K[\MNSnwmapsto]\nwmapsto & \K[\MNSsquigarrowrightleft]\squigarrowrightleft \\ \K[\MNSlcirclearrowleft]\lcirclearrowleft & \K[\MNSnwnwarrows]\nwnwarrows & \K[\MNSsquigarrowsenw]\squigarrowsenw \\ \K[\MNSlcirclearrowright]\lcirclearrowright & \K[\MNSnwrsquigarrow]\nwrsquigarrow & \K[\MNSsquigarrowswne]\squigarrowswne \\ \K[\MNSlcirclearrowup]\lcirclearrowup & \K[\MNSnwsearrow]\nwsearrow & \K[\MNSsquigarrowupdown]\squigarrowupdown \\ \K[\MNSlcurvearrowdown]\lcurvearrowdown & \K[\MNSNwsearrow]\Nwsearrow & \K[\MNSswarrow]\swarrow \\ \K[\MNSlcurvearrowleft]\lcurvearrowleft & \K[\MNSnwsearrows]\nwsearrows & \K[\MNSSwarrow]\Swarrow \\ \K[\MNSlcurvearrowne]\lcurvearrowne & \K[\strut\smash\MNSpartialvardlcircleleftint]\partialvardlcircleleftint$^*$ & \K[\MNSswarrowtail]\swarrowtail \\ \K[\MNSlcurvearrownw]\lcurvearrownw & \K[\strut\smash\MNSpartialvardlcirclerightint]\partialvardlcirclerightint$^*$ & \K[\MNSswlsquigarrow]\swlsquigarrow \\ \K[\MNSlcurvearrowright]\lcurvearrowright & \K[\strut\smash\MNSpartialvardrcircleleftint]\partialvardrcircleleftint$^*$ & \K[\MNSswmapsto]\swmapsto \\ \K[\MNSlcurvearrowse]\lcurvearrowse & \K[\strut\smash\MNSpartialvardrcirclerightint]\partialvardrcirclerightint$^*$ & \K[\MNSswnearrows]\swnearrows \\ \K[\MNSlcurvearrowsw]\lcurvearrowsw & \K[\strut\smash\MNSpartialvartlcircleleftint]\partialvartlcircleleftint$^*$ & \K[\MNSswrsquigarrow]\swrsquigarrow \\ \K[\MNSlcurvearrowup]\lcurvearrowup & \K[\strut\smash\MNSpartialvartlcirclerightint]\partialvartlcirclerightint$^*$ & \K[\MNSswswarrows]\swswarrows \\ \K[\MNSLeftarrow]\Leftarrow & \K[\strut\smash\MNSpartialvartrcircleleftint]\partialvartrcircleleftint$^*$ & \K[\MNStwoheaddownarrow]\twoheaddownarrow \\ \K[\MNSleftarrow]\leftarrow & \K[\strut\smash\MNSpartialvartrcirclerightint]\partialvartrcirclerightint$^*$ & \K[\MNStwoheadleftarrow]\twoheadleftarrow \\ \K[\MNSleftarrowtail]\leftarrowtail & \K[\MNSrcirclearrowdown]\rcirclearrowdown & \K[\MNStwoheadnearrow]\twoheadnearrow \\ \K[\MNSleftleftarrows]\leftleftarrows & \K[\MNSrcirclearrowleft]\rcirclearrowleft & \K[\MNStwoheadnwarrow]\twoheadnwarrow \\ \K[\MNSleftlsquigarrow]\leftlsquigarrow & \K[\MNSrcirclearrowright]\rcirclearrowright & \K[\MNStwoheadrightarrow]\twoheadrightarrow \\ \K[\MNSleftmapsto]\leftmapsto & \K[\MNSrcirclearrowup]\rcirclearrowup & \K[\MNStwoheadsearrow]\twoheadsearrow \\ \K[\MNSleftrightarrow]\leftrightarrow & \K[\MNSrcurvearrowdown]\rcurvearrowdown & \K[\MNStwoheadswarrow]\twoheadswarrow \\ \K[\MNSLeftrightarrow]\Leftrightarrow & \K[\MNSrcurvearrowleft]\rcurvearrowleft & \K[\MNStwoheaduparrow]\twoheaduparrow \\ \K[\MNSleftrightarrows]\leftrightarrows & \K[\MNSrcurvearrowne]\rcurvearrowne & \K[\MNSuparrow]\uparrow \\ \K[\MNSleftrsquigarrow]\leftrsquigarrow & \K[\MNSrcurvearrownw]\rcurvearrownw & \K[\MNSUparrow]\Uparrow \\ \K[\MNSlhookdownarrow]\lhookdownarrow & \K[\MNSrcurvearrowright]\rcurvearrowright & \K[\MNSuparrowtail]\uparrowtail \\ \K[\MNSlhookleftarrow]\lhookleftarrow & \K[\MNSrcurvearrowse]\rcurvearrowse & \K[\MNSupdownarrow]\updownarrow \\ \K[\MNSlhooknearrow]\lhooknearrow & \K[\MNSrcurvearrowsw]\rcurvearrowsw & \K[\MNSUpdownarrow]\Updownarrow \\ \K[\MNSlhooknwarrow]\lhooknwarrow & \K[\MNSrcurvearrowup]\rcurvearrowup & \K[\MNSupdownarrows]\updownarrows \\ \K[\MNSlhookrightarrow]\lhookrightarrow & \K[\MNSrhookdownarrow]\rhookdownarrow & \K[\MNSuplsquigarrow]\uplsquigarrow \\ \K[\MNSlhooksearrow]\lhooksearrow & \K[\MNSrhookleftarrow]\rhookleftarrow & \K[\MNSupmapsto]\upmapsto \\ \K[\MNSlhookswarrow]\lhookswarrow & \K[\MNSrhooknearrow]\rhooknearrow & \K[\MNSuprsquigarrow]\uprsquigarrow \\ \K[\MNSlhookuparrow]\lhookuparrow & \K[\MNSrhooknwarrow]\rhooknwarrow & \K[\MNSupuparrows]\upuparrows \\ \K[\MNSlightning]\lightning & \K[\MNSrhookrightarrow]\rhookrightarrow & \\ \K[\MNSLleftarrow]\Lleftarrow & \K[\MNSrhooksearrow]\rhooksearrow & \\ \end{longtable} \MNS\ additionally defines synonyms for some of the preceding symbols: \bigskip \newcommand*{\mnssyn}[1]{(same as \texttt{\string#1})} \begin{tabular}{ll@{\quad}l} \K[\MNSrcirclearrowup]\circlearrowleft & \mnssyn\rcirclearrowup \\ \K[\MNSlcirclearrowup]\circlearrowright & \mnssyn\lcirclearrowup \\ \K[\MNSrcurvearrowleft]\curvearrowleft & \mnssyn\rcurvearrowleft \\ \K[\MNSlcurvearrowright]\curvearrowright & \mnssyn\lcurvearrowright \\ \K[\MNSdashedleftarrow]\dashleftarrow & \mnssyn\dashedleftarrow \\ \K[\MNSdashedrightarrow]\dashrightarrow & \mnssyn\dashedrightarrow \\ \K[\MNSrhookleftarrow]\hookleftarrow & \mnssyn\rhookleftarrow \\ \K[\MNSlhookrightarrow]\hookrightarrow & \mnssyn\lhookrightarrow \\ \K[\MNSrightlsquigarrow]\leadsto & \mnssyn\rightlsquigarrow \\ \K[\MNSsquigarrowleftright]\leftrightsquigarrow & \mnssyn\squigarrowleftright \\ \K[\MNSrightmapsto]\mapsto & \mnssyn\rightmapsto \\ \K[\MNSrightlsquigarrow]\rightsquigarrow & \mnssyn\rightlsquigarrow \\ \end{tabular} \bigskip \begin{tablenote}[*] The \verb|\partialvar|\rule{2em}{1pt}\verb|int| macros are intended to be used internally by \MNS\ to produce various types of integrals. \end{tablenote} \end{longsymtable} \begin{longsymtable}[MNS]{\MNS\ Negated Arrows} \ltsubindex{arrows}{negated} \label{mns-narrows} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\MNSncurvearrowdownup]\ncurvearrowdownup & \K[\MNSnlhooknwarrow]\nlhooknwarrow & \K[\MNSnrightleftarrows]\nrightleftarrows \\ \K[\MNSncurvearrowleftright]\ncurvearrowleftright & \K[\MNSnlhookrightarrow]\nlhookrightarrow & \K[\MNSnrightlsquigarrow]\nrightlsquigarrow \\ \K[\MNSncurvearrownesw]\ncurvearrownesw & \K[\MNSnlhooksearrow]\nlhooksearrow & \K[\MNSnrightmapsto]\nrightmapsto \\ \K[\MNSncurvearrownwse]\ncurvearrownwse & \K[\MNSnlhookswarrow]\nlhookswarrow & \K[\MNSnrightrightarrows]\nrightrightarrows \\ \K[\MNSncurvearrowrightleft]\ncurvearrowrightleft & \K[\MNSnlhookuparrow]\nlhookuparrow & \K[\MNSnrightrsquigarrow]\nrightrsquigarrow \\ \K[\MNSncurvearrowsenw]\ncurvearrowsenw & \K[\MNSnLleftarrow]\nLleftarrow & \K[\MNSnRrightarrow]\nRrightarrow \\ \K[\MNSncurvearrowswne]\ncurvearrowswne & \K[\MNSnnearrow]\nnearrow & \K[\MNSnSearrow]\nSearrow \\ \K[\MNSncurvearrowupdown]\ncurvearrowupdown & \K[\MNSnNearrow]\nNearrow & \K[\MNSnsearrow]\nsearrow \\ \K[\MNSndasheddownarrow]\ndasheddownarrow & \K[\MNSnnearrowtail]\nnearrowtail & \K[\MNSnsearrowtail]\nsearrowtail \\ \K[\MNSndashedleftarrow]\ndashedleftarrow & \K[\MNSnnelsquigarrow]\nnelsquigarrow & \K[\MNSnselsquigarrow]\nselsquigarrow \\ \K[\MNSndashednearrow]\ndashednearrow & \K[\MNSnnemapsto]\nnemapsto & \K[\MNSnsemapsto]\nsemapsto \\ \K[\MNSndashednwarrow]\ndashednwarrow & \K[\MNSnnenearrows]\nnenearrows & \K[\MNSnsenwarrows]\nsenwarrows \\ \K[\MNSndashedrightarrow]\ndashedrightarrow & \K[\MNSnnersquigarrow]\nnersquigarrow & \K[\MNSnsersquigarrow]\nsersquigarrow \\ \K[\MNSndashedsearrow]\ndashedsearrow & \K[\MNSnNeswarrow]\nNeswarrow & \K[\MNSnsesearrows]\nsesearrows \\ \K[\MNSndashedswarrow]\ndashedswarrow & \K[\MNSnneswarrow]\nneswarrow & \K[\MNSnsquigarrowdownup]\nsquigarrowdownup \\ \K[\MNSndasheduparrow]\ndasheduparrow & \K[\MNSnneswarrows]\nneswarrows & \K[\MNSnsquigarrowleftright]\nsquigarrowleftright \\ \K[\MNSndownarrow]\ndownarrow & \K[\MNSnNwarrow]\nNwarrow & \K[\MNSnsquigarrownesw]\nsquigarrownesw \\ \K[\MNSnDownarrow]\nDownarrow & \K[\MNSnnwarrow]\nnwarrow & \K[\MNSnsquigarrownwse]\nsquigarrownwse \\ \K[\MNSndownarrowtail]\ndownarrowtail & \K[\MNSnnwarrowtail]\nnwarrowtail & \K[\MNSnsquigarrowrightleft]\nsquigarrowrightleft \\ \K[\MNSndowndownarrows]\ndowndownarrows & \K[\MNSnnwlsquigarrow]\nnwlsquigarrow & \K[\MNSnsquigarrowsenw]\nsquigarrowsenw \\ \K[\MNSndownlsquigarrow]\ndownlsquigarrow & \K[\MNSnnwmapsto]\nnwmapsto & \K[\MNSnsquigarrowswne]\nsquigarrowswne \\ \K[\MNSndownmapsto]\ndownmapsto & \K[\MNSnnwnwarrows]\nnwnwarrows & \K[\MNSnsquigarrowupdown]\nsquigarrowupdown \\ \K[\MNSndownrsquigarrow]\ndownrsquigarrow & \K[\MNSnnwrsquigarrow]\nnwrsquigarrow & \K[\MNSnswarrow]\nswarrow \\ \K[\MNSndownuparrows]\ndownuparrows & \K[\MNSnnwsearrow]\nnwsearrow & \K[\MNSnSwarrow]\nSwarrow \\ \K[\MNSnlcirclearrowdown]\nlcirclearrowdown & \K[\MNSnNwsearrow]\nNwsearrow & \K[\MNSnswarrowtail]\nswarrowtail \\ \K[\MNSnlcirclearrowleft]\nlcirclearrowleft & \K[\MNSnnwsearrows]\nnwsearrows & \K[\MNSnswlsquigarrow]\nswlsquigarrow \\ \K[\MNSnlcirclearrowright]\nlcirclearrowright & \K[\MNSnrcirclearrowdown]\nrcirclearrowdown & \K[\MNSnswmapsto]\nswmapsto \\ \K[\MNSnlcirclearrowup]\nlcirclearrowup & \K[\MNSnrcirclearrowleft]\nrcirclearrowleft & \K[\MNSnswnearrows]\nswnearrows \\ \K[\MNSnlcurvearrowdown]\nlcurvearrowdown & \K[\MNSnrcirclearrowright]\nrcirclearrowright & \K[\MNSnswrsquigarrow]\nswrsquigarrow \\ \K[\MNSnlcurvearrowleft]\nlcurvearrowleft & \K[\MNSnrcirclearrowup]\nrcirclearrowup & \K[\MNSnswswarrows]\nswswarrows \\ \K[\MNSnlcurvearrowne]\nlcurvearrowne & \K[\MNSnrcurvearrowdown]\nrcurvearrowdown & \K[\MNSntwoheaddownarrow]\ntwoheaddownarrow \\ \K[\MNSnlcurvearrownw]\nlcurvearrownw & \K[\MNSnrcurvearrowleft]\nrcurvearrowleft & \K[\MNSntwoheadleftarrow]\ntwoheadleftarrow \\ \K[\MNSnlcurvearrowright]\nlcurvearrowright & \K[\MNSnrcurvearrowne]\nrcurvearrowne & \K[\MNSntwoheadnearrow]\ntwoheadnearrow \\ \K[\MNSnlcurvearrowse]\nlcurvearrowse & \K[\MNSnrcurvearrownw]\nrcurvearrownw & \K[\MNSntwoheadnwarrow]\ntwoheadnwarrow \\ \K[\MNSnlcurvearrowsw]\nlcurvearrowsw & \K[\MNSnrcurvearrowright]\nrcurvearrowright & \K[\MNSntwoheadrightarrow]\ntwoheadrightarrow \\ \K[\MNSnlcurvearrowup]\nlcurvearrowup & \K[\MNSnrcurvearrowse]\nrcurvearrowse & \K[\MNSntwoheadsearrow]\ntwoheadsearrow \\ \K[\MNSnLeftarrow]\nLeftarrow & \K[\MNSnrcurvearrowsw]\nrcurvearrowsw & \K[\MNSntwoheadswarrow]\ntwoheadswarrow \\ \K[\MNSnleftarrow]\nleftarrow & \K[\MNSnrcurvearrowup]\nrcurvearrowup & \K[\MNSntwoheaduparrow]\ntwoheaduparrow \\ \K[\MNSnleftarrowtail]\nleftarrowtail & \K[\MNSnrhookdownarrow]\nrhookdownarrow & \K[\MNSnuparrow]\nuparrow \\ \K[\MNSnleftleftarrows]\nleftleftarrows & \K[\MNSnrhookleftarrow]\nrhookleftarrow & \K[\MNSnUparrow]\nUparrow \\ \K[\MNSnleftlsquigarrow]\nleftlsquigarrow & \K[\MNSnrhooknearrow]\nrhooknearrow & \K[\MNSnuparrowtail]\nuparrowtail \\ \K[\MNSnleftmapsto]\nleftmapsto & \K[\MNSnrhooknwarrow]\nrhooknwarrow & \K[\MNSnupdownarrow]\nupdownarrow \\ \K[\MNSnleftrightarrow]\nleftrightarrow & \K[\MNSnrhookrightarrow]\nrhookrightarrow & \K[\MNSnUpdownarrow]\nUpdownarrow \\ \K[\MNSnLeftrightarrow]\nLeftrightarrow & \K[\MNSnrhooksearrow]\nrhooksearrow & \K[\MNSnupdownarrows]\nupdownarrows \\ \K[\MNSnleftrightarrows]\nleftrightarrows & \K[\MNSnrhookswarrow]\nrhookswarrow & \K[\MNSnuplsquigarrow]\nuplsquigarrow \\ \K[\MNSnleftrsquigarrow]\nleftrsquigarrow & \K[\MNSnrhookuparrow]\nrhookuparrow & \K[\MNSnupmapsto]\nupmapsto \\ \K[\MNSnlhookdownarrow]\nlhookdownarrow & \K[\MNSnrightarrow]\nrightarrow & \K[\MNSnuprsquigarrow]\nuprsquigarrow \\ \K[\MNSnlhookleftarrow]\nlhookleftarrow & \K[\MNSnRightarrow]\nRightarrow & \K[\MNSnupuparrows]\nupuparrows \\ \K[\MNSnlhooknearrow]\nlhooknearrow & \K[\MNSnrightarrowtail]\nrightarrowtail & \\ \end{longtable} \MNS\ additionally defines synonyms for some of the preceding symbols: \bigskip \newcommand*{\mnssyn}[1]{(same as \texttt{\string#1})} \begin{tabular}{ll@{\quad}l} \K[\MNSnrcirclearrowup]\ncirclearrowleft & \mnssyn\nrcirclearrowup \\ \K[\MNSnlcirclearrowup]\ncirclearrowright & \mnssyn\nlcirclearrowup \\ \K[\MNSnrcurvearrowleft]\ncurvearrowleft & \mnssyn\nrcurvearrowleft \\ \K[\MNSnlcurvearrowright]\ncurvearrowright & \mnssyn\nlcurvearrowright \\ \K[\MNSndashedrightarrow]\ndasharrow & \mnssyn\ndashedrightarrow \\ \K[\MNSndashedleftarrow]\ndashleftarrow & \mnssyn\ndashedleftarrow \\ \K[\MNSndashedrightarrow]\ndashrightarrow & \mnssyn\ndashedrightarrow \\ \K[\MNSnleftarrow]\ngets & \mnssyn\nleftarrow \\ \K[\MNSnrhookleftarrow]\nhookleftarrow & \mnssyn\nrhookleftarrow \\ \K[\MNSnlhookrightarrow]\nhookrightarrow & \mnssyn\nlhookrightarrow \\ \K[\MNSnrightlsquigarrow]\nleadsto & \mnssyn\nrightlsquigarrow \\ \K[\MNSnsquigarrowleftright]\nleftrightsquigarrow & \mnssyn\nsquigarrowleftright \\ \K[\MNSnrightmapsto]\nmapsto & \mnssyn\nrightmapsto \\ \K[\MNSnrightlsquigarrow]\nrightsquigarrow & \mnssyn\nrightlsquigarrow \\ \K[\MNSnrightarrow]\nto & \mnssyn\nrightarrow \\ \end{tabular} \end{longsymtable} \begin{symtable}[MNS]{\MNS\ Harpoons} \index{harpoons} \index{restrictions} \label{mns-harpoons} \begin{tabular}{*3{ll}} \K[\MNSdownharpoonccw]\downharpoonccw$^*$ & \K[\MNSneswharpoons]\neswharpoons & \K[\MNSseharpooncw]\seharpooncw \\ \K[\MNSdownharpooncw]\downharpooncw$^*$ & \K[\MNSneswharpoonsenw]\neswharpoonsenw & \K[\MNSsenwharpoons]\senwharpoons \\ \K[\MNSdownupharpoons]\downupharpoons & \K[\MNSnwharpoonccw]\nwharpoonccw & \K[\MNSswharpoonccw]\swharpoonccw \\ \K[\MNSleftharpoonccw]\leftharpoonccw$^*$ & \K[\MNSnwharpooncw]\nwharpooncw & \K[\MNSswharpooncw]\swharpooncw \\ \K[\MNSleftharpooncw]\leftharpooncw$^*$ & \K[\MNSnwseharpoonnesw]\nwseharpoonnesw & \K[\MNSswneharpoons]\swneharpoons \\ \K[\MNSleftrightharpoondownup]\leftrightharpoondownup & \K[\MNSnwseharpoons]\nwseharpoons & \K[\MNSupdownharpoonleftright]\updownharpoonleftright \\ \K[\MNSleftrightharpoons]\leftrightharpoons & \K[\MNSnwseharpoonswne]\nwseharpoonswne & \K[\MNSupdownharpoonrightleft]\updownharpoonrightleft \\ \K[\MNSleftrightharpoonupdown]\leftrightharpoonupdown & \K[\MNSrightharpoonccw]\rightharpoonccw$^*$ & \K[\MNSupdownharpoons]\updownharpoons \\ \K[\MNSneharpoonccw]\neharpoonccw & \K[\MNSrightharpooncw]\rightharpooncw$^*$ & \K[\MNSupharpoonccw]\upharpoonccw$^*$ \\ \K[\MNSneharpooncw]\neharpooncw & \K[\MNSrightleftharpoons]\rightleftharpoons & \K[\MNSupharpooncw]\upharpooncw$^*$ \\ \K[\MNSneswharpoonnwse]\neswharpoonnwse & \K[\MNSseharpoonccw]\seharpoonccw & \\ \end{tabular} \bigskip \begin{tablenote}[*] Where marked, the ``\verb|ccw|'' suffix can be replaced with ``\verb|up|'' and the ``\verb|cw|'' suffix can be replaced with ``\verb|down|''. (In addition, \cmdI[\MNSupharpooncw]{\upharpooncw} can be written as \cmdI[\MNSupharpooncw]{\restriction}.) \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Negated Harpoons} \index{harpoons} \index{restrictions} \label{mns-nharpoons} \begin{tabular}{*3{ll}} \K[\MNSndownharpoonccw]\ndownharpoonccw$^*$ & \K[\MNSnneswharpoons]\nneswharpoons & \K[\MNSnseharpooncw]\nseharpooncw \\ \K[\MNSndownharpooncw]\ndownharpooncw$^*$ & \K[\MNSnneswharpoonsenw]\nneswharpoonsenw & \K[\MNSnsenwharpoons]\nsenwharpoons \\ \K[\MNSndownupharpoons]\ndownupharpoons & \K[\MNSnnwharpoonccw]\nnwharpoonccw & \K[\MNSnswharpoonccw]\nswharpoonccw \\ \K[\MNSnleftharpoonccw]\nleftharpoonccw$^*$ & \K[\MNSnnwharpooncw]\nnwharpooncw & \K[\MNSnswharpooncw]\nswharpooncw \\ \K[\MNSnleftharpooncw]\nleftharpooncw$^*$ & \K[\MNSnnwseharpoonnesw]\nnwseharpoonnesw & \K[\MNSnswneharpoons]\nswneharpoons \\ \K[\MNSnleftrightharpoondownup]\nleftrightharpoondownup & \K[\MNSnnwseharpoons]\nnwseharpoons & \K[\MNSnupdownharpoonleftright]\nupdownharpoonleftright \\ \K[\MNSnleftrightharpoons]\nleftrightharpoons & \K[\MNSnnwseharpoonswne]\nnwseharpoonswne & \K[\MNSnupdownharpoonrightleft]\nupdownharpoonrightleft \\ \K[\MNSnleftrightharpoonupdown]\nleftrightharpoonupdown & \K[\MNSnrightharpoonccw]\nrightharpoonccw$^*$ & \K[\MNSnupdownharpoons]\nupdownharpoons \\ \K[\MNSnneharpoonccw]\nneharpoonccw & \K[\MNSnrightharpooncw]\nrightharpooncw$^*$ & \K[\MNSnupharpoonccw]\nupharpoonccw$^*$ \\ \K[\MNSnneharpooncw]\nneharpooncw & \K[\MNSnrightleftharpoons]\nrightleftharpoons & \K[\MNSnupharpooncw]\nupharpooncw$^*$ \\ \K[\MNSnneswharpoonnwse]\nneswharpoonnwse & \K[\MNSnseharpoonccw]\nseharpoonccw & \\ \end{tabular} \bigskip \begin{tablenote}[*] Where marked, the ``\verb|ccw|'' suffix can be replaced with ``\verb|up|'' and the ``\verb|cw|'' suffix can be replaced with ``\verb|down|''. (In addition, \cmdI[\MNSnupharpooncw]{\nupharpooncw} can be written as \cmdI[\MNSnupharpooncw]{\nrestriction}.) \end{tablenote} \end{symtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Arrows} \ltindex{arrows} \ltindex{lightning} \label{fdsym-arrows} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMacwcirclearrowdown]\acwcirclearrowdown & \K[\FDSYMleftarrow]\leftarrow & \K[\FDSYMrightrightarrows]\rightrightarrows \\ \K[\FDSYMacwcirclearrowleft]\acwcirclearrowleft & \K[\FDSYMleftarrowtail]\leftarrowtail & \K[\FDSYMrightwavearrow]\rightwavearrow \\ \K[\FDSYMacwcirclearrowright]\acwcirclearrowright & \K[\FDSYMleftbkarrow]\leftbkarrow & \K[\FDSYMRrightarrow]\Rrightarrow \\ \K[\FDSYMacwcirclearrowup]\acwcirclearrowup & \K[\FDSYMleftleftarrows]\leftleftarrows & \K[\FDSYMRsh]\Rsh \\ \K[\FDSYMacwleftarcarrow]\acwleftarcarrow & \K[\FDSYMleftmapsto]\leftmapsto & \K[\FDSYMsearrow]\searrow \\ \K[\FDSYMacwnearcarrow]\acwnearcarrow & \K[\FDSYMLeftmapsto]\Leftmapsto & \K[\FDSYMSearrow]\Searrow \\ \K[\FDSYMacwnwarcarrow]\acwnwarcarrow & \K[\FDSYMLeftrightarrow]\Leftrightarrow & \K[\FDSYMsearrowtail]\searrowtail \\ \K[\FDSYMacwoverarcarrow]\acwoverarcarrow & \K[\FDSYMleftrightarrow]\leftrightarrow & \K[\FDSYMsebkarrow]\sebkarrow \\ \K[\FDSYMacwrightarcarrow]\acwrightarcarrow & \K[\FDSYMleftrightarrows]\leftrightarrows & \K[\FDSYMsenwarrows]\senwarrows \\ \K[\FDSYMacwsearcarrow]\acwsearcarrow & \K[\FDSYMleftrightwavearrow]\leftrightwavearrow & \K[\FDSYMsesearrows]\sesearrows \\ \K[\FDSYMacwswarcarrow]\acwswarcarrow & \K[\FDSYMleftwavearrow]\leftwavearrow & \K[\FDSYMSwarrow]\Swarrow \\ \K[\FDSYMacwunderarcarrow]\acwunderarcarrow & \K[\FDSYMlightning]\lightning & \K[\FDSYMswarrow]\swarrow \\ \K[\FDSYMbdleftarcarrow]\bdleftarcarrow & \K[\FDSYMLleftarrow]\Lleftarrow & \K[\FDSYMswarrowtail]\swarrowtail \\ \K[\FDSYMbdnearcarrow]\bdnearcarrow & \K[\FDSYMLongleftarrow]\Longleftarrow & \K[\FDSYMswbkarrow]\swbkarrow \\ \K[\FDSYMbdnwarcarrow]\bdnwarcarrow & \K[\FDSYMlongleftarrow]\longleftarrow & \K[\FDSYMswnearrows]\swnearrows \\ \K[\FDSYMbdoverarcarrow]\bdoverarcarrow & \K[\FDSYMlongleftrightarrow]\longleftrightarrow & \K[\FDSYMswswarrows]\swswarrows \\ \K[\FDSYMbdrightarcarrow]\bdrightarcarrow & \K[\FDSYMLongleftrightarrow]\Longleftrightarrow & \K[\FDSYMtwoheaddownarrow]\twoheaddownarrow \\ \K[\FDSYMbdsearcarrow]\bdsearcarrow & \K[\FDSYMlongleftwavearrow]\longleftwavearrow & \K[\FDSYMtwoheadleftarrow]\twoheadleftarrow \\ \K[\FDSYMbdswarcarrow]\bdswarcarrow & \K[\FDSYMLongmapsfrom]\Longmapsfrom & \K[\FDSYMtwoheadnearrow]\twoheadnearrow \\ \K[\FDSYMbdunderarcarrow]\bdunderarcarrow & \K[\FDSYMlongmapsfrom]\longmapsfrom & \K[\FDSYMtwoheadnwarrow]\twoheadnwarrow \\ \K[\FDSYMcwcirclearrowdown]\cwcirclearrowdown & \K[\FDSYMLongmapsto]\Longmapsto & \K[\FDSYMtwoheadrightarrow]\twoheadrightarrow \\ \K[\FDSYMcwcirclearrowleft]\cwcirclearrowleft & \K[\FDSYMlongmapsto]\longmapsto & \K[\FDSYMtwoheadsearrow]\twoheadsearrow \\ \K[\FDSYMcwcirclearrowright]\cwcirclearrowright & \K[\FDSYMlongrightarrow]\longrightarrow & \K[\FDSYMtwoheadswarrow]\twoheadswarrow \\ \K[\FDSYMcwcirclearrowup]\cwcirclearrowup & \K[\FDSYMLongrightarrow]\Longrightarrow & \K[\FDSYMtwoheaduparrow]\twoheaduparrow \\ \K[\FDSYMcwleftarcarrow]\cwleftarcarrow & \K[\FDSYMlongrightwavearrow]\longrightwavearrow & \K[\FDSYMuparrow]\uparrow \\ \K[\FDSYMcwnearcarrow]\cwnearcarrow & \K[\FDSYMlooparrowleft]\looparrowleft & \K[\FDSYMUparrow]\Uparrow \\ \K[\FDSYMcwnwarcarrow]\cwnwarcarrow & \K[\FDSYMlooparrowright]\looparrowright & \K[\FDSYMuparrowtail]\uparrowtail \\ \K[\FDSYMcwoverarcarrow]\cwoverarcarrow & \K[\FDSYMLsh]\Lsh & \K[\FDSYMupbkarrow]\upbkarrow \\ \K[\FDSYMcwrightarcarrow]\cwrightarcarrow & \K[\FDSYMnearrow]\nearrow & \K[\FDSYMUpdownarrow]\Updownarrow \\ \K[\FDSYMcwsearcarrow]\cwsearcarrow & \K[\FDSYMNearrow]\Nearrow & \K[\FDSYMupdownarrow]\updownarrow \\ \K[\FDSYMcwswarcarrow]\cwswarcarrow & \K[\FDSYMnearrowtail]\nearrowtail & \K[\FDSYMupdownarrows]\updownarrows \\ \K[\FDSYMcwunderarcarrow]\cwunderarcarrow & \K[\FDSYMnebkarrow]\nebkarrow & \K[\FDSYMupdownwavearrow]\updownwavearrow \\ \K[\FDSYMDdownarrow]\Ddownarrow & \K[\FDSYMnenearrows]\nenearrows & \K[\FDSYMupmapsto]\upmapsto \\ \K[\FDSYMDownarrow]\Downarrow & \K[\FDSYMNeswarrow]\Neswarrow & \K[\FDSYMUpmapsto]\Upmapsto \\ \K[\FDSYMdownarrow]\downarrow & \K[\FDSYMneswarrow]\neswarrow & \K[\FDSYMupuparrows]\upuparrows \\ \K[\FDSYMdownarrowtail]\downarrowtail & \K[\FDSYMneswarrows]\neswarrows & \K[\FDSYMupwavearrow]\upwavearrow \\ \K[\FDSYMdownbkarrow]\downbkarrow & \K[\FDSYMNwarrow]\Nwarrow & \K[\FDSYMUuparrow]\Uuparrow \\ \K[\FDSYMdowndownarrows]\downdownarrows & \K[\FDSYMnwarrow]\nwarrow & \K[\FDSYMvardownwavearrow]\vardownwavearrow \\ \K[\FDSYMDownmapsto]\Downmapsto & \K[\FDSYMnwarrowtail]\nwarrowtail & \K[\FDSYMvarhookdownarrow]\varhookdownarrow \\ \K[\FDSYMdownmapsto]\downmapsto & \K[\FDSYMnwbkarrow]\nwbkarrow & \K[\FDSYMvarhookleftarrow]\varhookleftarrow \\ \K[\FDSYMdownuparrows]\downuparrows & \K[\FDSYMnwnwarrows]\nwnwarrows & \K[\FDSYMvarhooknearrow]\varhooknearrow \\ \K[\FDSYMdownwavearrow]\downwavearrow & \K[\FDSYMNwsearrow]\Nwsearrow & \K[\FDSYMvarhooknwarrow]\varhooknwarrow \\ \K[\FDSYMhookdownarrow]\hookdownarrow & \K[\FDSYMnwsearrow]\nwsearrow & \K[\FDSYMvarhookrightarrow]\varhookrightarrow \\ \K[\FDSYMhookleftarrow]\hookleftarrow & \K[\FDSYMnwsearrows]\nwsearrows & \K[\FDSYMvarhooksearrow]\varhooksearrow \\ \K[\FDSYMhooknearrow]\hooknearrow & \K[\FDSYMRdsh]\Rdsh & \K[\FDSYMvarhookswarrow]\varhookswarrow \\ \K[\FDSYMhooknwarrow]\hooknwarrow & \K[\FDSYMRightarrow]\Rightarrow & \K[\FDSYMvarhookuparrow]\varhookuparrow \\ \K[\FDSYMhookrightarrow]\hookrightarrow & \K[\FDSYMrightarrow]\rightarrow & \K[\FDSYMvarleftrightwavearrow]\varleftrightwavearrow \\ \K[\FDSYMhooksearrow]\hooksearrow & \K[\FDSYMrightarrowtail]\rightarrowtail & \K[\FDSYMvarleftwavearrow]\varleftwavearrow \\ \K[\FDSYMhookswarrow]\hookswarrow & \K[\FDSYMrightbkarrow]\rightbkarrow & \K[\FDSYMvarrightwavearrow]\varrightwavearrow \\ \K[\FDSYMhookuparrow]\hookuparrow & \K[\FDSYMrightleftarrows]\rightleftarrows & \K[\FDSYMvarupdownwavearrow]\varupdownwavearrow \\ \K[\FDSYMLdsh]\Ldsh & \K[\FDSYMRightmapsto]\Rightmapsto & \K[\FDSYMvarupwavearrow]\varupwavearrow \\ \K[\FDSYMLeftarrow]\Leftarrow & \K[\FDSYMrightmapsto]\rightmapsto & \\ \end{longtable} \FDSYM\ defines synonyms for most of the preceding symbols: \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMacwgapcirclearrow]{\acwgapcirclearrow} & \K[\FDSYMleftrightsquigarrow]{\leftrightsquigarrow} & \K[\FDSYMrhooknwarrow]{\rhooknwarrow} \\ \K[\FDSYMacwopencirclearrow]{\acwopencirclearrow} & \K[\FDSYMleftrsquigarrow]{\leftrsquigarrow} & \K[\FDSYMrhookrightarrow]{\rhookrightarrow} \\ \K[\FDSYMcirclearrowleft]{\circlearrowleft} & \K[\FDSYMleftsquigarrow]{\leftsquigarrow} & \K[\FDSYMrhooksearrow]{\rhooksearrow} \\ \K[\FDSYMcirclearrowright]{\circlearrowright} & \K[\FDSYMleftupcurvedarrow]{\leftupcurvedarrow} & \K[\FDSYMrhookswarrow]{\rhookswarrow} \\ \K[\FDSYMcurvearrowleft]{\curvearrowleft} & \K[\FDSYMlhookdownarrow]{\lhookdownarrow} & \K[\FDSYMrhookuparrow]{\rhookuparrow} \\ \K[\FDSYMcurvearrowright]{\curvearrowright} & \K[\FDSYMlhookleftarrow]{\lhookleftarrow} & \K[\FDSYMrightcurvedarrow]{\rightcurvedarrow} \\ \K[\FDSYMcwgapcirclearrow]{\cwgapcirclearrow} & \K[\FDSYMlhooknearrow]{\lhooknearrow} & \K[\FDSYMrightdowncurvedarrow]{\rightdowncurvedarrow} \\ \K[\FDSYMcwopencirclearrow]{\cwopencirclearrow} & \K[\FDSYMlhooknwarrow]{\lhooknwarrow} & \K[\FDSYMrightlcurvearrow]{\rightlcurvearrow} \\ \K[\FDSYMdasharrow]{\dasharrow} & \K[\FDSYMlhookrightarrow]{\lhookrightarrow} & \K[\FDSYMrightleftcurvearrow]{\rightleftcurvearrow} \\ \K[\FDSYMdashleftarrow]{\dashleftarrow} & \K[\FDSYMlhooksearrow]{\lhooksearrow} & \K[\FDSYMrightleftsquigarrow]{\rightleftsquigarrow} \\ \K[\FDSYMdashrightarrow]{\dashrightarrow} & \K[\FDSYMlhookswarrow]{\lhookswarrow} & \K[\FDSYMrightlsquigarrow]{\rightlsquigarrow} \\ \K[\FDSYMdownlcurvearrow]{\downlcurvearrow} & \K[\FDSYMlhookuparrow]{\lhookuparrow} & \K[\FDSYMrightrcurvearrow]{\rightrcurvearrow} \\ \K[\FDSYMdownleftcurvedarrow]{\downleftcurvedarrow} & \K[\FDSYMlongleadsto]{\longleadsto} & \K[\FDSYMrightrsquigarrow]{\rightrsquigarrow} \\ \K[\FDSYMdownlsquigarrow]{\downlsquigarrow} & \K[\FDSYMlongleftsquigarrow]{\longleftsquigarrow} & \K[\FDSYMrightsquigarrow]{\rightsquigarrow} \\ \K[\FDSYMdownrcurvearrow]{\downrcurvearrow} & \K[\FDSYMlongrightsquigarrow]{\longrightsquigarrow} & \K[\FDSYMrightupcurvedarrow]{\rightupcurvedarrow} \\ \K[\FDSYMdownrightcurvedarrow]{\downrightcurvedarrow} & \K[\FDSYMmapsdown]{\mapsdown} & \K[\FDSYMselcurvearrow]{\selcurvearrow} \\ \K[\FDSYMdownrsquigarrow]{\downrsquigarrow} & \K[\FDSYMMapsdown]{\Mapsdown} & \K[\FDSYMsenwcurvearrow]{\senwcurvearrow} \\ \K[\FDSYMdownupcurvearrow]{\downupcurvearrow} & \K[\FDSYMmapsfrom]{\mapsfrom} & \K[\FDSYMsercurvearrow]{\sercurvearrow} \\ \K[\FDSYMdownupsquigarrow]{\downupsquigarrow} & \K[\FDSYMMapsfrom]{\Mapsfrom} & \K[\FDSYMswlcurvearrow]{\swlcurvearrow} \\ \K[\FDSYMdownzigzagarrow]{\downzigzagarrow} & \K[\FDSYMmapsto]{\mapsto} & \K[\FDSYMswnecurvearrow]{\swnecurvearrow} \\ \K[\FDSYMgets]{\gets} & \K[\FDSYMMapsto]{\Mapsto} & \K[\FDSYMswrcurvearrow]{\swrcurvearrow} \\ \K[\FDSYMhknearrow]{\hknearrow} & \K[\FDSYMmapsup]{\mapsup} & \K[\FDSYMto]{\to} \\ \K[\FDSYMhknwarrow]{\hknwarrow} & \K[\FDSYMMapsup]{\Mapsup} & \K[\FDSYMupdowncurvearrow]{\updowncurvearrow} \\ \K[\FDSYMhksearrow]{\hksearrow} & \K[\FDSYMnelcurvearrow]{\nelcurvearrow} & \K[\FDSYMupdownsquigarrow]{\updownsquigarrow} \\ \K[\FDSYMhkswarrow]{\hkswarrow} & \K[\FDSYMnercurvearrow]{\nercurvearrow} & \K[\FDSYMuplcurvearrow]{\uplcurvearrow} \\ \K[\FDSYMleadsto]{\leadsto} & \K[\FDSYMneswcurvearrow]{\neswcurvearrow} & \K[\FDSYMupleftcurvedarrow]{\upleftcurvedarrow} \\ \K[\FDSYMleftcurvedarrow]{\leftcurvedarrow} & \K[\FDSYMnwlcurvearrow]{\nwlcurvearrow} & \K[\FDSYMuplsquigarrow]{\uplsquigarrow} \\ \K[\FDSYMleftdowncurvedarrow]{\leftdowncurvedarrow} & \K[\FDSYMnwrcurvearrow]{\nwrcurvearrow} & \K[\FDSYMuprcurvearrow]{\uprcurvearrow} \\ \K[\FDSYMleftlcurvearrow]{\leftlcurvearrow} & \K[\FDSYMnwsecurvearrow]{\nwsecurvearrow} & \K[\FDSYMuprightcurvearrow]{\uprightcurvearrow} \\ \K[\FDSYMleftlsquigarrow]{\leftlsquigarrow} & \K[\FDSYMrhookdownarrow]{\rhookdownarrow} & \K[\FDSYMuprsquigarrow]{\uprsquigarrow} \\ \K[\FDSYMleftrcurvearrow]{\leftrcurvearrow} & \K[\FDSYMrhookleftarrow]{\rhookleftarrow} & \\ \K[\FDSYMleftrightcurvearrow]{\leftrightcurvearrow} & \K[\FDSYMrhooknearrow]{\rhooknearrow} & \\ \end{longtable} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Negated Arrows} \ltsubindex{arrows}{negated} \label{fdsym-narrows} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMnacwcirclearrowdown]\nacwcirclearrowdown & \K[\FDSYMnleftarrow]\nleftarrow & \K[\FDSYMnRrightarrow]\nRrightarrow \\ \K[\FDSYMnacwcirclearrowleft]\nacwcirclearrowleft & \K[\FDSYMnLeftarrow]\nLeftarrow & \K[\FDSYMnsearrow]\nsearrow \\ \K[\FDSYMnacwcirclearrowright]\nacwcirclearrowright & \K[\FDSYMnleftarrowtail]\nleftarrowtail & \K[\FDSYMnSearrow]\nSearrow \\ \K[\FDSYMnacwcirclearrowup]\nacwcirclearrowup & \K[\FDSYMnleftbkarrow]\nleftbkarrow & \K[\FDSYMnsearrowtail]\nsearrowtail \\ \K[\FDSYMnacwleftarcarrow]\nacwleftarcarrow & \K[\FDSYMnleftleftarrows]\nleftleftarrows & \K[\FDSYMnsebkarrow]\nsebkarrow \\ \K[\FDSYMnacwnearcarrow]\nacwnearcarrow & \K[\FDSYMnleftmapsto]\nleftmapsto & \K[\FDSYMnsenwarrows]\nsenwarrows \\ \K[\FDSYMnacwnwarcarrow]\nacwnwarcarrow & \K[\FDSYMnLeftmapsto]\nLeftmapsto & \K[\FDSYMnsesearrows]\nsesearrows \\ \K[\FDSYMnacwoverarcarrow]\nacwoverarcarrow & \K[\FDSYMnleftrightarrow]\nleftrightarrow & \K[\FDSYMnswarrow]\nswarrow \\ \K[\FDSYMnacwrightarcarrow]\nacwrightarcarrow & \K[\FDSYMnLeftrightarrow]\nLeftrightarrow & \K[\FDSYMnSwarrow]\nSwarrow \\ \K[\FDSYMnacwsearcarrow]\nacwsearcarrow & \K[\FDSYMnleftrightarrows]\nleftrightarrows & \K[\FDSYMnswarrowtail]\nswarrowtail \\ \K[\FDSYMnacwswarcarrow]\nacwswarcarrow & \K[\FDSYMnleftrightwavearrow]\nleftrightwavearrow & \K[\FDSYMnswbkarrow]\nswbkarrow \\ \K[\FDSYMnacwunderarcarrow]\nacwunderarcarrow & \K[\FDSYMnleftwavearrow]\nleftwavearrow & \K[\FDSYMnswnearrows]\nswnearrows \\ \K[\FDSYMnbdleftarcarrow]\nbdleftarcarrow & \K[\FDSYMnLleftarrow]\nLleftarrow & \K[\FDSYMnswswarrows]\nswswarrows \\ \K[\FDSYMnbdnearcarrow]\nbdnearcarrow & \K[\FDSYMnlongleftarrow]\nlongleftarrow & \K[\FDSYMntwoheaddownarrow]\ntwoheaddownarrow \\ \K[\FDSYMnbdnwarcarrow]\nbdnwarcarrow & \K[\FDSYMnLongleftarrow]\nLongleftarrow & \K[\FDSYMntwoheadleftarrow]\ntwoheadleftarrow \\ \K[\FDSYMnbdoverarcarrow]\nbdoverarcarrow & \K[\FDSYMnlongleftrightarrow]\nlongleftrightarrow & \K[\FDSYMntwoheadnearrow]\ntwoheadnearrow \\ \K[\FDSYMnbdrightarcarrow]\nbdrightarcarrow & \K[\FDSYMnLongleftrightarrow]\nLongleftrightarrow & \K[\FDSYMntwoheadnwarrow]\ntwoheadnwarrow \\ \K[\FDSYMnbdsearcarrow]\nbdsearcarrow & \K[\FDSYMnlongleftwavearrow]\nlongleftwavearrow & \K[\FDSYMntwoheadrightarrow]\ntwoheadrightarrow \\ \K[\FDSYMnbdswarcarrow]\nbdswarcarrow & \K[\FDSYMnlongmapsfrom]\nlongmapsfrom & \K[\FDSYMntwoheadsearrow]\ntwoheadsearrow \\ \K[\FDSYMnbdunderarcarrow]\nbdunderarcarrow & \K[\FDSYMnLongmapsfrom]\nLongmapsfrom & \K[\FDSYMntwoheadswarrow]\ntwoheadswarrow \\ \K[\FDSYMncwcirclearrowdown]\ncwcirclearrowdown & \K[\FDSYMnlongmapsto]\nlongmapsto & \K[\FDSYMntwoheaduparrow]\ntwoheaduparrow \\ \K[\FDSYMncwcirclearrowleft]\ncwcirclearrowleft & \K[\FDSYMnLongmapsto]\nLongmapsto & \K[\FDSYMnuparrow]\nuparrow \\ \K[\FDSYMncwcirclearrowright]\ncwcirclearrowright & \K[\FDSYMnlongrightarrow]\nlongrightarrow & \K[\FDSYMnUparrow]\nUparrow \\ \K[\FDSYMncwcirclearrowup]\ncwcirclearrowup & \K[\FDSYMnLongrightarrow]\nLongrightarrow & \K[\FDSYMnuparrowtail]\nuparrowtail \\ \K[\FDSYMncwleftarcarrow]\ncwleftarcarrow & \K[\FDSYMnlongrightwavearrow]\nlongrightwavearrow & \K[\FDSYMnupbkarrow]\nupbkarrow \\ \K[\FDSYMncwnearcarrow]\ncwnearcarrow & \K[\FDSYMnnearrow]\nnearrow & \K[\FDSYMnupdownarrow]\nupdownarrow \\ \K[\FDSYMncwnwarcarrow]\ncwnwarcarrow & \K[\FDSYMnNearrow]\nNearrow & \K[\FDSYMnUpdownarrow]\nUpdownarrow \\ \K[\FDSYMncwoverarcarrow]\ncwoverarcarrow & \K[\FDSYMnnearrowtail]\nnearrowtail & \K[\FDSYMnupdownarrows]\nupdownarrows \\ \K[\FDSYMncwrightarcarrow]\ncwrightarcarrow & \K[\FDSYMnnebkarrow]\nnebkarrow & \K[\FDSYMnupdownwavearrow]\nupdownwavearrow \\ \K[\FDSYMncwsearcarrow]\ncwsearcarrow & \K[\FDSYMnnenearrows]\nnenearrows & \K[\FDSYMnupmapsto]\nupmapsto \\ \K[\FDSYMncwswarcarrow]\ncwswarcarrow & \K[\FDSYMnneswarrow]\nneswarrow & \K[\FDSYMnUpmapsto]\nUpmapsto \\ \K[\FDSYMncwunderarcarrow]\ncwunderarcarrow & \K[\FDSYMnNeswarrow]\nNeswarrow & \K[\FDSYMnupuparrows]\nupuparrows \\ \K[\FDSYMnDdownarrow]\nDdownarrow & \K[\FDSYMnneswarrows]\nneswarrows & \K[\FDSYMnupwavearrow]\nupwavearrow \\ \K[\FDSYMndownarrow]\ndownarrow & \K[\FDSYMnnwarrow]\nnwarrow & \K[\FDSYMnUuparrow]\nUuparrow \\ \K[\FDSYMnDownarrow]\nDownarrow & \K[\FDSYMnNwarrow]\nNwarrow & \K[\FDSYMnvardownwavearrow]\nvardownwavearrow \\ \K[\FDSYMndownarrowtail]\ndownarrowtail & \K[\FDSYMnnwarrowtail]\nnwarrowtail & \K[\FDSYMnvarhookdownarrow]\nvarhookdownarrow \\ \K[\FDSYMndownbkarrow]\ndownbkarrow & \K[\FDSYMnnwbkarrow]\nnwbkarrow & \K[\FDSYMnvarhookleftarrow]\nvarhookleftarrow \\ \K[\FDSYMndowndownarrows]\ndowndownarrows & \K[\FDSYMnnwnwarrows]\nnwnwarrows & \K[\FDSYMnvarhooknearrow]\nvarhooknearrow \\ \K[\FDSYMndownmapsto]\ndownmapsto & \K[\FDSYMnnwsearrow]\nnwsearrow & \K[\FDSYMnvarhooknwarrow]\nvarhooknwarrow \\ \K[\FDSYMnDownmapsto]\nDownmapsto & \K[\FDSYMnNwsearrow]\nNwsearrow & \K[\FDSYMnvarhookrightarrow]\nvarhookrightarrow \\ \K[\FDSYMndownuparrows]\ndownuparrows & \K[\FDSYMnnwsearrows]\nnwsearrows & \K[\FDSYMnvarhooksearrow]\nvarhooksearrow \\ \K[\FDSYMndownwavearrow]\ndownwavearrow & \K[\FDSYMnrightarrow]\nrightarrow & \K[\FDSYMnvarhookswarrow]\nvarhookswarrow \\ \K[\FDSYMnhookdownarrow]\nhookdownarrow & \K[\FDSYMnRightarrow]\nRightarrow & \K[\FDSYMnvarhookuparrow]\nvarhookuparrow \\ \K[\FDSYMnhookleftarrow]\nhookleftarrow & \K[\FDSYMnrightarrowtail]\nrightarrowtail & \K[\FDSYMnvarleftrightwavearrow]\nvarleftrightwavearrow \\ \K[\FDSYMnhooknearrow]\nhooknearrow & \K[\FDSYMnrightbkarrow]\nrightbkarrow & \K[\FDSYMnvarleftwavearrow]\nvarleftwavearrow \\ \K[\FDSYMnhooknwarrow]\nhooknwarrow & \K[\FDSYMnrightleftarrows]\nrightleftarrows & \K[\FDSYMnvarrightwavearrow]\nvarrightwavearrow \\ \K[\FDSYMnhookrightarrow]\nhookrightarrow & \K[\FDSYMnrightmapsto]\nrightmapsto & \K[\FDSYMnvarupdownwavearrow]\nvarupdownwavearrow \\ \K[\FDSYMnhooksearrow]\nhooksearrow & \K[\FDSYMnRightmapsto]\nRightmapsto & \K[\FDSYMnvarupwavearrow]\nvarupwavearrow \\ \K[\FDSYMnhookswarrow]\nhookswarrow & \K[\FDSYMnrightrightarrows]\nrightrightarrows & \\ \K[\FDSYMnhookuparrow]\nhookuparrow & \K[\FDSYMnrightwavearrow]\nrightwavearrow & \\ \end{longtable} \FDSYM\ defines synonyms for most of the preceding symbols: \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\FDSYMnacwgapcirclearrow]{\nacwgapcirclearrow} & \K[\FDSYMnleftdowncurvedarrow]{\nleftdowncurvedarrow} & \K[\FDSYMnrightcurvedarrow]{\nrightcurvedarrow} \\ \K[\FDSYMnacwopencirclearrow]{\nacwopencirclearrow} & \K[\FDSYMnleftlcurvearrow]{\nleftlcurvearrow} & \K[\FDSYMnrightdowncurvedarrow]{\nrightdowncurvedarrow} \\ \K[\FDSYMncirclearrowleft]{\ncirclearrowleft} & \K[\FDSYMnleftlsquigarrow]{\nleftlsquigarrow} & \K[\FDSYMnrightlcurvearrow]{\nrightlcurvearrow} \\ \K[\FDSYMncirclearrowright]{\ncirclearrowright} & \K[\FDSYMnleftrcurvearrow]{\nleftrcurvearrow} & \K[\FDSYMnrightleftcurvearrow]{\nrightleftcurvearrow} \\ \K[\FDSYMncurvearrowleft]{\ncurvearrowleft} & \K[\FDSYMnleftrightcurvearrow]{\nleftrightcurvearrow} & \K[\FDSYMnrightleftsquigarrow]{\nrightleftsquigarrow} \\ \K[\FDSYMncurvearrowright]{\ncurvearrowright} & \K[\FDSYMnleftrightsquigarrow]{\nleftrightsquigarrow} & \K[\FDSYMnrightlsquigarrow]{\nrightlsquigarrow} \\ \K[\FDSYMncwgapcirclearrow]{\ncwgapcirclearrow} & \K[\FDSYMnleftrsquigarrow]{\nleftrsquigarrow} & \K[\FDSYMnrightrcurvearrow]{\nrightrcurvearrow} \\ \K[\FDSYMncwopencirclearrow]{\ncwopencirclearrow} & \K[\FDSYMnleftsquigarrow]{\nleftsquigarrow} & \K[\FDSYMnrightrsquigarrow]{\nrightrsquigarrow} \\ \K[\FDSYMndasharrow]{\ndasharrow} & \K[\FDSYMnleftupcurvedarrow]{\nleftupcurvedarrow} & \K[\FDSYMnrightsquigarrow]{\nrightsquigarrow} \\ \K[\FDSYMndashleftarrow]{\ndashleftarrow} & \K[\FDSYMnlongleadsto]{\nlongleadsto} & \K[\FDSYMnrightupcurvedarrow]{\nrightupcurvedarrow} \\ \K[\FDSYMndashrightarrow]{\ndashrightarrow} & \K[\FDSYMnlongleftsquigarrow]{\nlongleftsquigarrow} & \K[\FDSYMnselcurvearrow]{\nselcurvearrow} \\ \K[\FDSYMndownlcurvearrow]{\ndownlcurvearrow} & \K[\FDSYMnlongrightsquigarrow]{\nlongrightsquigarrow} & \K[\FDSYMnsenwcurvearrow]{\nsenwcurvearrow} \\ \K[\FDSYMndownleftcurvedarrow]{\ndownleftcurvedarrow} & \K[\FDSYMnmapsdown]{\nmapsdown} & \K[\FDSYMnsercurvearrow]{\nsercurvearrow} \\ \K[\FDSYMndownlsquigarrow]{\ndownlsquigarrow} & \K[\FDSYMnMapsdown]{\nMapsdown} & \K[\FDSYMnswlcurvearrow]{\nswlcurvearrow} \\ \K[\FDSYMndownrcurvearrow]{\ndownrcurvearrow} & \K[\FDSYMnmapsfrom]{\nmapsfrom} & \K[\FDSYMnswnecurvearrow]{\nswnecurvearrow} \\ \K[\FDSYMndownrightcurvedarrow]{\ndownrightcurvedarrow} & \K[\FDSYMnMapsfrom]{\nMapsfrom} & \K[\FDSYMnswrcurvearrow]{\nswrcurvearrow} \\ \K[\FDSYMndownrsquigarrow]{\ndownrsquigarrow} & \K[\FDSYMnmapsto]{\nmapsto} & \K[\FDSYMnto]{\nto} \\ \K[\FDSYMndownupcurvearrow]{\ndownupcurvearrow} & \K[\FDSYMnMapsto]{\nMapsto} & \K[\FDSYMnupdowncurvearrow]{\nupdowncurvearrow} \\ \K[\FDSYMndownupsquigarrow]{\ndownupsquigarrow} & \K[\FDSYMnmapsup]{\nmapsup} & \K[\FDSYMnupdownsquigarrow]{\nupdownsquigarrow} \\ \K[\FDSYMngets]{\ngets} & \K[\FDSYMnMapsup]{\nMapsup} & \K[\FDSYMnuplcurvearrow]{\nuplcurvearrow} \\ \K[\FDSYMnhknearrow]{\nhknearrow} & \K[\FDSYMnnelcurvearrow]{\nnelcurvearrow} & \K[\FDSYMnupleftcurvedarrow]{\nupleftcurvedarrow} \\ \K[\FDSYMnhknwarrow]{\nhknwarrow} & \K[\FDSYMnnercurvearrow]{\nnercurvearrow} & \K[\FDSYMnuplsquigarrow]{\nuplsquigarrow} \\ \K[\FDSYMnhksearrow]{\nhksearrow} & \K[\FDSYMnneswcurvearrow]{\nneswcurvearrow} & \K[\FDSYMnuprcurvearrow]{\nuprcurvearrow} \\ \K[\FDSYMnhkswarrow]{\nhkswarrow} & \K[\FDSYMnnwlcurvearrow]{\nnwlcurvearrow} & \K[\FDSYMnuprightcurvearrow]{\nuprightcurvearrow} \\ \K[\FDSYMnleadsto]{\nleadsto} & \K[\FDSYMnnwrcurvearrow]{\nnwrcurvearrow} & \K[\FDSYMnuprsquigarrow]{\nuprsquigarrow} \\ \K[\FDSYMnleftcurvedarrow]{\nleftcurvedarrow} & \K[\FDSYMnnwsecurvearrow]{\nnwsecurvearrow} & \\ \end{longtable} \end{longsymtable} \begin{symtable}[FDSYM]{\FDSYM\ Harpoons} \index{harpoons} \index{restrictions} \label{fdsym-harpoons} \begin{tabular}{*3{ll}} \K[\FDSYMdownharpoonleft]\downharpoonleft & \K[\FDSYMneswharpoons]\neswharpoons & \K[\FDSYMseharpoonsw]\seharpoonsw \\ \K[\FDSYMdownharpoonright]\downharpoonright & \K[\FDSYMneswharpoonsenw]\neswharpoonsenw & \K[\FDSYMsenwharpoons]\senwharpoons \\ \K[\FDSYMdownupharpoons]\downupharpoons & \K[\FDSYMnwharpoonne]\nwharpoonne & \K[\FDSYMswharpoonnw]\swharpoonnw \\ \K[\FDSYMleftharpoondown]\leftharpoondown & \K[\FDSYMnwharpoonsw]\nwharpoonsw & \K[\FDSYMswharpoonse]\swharpoonse \\ \K[\FDSYMleftharpoonup]\leftharpoonup & \K[\FDSYMnwseharpoonnesw]\nwseharpoonnesw & \K[\FDSYMswneharpoons]\swneharpoons \\ \K[\FDSYMleftrightharpoondownup]\leftrightharpoondownup & \K[\FDSYMnwseharpoons]\nwseharpoons & \K[\FDSYMupdownharpoonleftright]\updownharpoonleftright \\ \K[\FDSYMleftrightharpoons]\leftrightharpoons & \K[\FDSYMnwseharpoonswne]\nwseharpoonswne & \K[\FDSYMupdownharpoonrightleft]\updownharpoonrightleft \\ \K[\FDSYMleftrightharpoonupdown]\leftrightharpoonupdown & \K[\FDSYMrightharpoondown]\rightharpoondown & \K[\FDSYMupdownharpoons]\updownharpoons \\ \K[\FDSYMneharpoonnw]\neharpoonnw & \K[\FDSYMrightharpoonup]\rightharpoonup & \K[\FDSYMupharpoonleft]\upharpoonleft \\ \K[\FDSYMneharpoonse]\neharpoonse & \K[\FDSYMrightleftharpoons]\rightleftharpoons & \K[\FDSYMupharpoonright]\upharpoonright \\ \K[\FDSYMneswharpoonnwse]\neswharpoonnwse & \K[\FDSYMseharpoonne]\seharpoonne & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMrestriction]{\restriction} as a synonym for \cmdI[\string\FDSYMupharpoonright]{\upharpoonright}, \cmdI[\string\FDSYMupdownharpoonsleftright]{\updownharpoonsleftright} as a synonym for \cmdI[\string\FDSYMupdownharpoons]{\updownharpoons}, and \cmdI[\string\FDSYMdownupharpoonsleftright]{\downupharpoonsleftright} as a synonym for \cmdI[\string\FDSYMdownupharpoons]{\downupharpoons}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Negated Harpoons} \index{harpoons} \index{restrictions} \label{fdsym-nharpoons} \begin{tabular}{*3{ll}} \K[\FDSYMndownharpoonleft]\ndownharpoonleft & \K[\FDSYMnneswharpoons]\nneswharpoons & \K[\FDSYMnseharpoonsw]\nseharpoonsw \\ \K[\FDSYMndownharpoonright]\ndownharpoonright & \K[\FDSYMnneswharpoonsenw]\nneswharpoonsenw & \K[\FDSYMnsenwharpoons]\nsenwharpoons \\ \K[\FDSYMndownupharpoons]\ndownupharpoons & \K[\FDSYMnnwharpoonne]\nnwharpoonne & \K[\FDSYMnswharpoonnw]\nswharpoonnw \\ \K[\FDSYMnleftharpoondown]\nleftharpoondown & \K[\FDSYMnnwharpoonsw]\nnwharpoonsw & \K[\FDSYMnswharpoonse]\nswharpoonse \\ \K[\FDSYMnleftharpoonup]\nleftharpoonup & \K[\FDSYMnnwseharpoonnesw]\nnwseharpoonnesw & \K[\FDSYMnswneharpoons]\nswneharpoons \\ \K[\FDSYMnleftrightharpoondownup]\nleftrightharpoondownup & \K[\FDSYMnnwseharpoons]\nnwseharpoons & \K[\FDSYMnupdownharpoonleftright]\nupdownharpoonleftright \\ \K[\FDSYMnleftrightharpoons]\nleftrightharpoons & \K[\FDSYMnnwseharpoonswne]\nnwseharpoonswne & \K[\FDSYMnupdownharpoonrightleft]\nupdownharpoonrightleft \\ \K[\FDSYMnleftrightharpoonupdown]\nleftrightharpoonupdown & \K[\FDSYMnrightharpoondown]\nrightharpoondown & \K[\FDSYMnupdownharpoons]\nupdownharpoons \\ \K[\FDSYMnneharpoonnw]\nneharpoonnw & \K[\FDSYMnrightharpoonup]\nrightharpoonup & \K[\FDSYMnupharpoonleft]\nupharpoonleft \\ \K[\FDSYMnneharpoonse]\nneharpoonse & \K[\FDSYMnrightleftharpoons]\nrightleftharpoons & \K[\FDSYMnupharpoonright]\nupharpoonright \\ \K[\FDSYMnneswharpoonnwse]\nneswharpoonnwse & \K[\FDSYMnseharpoonne]\nseharpoonne & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMnrestriction]{\nrestriction} as a synonym for \cmdI[\string\FDSYMnupharpoonright]{\nupharpoonright}, \cmdI[\string\FDSYMndownupharpoonsleftright]{\ndownupharpoonsleftright} as a synonym for \cmdI[\string\FDSYMndownupharpoons]{\ndownupharpoons}, and \cmdI[\string\FDSYMnupdownharpoonsleftright]{\nupdownharpoonsleftright} as a synonym for \cmdI[\string\FDSYMnupdownharpoons]{\nupdownharpoons}. \end{tablenote} \end{symtable} \begin{longsymtable}[BSK]{\BSK\ Arrows} \ltindex{arrows} \ltindex{carriage return} \label{boisik-arrows} \begin{longtable}{*2{ll}} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\BSKbarleftarrow]\barleftarrow & \K[\BSKLsh]\Lsh \\ \K[\BSKbarleftarrowrightarrowbar]\barleftarrowrightarrowbar & \K[\BSKmapsdown]\mapsdown \\ \K[\BSKbarovernorthwestarrow]\barovernorthwestarrow & \K[\BSKMapsfrom]\Mapsfrom \\ \K[\BSKcarriagereturn]\carriagereturn & \K[\BSKmapsfrom]\mapsfrom \\ \K[\BSKcirclearrowleft]\circlearrowleft & \K[\BSKMapsto]\Mapsto \\ \K[\BSKcirclearrowright]\circlearrowright & \K[\BSKmapsto]\mapsto \\ \K[\BSKcupleftarrow]\cupleftarrow & \K[\BSKmapsup]\mapsup \\ \K[\BSKcurlyveedownarrow]\curlyveedownarrow & \K[\BSKNearrow]\Nearrow \\ \K[\BSKcurlyveeuparrow]\curlyveeuparrow & \K[\BSKnearrowcorner]\nearrowcorner \\ \K[\BSKcurlywedgedownarrow]\curlywedgedownarrow & \K[\BSKnnearrow]\nnearrow \\ \K[\BSKcurlywedgeuparrow]\curlywedgeuparrow & \K[\BSKnnwarrow]\nnwarrow \\ \K[\BSKcurvearrowbotleft]\curvearrowbotleft & \K[\BSKNwarrow]\Nwarrow \\ \K[\BSKcurvearrowbotleftright]\curvearrowbotleftright & \K[\BSKnwarrowcorner]\nwarrowcorner \\ \K[\BSKcurvearrowbotright]\curvearrowbotright & \K[\BSKrightarrowbar]\rightarrowbar \\ \K[\BSKcurvearrowleft]\curvearrowleft & \K[\BSKrightarrowcircle]\rightarrowcircle \\ \K[\BSKcurvearrowleftright]\curvearrowleftright & \K[\BSKrightarrowtail]\rightarrowtail \\ \K[\BSKcurvearrowright]\curvearrowright & \K[\BSKrightarrowTriangle]\rightarrowTriangle \\ \K[\BSKdlsh]\dlsh & \K[\BSKrightarrowtriangle]\rightarrowtriangle \\ \K[\BSKdownblackarrow]\downblackarrow & \K[\BSKrightblackarrow]\rightblackarrow \\ \K[\BSKdowndasharrow]\downdasharrow & \K[\BSKrightdasharrow]\rightdasharrow \\ \K[\BSKdowndownarrows]\downdownarrows & \K[\BSKrightleftarrows]\rightleftarrows \\ \K[\BSKdowntouparrow]\downtouparrow & \K[\BSKrightrightarrows]\rightrightarrows \\ \K[\BSKdownwhitearrow]\downwhitearrow & \K[\BSKrightsquigarrow]\rightsquigarrow \\ \K[\BSKdownzigzagarrow]\downzigzagarrow & \K[\BSKrightthreearrows]\rightthreearrows \\ \K[\BSKdrsh]\drsh & \K[\BSKrighttoleftarrow]\righttoleftarrow \\ \K[\BSKeqleftrightarrow]\eqleftrightarrow & \K[\BSKrightwhitearrow]\rightwhitearrow \\ \K[\BSKhookleftarrow]\hookleftarrow & \K[\BSKrightwhiteroundarrow]\rightwhiteroundarrow \\ \K[\BSKhookrightarrow]\hookrightarrow & \K[\BSKRrightarrow]\Rrightarrow \\ \K[\BSKleftarrowtail]\leftarrowtail & \K[\BSKRsh]\Rsh \\ \K[\BSKleftarrowTriangle]\leftarrowTriangle & \K[\BSKSearrow]\Searrow \\ \K[\BSKleftarrowtriangle]\leftarrowtriangle & \K[\BSKssearrow]\ssearrow \\ \K[\BSKleftblackarrow]\leftblackarrow & \K[\BSKsswarrow]\sswarrow \\ \K[\BSKleftdasharrow]\leftdasharrow & \K[\BSKSwarrow]\Swarrow \\ \K[\BSKleftleftarrows]\leftleftarrows & \K[\BSKtwoheaddownarrow]\twoheaddownarrow \\ \K[\BSKleftrightarroweq]\leftrightarroweq & \K[\BSKtwoheadleftarrow]\twoheadleftarrow \\ \K[\BSKleftrightarrows]\leftrightarrows & \K[\BSKtwoheadrightarrow]\twoheadrightarrow \\ \K[\BSKleftrightarrowTriangle]\leftrightarrowTriangle & \K[\BSKtwoheaduparrow]\twoheaduparrow \\ \K[\BSKleftrightarrowtriangle]\leftrightarrowtriangle & \K[\BSKtwoheadwhiteuparrow]\twoheadwhiteuparrow \\ \K[\BSKleftrightblackarrow]\leftrightblackarrow & \K[\BSKtwoheadwhiteuparrowpedestal]\twoheadwhiteuparrowpedestal \\ \K[\BSKleftrightsquigarrow]\leftrightsquigarrow & \K[\BSKupblackarrow]\upblackarrow \\ \K[\BSKleftsquigarrow]\leftsquigarrow & \K[\BSKupdasharrow]\updasharrow \\ \K[\BSKlefttorightarrow]\lefttorightarrow & \K[\BSKupdownarrowbar]\updownarrowbar \\ \K[\BSKleftwhitearrow]\leftwhitearrow & \K[\BSKupdownblackarrow]\updownblackarrow \\ \K[\BSKleftwhiteroundarrow]\leftwhiteroundarrow & \K[\BSKupdownwhitearrow]\updownwhitearrow \\ \K[\BSKleftzigzagarrow]\leftzigzagarrow & \K[\BSKuptodownarrow]\uptodownarrow \\ \K[\BSKlinefeed]\linefeed & \K[\BSKupuparrows]\upuparrows \\ \K[\BSKLleftarrow]\Lleftarrow & \K[\BSKupwhitearrow]\upwhitearrow \\ \K[\BSKlooparrowdownleft]\looparrowdownleft & \K[\BSKwhitearrowupfrombar]\whitearrowupfrombar \\ \K[\BSKlooparrowdownright]\looparrowdownright & \K[\BSKwhitearrowuppedestal]\whitearrowuppedestal \\ \K[\BSKlooparrowleft]\looparrowleft & \K[\BSKwhitearrowuppedestalhbar]\whitearrowuppedestalhbar \\ \K[\BSKlooparrowright]\looparrowright & \K[\BSKwhitearrowuppedestalvbar]\whitearrowuppedestalvbar \\ \end{longtable} \begin{tablenote} Many of these symbols are defined only if the \optname{boisik}{arrows} package option is specified. \end{tablenote} \end{longsymtable} \begin{symtable}[BSK]{\BSK\ Negated Arrows} \index{arrows} \label{boisik-narrows} \begin{tabular}{*3{ll}} \K[\BSKnHdownarrow]\nHdownarrow & \K[\BSKnLeftrightarroW]\nLeftrightarroW & \K[\BSKnRightarrow]\nRightarrow \\ \K[\BSKnHuparrow]\nHuparrow & \K[\BSKnleftrightarrow]\nleftrightarrow & \K[\BSKnVleftarrow]\nVleftarrow \\ \K[\BSKnLeftarrow]\nLeftarrow & \K[\BSKnLeftrightarrow]\nLeftrightarrow & \K[\BSKnVrightarrow]\nVrightarrow \\ \K[\BSKnleftarrow]\nleftarrow & \K[\BSKnrightarrow]\nrightarrow & \\ \end{tabular} \bigskip \begin{tablenote} Many of these symbols are defined only if the \optname{boisik}{arrows} package option is specified. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Harpoons} \index{harpoons} \label{bsk-harpoons} \begin{tabular}{*3{ll}} \K[\BSKdownharpoonleft]\downharpoonleft & \K[\BSKleftrightharpoons]\leftrightharpoons & \K[\BSKupharpoonleft]\upharpoonleft \\ \K[\BSKdownharpoonright]\downharpoonright & \K[\BSKrightharpoondown]\rightharpoondown & \K[\BSKupharpoonright]\upharpoonright \\ \K[\BSKleftharpoondown]\leftharpoondown & \K[\BSKrightharpoonup]\rightharpoonup & \\ \K[\BSKleftharpoonup]\leftharpoonup & \K[\BSKrightleftharpoons]\rightleftharpoons & \\ \end{tabular} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Arrows} \ltindex{arrows} \ltindex{carriage return} \label{stix-arrows} \begin{longtable}{*2{ll}} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXacwcirclearrow]\acwcirclearrow & \K[\STIXlongmapsto]\longmapsto \\ \K[\STIXacwgapcirclearrow]\acwgapcirclearrow & \K[\STIXLongmapsto]\Longmapsto \\ \K[\STIXacwleftarcarrow]\acwleftarcarrow & \K[\STIXlongrightarrow]\longrightarrow \\ \K[\STIXacwoverarcarrow]\acwoverarcarrow & \K[\STIXLongrightarrow]\Longrightarrow \\ \K[\STIXacwunderarcarrow]\acwunderarcarrow & \K[\STIXlongrightsquigarrow]\longrightsquigarrow \\ \K[\STIXbarleftarrow]\barleftarrow & \K[\STIXlooparrowleft]\looparrowleft \\ \K[\STIXbarleftarrowrightarrowbar]\barleftarrowrightarrowbar$^*$ & \K[\STIXlooparrowright]\looparrowright \\ \K[\STIXbarrightarrowdiamond]\barrightarrowdiamond & \K[\STIXLsh]\Lsh \\ \K[\STIXbaruparrow]\baruparrow & \K[\STIXmapsdown]\mapsdown \\ \K[\STIXbsimilarleftarrow]\bsimilarleftarrow & \K[\STIXMapsfrom]\Mapsfrom \\ \K[\STIXbsimilarrightarrow]\bsimilarrightarrow & \K[\STIXmapsfrom]\mapsfrom \\ \K[\STIXcarriagereturn]\carriagereturn$^*$ & \K[\STIXmapsto]\mapsto \\ \K[\STIXccwundercurvearrow]\ccwundercurvearrow & \K[\STIXMapsto]\Mapsto \\ \K[\STIXcirclearrowleft]\circlearrowleft & \K[\STIXmapsup]\mapsup \\ \K[\STIXcirclearrowright]\circlearrowright & \K[\STIXNearrow]\Nearrow \\ \K[\STIXcircleonleftarrow]\circleonleftarrow & \K[\STIXnearrow]\nearrow \\ \K[\STIXcircleonrightarrow]\circleonrightarrow & \K[\STIXneovnwarrow]\neovnwarrow$^*$ \\ \K[\STIXcurvearrowleft]\curvearrowleft & \K[\STIXneovsearrow]\neovsearrow$^*$ \\ \K[\STIXcurvearrowleftplus]\curvearrowleftplus & \K[\STIXneswarrow]\neswarrow \\ \K[\STIXcurvearrowright]\curvearrowright & \K[\STIXnwarrow]\nwarrow \\ \K[\STIXcurvearrowrightminus]\curvearrowrightminus & \K[\STIXNwarrow]\Nwarrow \\ \K[\STIXcwcirclearrow]\cwcirclearrow & \K[\STIXnwovnearrow]\nwovnearrow$^*$ \\ \K[\STIXcwgapcirclearrow]\cwgapcirclearrow & \K[\STIXnwsearrow]\nwsearrow \\ \K[\STIXcwrightarcarrow]\cwrightarcarrow & \K[\STIXrdiagovsearrow]\rdiagovsearrow$^*$ \\ \K[\STIXcwundercurvearrow]\cwundercurvearrow & \K[\STIXRdsh]\Rdsh \\ \K[\STIXdbkarow]\dbkarow & \K[\STIXRightarrow]\Rightarrow \\ \K[\STIXDDownarrow]\DDownarrow & \K[\STIXrightarrow]\rightarrow \\ \K[\STIXDdownarrow]\Ddownarrow & \K[\STIXrightarrowapprox]\rightarrowapprox \\ \K[\STIXdiamondleftarrow]\diamondleftarrow & \K[\STIXrightarrowbackapprox]\rightarrowbackapprox \\ \K[\STIXdiamondleftarrowbar]\diamondleftarrowbar & \K[\STIXrightarrowbar]\rightarrowbar \\ \K[\STIXdownarrow]\downarrow & \K[\STIXrightarrowbsimilar]\rightarrowbsimilar \\ \K[\STIXDownarrow]\Downarrow & \K[\STIXrightarrowdiamond]\rightarrowdiamond \\ \K[\STIXdownarrowbar]\downarrowbar & \K[\STIXrightarrowonoplus]\rightarrowonoplus \\ \K[\STIXdownarrowbarred]\downarrowbarred & \K[\STIXrightarrowplus]\rightarrowplus \\ \K[\STIXdowndasharrow]\downdasharrow$^*$ & \K[\STIXrightarrowshortleftarrow]\rightarrowshortleftarrow \\ \K[\STIXdowndownarrows]\downdownarrows & \K[\STIXrightarrowsimilar]\rightarrowsimilar \\ \K[\STIXdownrightcurvedarrow]\downrightcurvedarrow$^*$ & \K[\STIXrightarrowtail]\rightarrowtail \\ \K[\STIXdownuparrows]\downuparrows & \K[\STIXrightarrowtriangle]\rightarrowtriangle \\ \K[\STIXdownwhitearrow]\downwhitearrow$^*$ & \K[\STIXrightarrowx]\rightarrowx \\ \K[\STIXdownzigzagarrow]\downzigzagarrow & \K[\STIXrightbkarrow]\rightbkarrow \\ \K[\STIXdraftingarrow]\draftingarrow$^*$ & \K[\STIXrightcurvedarrow]\rightcurvedarrow \\ \K[\STIXdrbkarow]\drbkarow & \K[\STIXrightdasharrow]\rightdasharrow$^*$ \\ \K[\STIXequalleftarrow]\equalleftarrow & \K[\STIXrightdotarrow]\rightdotarrow \\ \K[\STIXequalrightarrow]\equalrightarrow & \K[\STIXrightdowncurvedarrow]\rightdowncurvedarrow \\ \K[\STIXfdiagovnearrow]\fdiagovnearrow$^*$ & \K[\STIXrightleftarrows]\rightleftarrows \\ \K[\STIXhknearrow]\hknearrow & \K[\STIXrightrightarrows]\rightrightarrows \\ \K[\STIXhknwarrow]\hknwarrow & \K[\STIXrightsquigarrow]\rightsquigarrow \\ \K[\STIXhksearow]\hksearow & \K[\STIXrightthreearrows]\rightthreearrows \\ \K[\STIXhkswarow]\hkswarow & \K[\STIXrightwavearrow]\rightwavearrow \\ \K[\STIXhookleftarrow]\hookleftarrow & \K[\STIXrightwhitearrow]\rightwhitearrow$^*$ \\ \K[\STIXhookrightarrow]\hookrightarrow & \K[\STIXRRightarrow]\RRightarrow \\ \K[\STIXLdsh]\Ldsh & \K[\STIXRrightarrow]\Rrightarrow \\ \K[\STIXleftarrow]\leftarrow & \K[\STIXRsh]\Rsh \\ \K[\STIXLeftarrow]\Leftarrow & \K[\STIXsearrow]\searrow \\ \K[\STIXleftarrowapprox]\leftarrowapprox & \K[\STIXSearrow]\Searrow \\ \K[\STIXleftarrowbackapprox]\leftarrowbackapprox & \K[\STIXseovnearrow]\seovnearrow$^*$ \\ \K[\STIXleftarrowbsimilar]\leftarrowbsimilar & \K[\STIXshortrightarrowleftarrow]\shortrightarrowleftarrow \\ \K[\STIXleftarrowonoplus]\leftarrowonoplus & \K[\STIXsimilarleftarrow]\similarleftarrow \\ \K[\STIXleftarrowplus]\leftarrowplus & \K[\STIXsimilarrightarrow]\similarrightarrow \\ \K[\STIXleftarrowshortrightarrow]\leftarrowshortrightarrow & \K[\STIXswarrow]\swarrow \\ \K[\STIXleftarrowsimilar]\leftarrowsimilar & \K[\STIXSwarrow]\Swarrow \\ \K[\STIXleftarrowtail]\leftarrowtail & \K[\STIXtoea]\toea \\ \K[\STIXleftarrowtriangle]\leftarrowtriangle & \K[\STIXtona]\tona \\ \K[\STIXleftarrowx]\leftarrowx & \K[\STIXtosa]\tosa \\ \K[\STIXleftbkarrow]\leftbkarrow & \K[\STIXtowa]\towa \\ \K[\STIXleftcurvedarrow]\leftcurvedarrow & \K[\STIXtwoheaddownarrow]\twoheaddownarrow \\ \K[\STIXleftdasharrow]\leftdasharrow$^*$ & \K[\STIXtwoheadleftarrow]\twoheadleftarrow \\ \K[\STIXleftdbkarrow]\leftdbkarrow & \K[\STIXtwoheadleftarrowtail]\twoheadleftarrowtail \\ \K[\STIXleftdotarrow]\leftdotarrow & \K[\STIXtwoheadleftdbkarrow]\twoheadleftdbkarrow \\ \K[\STIXleftdowncurvedarrow]\leftdowncurvedarrow & \K[\STIXtwoheadmapsfrom]\twoheadmapsfrom \\ \K[\STIXleftleftarrows]\leftleftarrows & \K[\STIXtwoheadmapsto]\twoheadmapsto \\ \K[\STIXLeftrightarrow]\Leftrightarrow & \K[\STIXtwoheadrightarrow]\twoheadrightarrow \\ \K[\STIXleftrightarrow]\leftrightarrow & \K[\STIXtwoheadrightarrowtail]\twoheadrightarrowtail \\ \K[\STIXleftrightarrowcircle]\leftrightarrowcircle & \K[\STIXtwoheaduparrow]\twoheaduparrow \\ \K[\STIXleftrightarrows]\leftrightarrows & \K[\STIXtwoheaduparrowcircle]\twoheaduparrowcircle \\ \K[\STIXleftrightarrowtriangle]\leftrightarrowtriangle & \K[\STIXuparrow]\uparrow \\ \K[\STIXleftrightsquigarrow]\leftrightsquigarrow & \K[\STIXUparrow]\Uparrow \\ \K[\STIXleftsquigarrow]\leftsquigarrow & \K[\STIXuparrowbarred]\uparrowbarred \\ \K[\STIXleftthreearrows]\leftthreearrows & \K[\STIXupdasharrow]\updasharrow$^*$ \\ \K[\STIXleftwavearrow]\leftwavearrow & \K[\STIXUpdownarrow]\Updownarrow \\ \K[\STIXleftwhitearrow]\leftwhitearrow$^*$ & \K[\STIXupdownarrow]\updownarrow \\ \K[\STIXlinefeed]\linefeed$^*$ & \K[\STIXupdownarrowbar]\updownarrowbar$^*$ \\ \K[\STIXLLeftarrow]\LLeftarrow & \K[\STIXupdownarrows]\updownarrows \\ \K[\STIXLleftarrow]\Lleftarrow & \K[\STIXuprightcurvearrow]\uprightcurvearrow$^*$ \\ \K[\STIXlongleftarrow]\longleftarrow & \K[\STIXupuparrows]\upuparrows \\ \K[\STIXLongleftarrow]\Longleftarrow & \K[\STIXupwhitearrow]\upwhitearrow$^*$ \\ \K[\STIXLongleftrightarrow]\Longleftrightarrow & \K[\STIXUUparrow]\UUparrow \\ \K[\STIXlongleftrightarrow]\longleftrightarrow & \K[\STIXUuparrow]\Uuparrow \\ \K[\STIXlongleftsquigarrow]\longleftsquigarrow & \K[\STIXvarcarriagereturn]\varcarriagereturn$^*$ \\ \K[\STIXLongmapsfrom]\Longmapsfrom & \K[\STIXwhitearrowupfrombar]\whitearrowupfrombar$^*$ \\ \K[\STIXlongmapsfrom]\longmapsfrom & \\ \end{longtable} \begin{tablenote}[*] Defined as an ordinary character, not as a binary relation. \end{tablenote} \bigskip \begin{tablenote} \STIX\ defines \cmdI[\string\STIXacwopencirclearrow]{\acwopencirclearrow} as a synonym for \cmdI[\string\STIXcirclearrowleft]{\circlearrowleft}, \cmdI[\string\STIXcwopencirclearrow]{\cwopencirclearrow} as a synonym for \cmdI[\string\STIXcirclearrowright]{\circlearrowright}, \cmdI[\string\STIXleadsto]{\leadsto} as a synonym for \cmdI[\string\STIXrightsquigarrow]{\rightsquigarrow}, \cmdI[\string\STIXdashleftarrow]{\dashleftarrow} as a synonym for \cmdI[\string\STIXleftdbkarrow]{\leftdbkarrow}, and \cmdI[\string\STIXdashrightarrow]{\dashrightarrow} and \cmdI[\string\STIXdasharrow]{\dasharrow} as synonyms for \cmdI[\string\STIXdbkarow]{\dbkarow}. \end{tablenote} \end{longsymtable} \begin{symtable}[STIX]{\STIX\ Negated Arrows} \index{arrows} \label{stix-narrows} \begin{tabular}{*2{ll}} \K[\STIXnHdownarrow]\nHdownarrow$^*$ & \K[\STIXnvLeftrightarrow]\nvLeftrightarrow \\ \K[\STIXnHuparrow]\nHuparrow$^*$ & \K[\STIXnVrightarrow]\nVrightarrow \\ \K[\STIXnleftarrow]\nleftarrow$^\dag$ & \K[\STIXnvRightarrow]\nvRightarrow \\ \K[\STIXnLeftarrow]\nLeftarrow & \K[\STIXnvrightarrow]\nvrightarrow \\ \K[\STIXnleftrightarrow]\nleftrightarrow & \K[\STIXnVrightarrowtail]\nVrightarrowtail \\ \K[\STIXnLeftrightarrow]\nLeftrightarrow & \K[\STIXnvrightarrowtail]\nvrightarrowtail \\ \K[\STIXnRightarrow]\nRightarrow & \K[\STIXnvtwoheadleftarrow]\nvtwoheadleftarrow \\ \K[\STIXnrightarrow]\nrightarrow & \K[\STIXnVtwoheadleftarrow]\nVtwoheadleftarrow \\ \K[\STIXnvleftarrow]\nvleftarrow & \K[\STIXnvtwoheadleftarrowtail]\nvtwoheadleftarrowtail \\ \K[\STIXnvLeftarrow]\nvLeftarrow & \K[\STIXnVtwoheadleftarrowtail]\nVtwoheadleftarrowtail \\ \K[\STIXnVleftarrow]\nVleftarrow & \K[\STIXnVtwoheadrightarrow]\nVtwoheadrightarrow \\ \K[\STIXnVleftarrowtail]\nVleftarrowtail & \K[\STIXnvtwoheadrightarrow]\nvtwoheadrightarrow \\ \K[\STIXnvleftarrowtail]\nvleftarrowtail & \K[\STIXnvtwoheadrightarrowtail]\nvtwoheadrightarrowtail \\ \K[\STIXnvleftrightarrow]\nvleftrightarrow & \K[\STIXnVtwoheadrightarrowtail]\nVtwoheadrightarrowtail \\ \K[\STIXnVleftrightarrow]\nVleftrightarrow & \\ \end{tabular} \bigskip \begin{tablenote}[*] Defined as an ordinary character, not as a binary relation. \end{tablenote} \bigskip \begin{tablenote}[\dag] \STIX\ defines \cmdI[\string\STIXngets]{\ngets} as a synonym for \cmdI[\string\STIXnleftarrow]{\nleftarrow}. \end{tablenote} \end{symtable} \begin{longsymtable}[STIX]{\STIX\ Harpoons} \ltindex{harpoons} \ltindex{restrictions} \label{stix-harpoons} \begin{longtable}{*2{ll}} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXbardownharpoonleft]\bardownharpoonleft & \K[\STIXleftrightharpoons]\leftrightharpoons \\ \K[\STIXbardownharpoonright]\bardownharpoonright & \K[\STIXleftrightharpoonsdown]\leftrightharpoonsdown \\ \K[\STIXbarleftharpoondown]\barleftharpoondown & \K[\STIXleftrightharpoonsup]\leftrightharpoonsup \\ \K[\STIXbarleftharpoonup]\barleftharpoonup & \K[\STIXleftrightharpoonupdown]\leftrightharpoonupdown \\ \K[\STIXbarrightharpoondown]\barrightharpoondown & \K[\STIXleftrightharpoonupup]\leftrightharpoonupup \\ \K[\STIXbarrightharpoonup]\barrightharpoonup & \K[\STIXrightharpoondown]\rightharpoondown \\ \K[\STIXbarupharpoonleft]\barupharpoonleft & \K[\STIXrightharpoondownbar]\rightharpoondownbar \\ \K[\STIXbarupharpoonright]\barupharpoonright & \K[\STIXrightharpoonsupdown]\rightharpoonsupdown \\ \K[\STIXdashleftharpoondown]\dashleftharpoondown & \K[\STIXrightharpoonup]\rightharpoonup \\ \K[\STIXdashrightharpoondown]\dashrightharpoondown & \K[\STIXrightharpoonupbar]\rightharpoonupbar \\ \K[\STIXdownharpoonleft]\downharpoonleft & \K[\STIXrightharpoonupdash]\rightharpoonupdash \\ \K[\STIXdownharpoonleftbar]\downharpoonleftbar & \K[\STIXrightleftharpoons]\rightleftharpoons \\ \K[\STIXdownharpoonright]\downharpoonright & \K[\STIXrightleftharpoonsdown]\rightleftharpoonsdown \\ \K[\STIXdownharpoonrightbar]\downharpoonrightbar & \K[\STIXrightleftharpoonsup]\rightleftharpoonsup \\ \K[\STIXdownharpoonsleftright]\downharpoonsleftright & \K[\STIXupdownharpoonleftleft]\updownharpoonleftleft \\ \K[\STIXdownupharpoonsleftright]\downupharpoonsleftright & \K[\STIXupdownharpoonleftright]\updownharpoonleftright \\ \K[\STIXleftharpoondown]\leftharpoondown & \K[\STIXupdownharpoonrightleft]\updownharpoonrightleft \\ \K[\STIXleftharpoondownbar]\leftharpoondownbar & \K[\STIXupdownharpoonrightright]\updownharpoonrightright \\ \K[\STIXleftharpoonsupdown]\leftharpoonsupdown & \K[\STIXupdownharpoonsleftright]\updownharpoonsleftright \\ \K[\STIXleftharpoonup]\leftharpoonup & \K[\STIXupharpoonleft]\upharpoonleft \\ \K[\STIXleftharpoonupbar]\leftharpoonupbar & \K[\STIXupharpoonleftbar]\upharpoonleftbar \\ \K[\STIXleftharpoonupdash]\leftharpoonupdash & \K[\STIXupharpoonright]\upharpoonright$^*$ \\ \K[\STIXleftrightharpoondowndown]\leftrightharpoondowndown & \K[\STIXupharpoonrightbar]\upharpoonrightbar \\ \K[\STIXleftrightharpoondownup]\leftrightharpoondownup & \K[\STIXupharpoonsleftright]\upharpoonsleftright \\ \end{longtable} \begin{tablenote}[*] \STIX\ defines \cmdI[\string\STIXrestriction]{\restriction} as a synonym for \cmdI[\string\STIXupharpoonright]{\upharpoonright}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[PDFMSYM]{\PDFMSYM\ Arrows} \ltindex{arrows} \ltindex{carriage return} \ltindex{lightning} \label{pdfmsym-arrows} \begin{longtable}{*2{ll}} \multicolumn{4}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{4}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \X[\PDFMSYMlightning]\lightning \\ \X\longvarCircleleftarrow & \X\varCircleleftarrow \\ \X\longvarcircleleftarrow & \X\varcircleleftarrow \\ \X\longvarCirclerightarrow & \X\varCirclerightarrow \\ \X\longvarcirclerightarrow & \X\varcirclerightarrow \\ \X\longvardoubleleftarrow & \X\vardoubleleftarrow \\ \X\longvardoublerightarrow & \X\vardoublerightarrow \\ \X\longvardownhookleftarrow & \X\vardownhookleftarrow \\ \X\longvardownhookrightarrow & \X\vardownhookrightarrow \\ \X\longvarLeftarrow & \X\varLeftarrow \\ \X\longvarleftarrow & \X\varleftarrow \\ \X\longvarleftarrows & \X\varleftarrows \\ \X\longvarleftrightarrow & \X\varleftrightarrow \\ \X\longvarleftrightarrows & \X\varleftrightarrows \\ \X\longvarLleftarrow & \X\varLleftarrow \\ \X\longvarLleftRrightarrow & \X\varLleftRrightarrow \\ \X\longvarmapsfrom & \X\varmapsfrom \\ \X\longvarmapsto & \X\varmapsto \\ \X\longvarRibbonleftarrow & \X\varRibbonleftarrow \\ \X\longvarRibbonrightarrow & \X\varRibbonrightarrow \\ \X\longvarRightarrow & \X\varRightarrow \\ \X\longvarrightarrow & \X\varrightarrow \\ \X\longvarrightarrows & \X\varrightarrows \\ \X\longvarrightleftarrows & \X\varrightleftarrows \\ \X\longvarRrightarrow & \X\varRrightarrow \\ \X\longvarSquareleftarrow & \X\varSquareleftarrow \\ \X\longvarSquarerightarrow & \X\varSquarerightarrow \\ \X\longvaruphookleftarrow & \X\varuphookleftarrow \\ \X\longvaruphookrightarrow & \X\varuphookrightarrow \\ \end{longtable} \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{longsymtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Harpoons} \index{harpoons} \label{pdfmsym-harpoons} \begin{tabular}{*2{ll}} \X\longvarleftharp & \X\varleftharp \\ \X\longvarleftrightharp & \X\varleftrightharp \\ \X\longvarrightharp & \X\varrightharp \\ \X\longvarrightleftharp & \X\varrightleftharp \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[CHEMB]{\CHEMB\ Arrows} \index{arrows} \label{chemarrow-arrows} \begin{tabular}{ll} \X\chemarrow \end{tabular} \end{symtable} \begin{symtable}[FGE]{\FGE\ Arrows} \index{arrows} \idxboth{fletched}{arrows} \idxboth{Frege logic}{symbols} \label{fge-arrows} \begin{tabular}{ll@{\qquad}ll} \K\fgerightarrow & \K\fgeuparrow \\ \end{tabular} \end{symtable} \begin{symtable}[NEWCM]{\NEWCM\ Arrows} \index{arrows} \label{newcm-arrows} \begin{tabular}{ll@{\qquad}ll} \K[\NCMtwoheadhookleftarrow]\twoheadhookleftarrow & \K[\NCMtwoheadhookrightarrow]\twoheadhookrightarrow \\ \end{tabular} \bigskip \begin{tablenote} \NEWCM\ additionally provides many of the other arrows appearing in this chapter. \seepackagenote{NEWCM}{newcomputermodern}. \end{tablenote} \end{symtable} \begin{symtable}[NEWCM]{\NEWCM\ Negated Arrows} \subindex{arrows}{negated} \label{newcm-narrows} \begin{tabular}{ll@{\qquad}ll} \K[\NCMnleftleftarrows]\nleftleftarrows & \K[\NCMnrightrightarrows]\nrightrightarrows \\ \end{tabular} \bigskip \begin{tablenote} \NEWCM\ additionally provides many of the other negated arrows appearing in this chapter. \seepackagenote{NEWCM}{newcomputermodern}. \end{tablenote} \end{symtable} \begin{symtable}[OLDARR]{\OLDARR\ Arrows} \index{arrows} \label{old-arrows} \begin{tabular}{*3{ll}} \K[\OLDdownarrow]\downarrow & \K[\OLDlongleftrightarrow]\longleftrightarrow & \K[\OLDnwarrow]\nwarrow \\ \K[\OLDhookleftarrow]\hookleftarrow & \K[\OLDlongmapsfrom]\longmapsfrom$^*$ & \K[\OLDrightarrow]\rightarrow \\ \K[\OLDhookrightarrow]\hookrightarrow & \K[\OLDlongmapsto]\longmapsto & \K[\OLDsearrow]\searrow \\ \K[\OLDleftarrow]\leftarrow & \K[\OLDlongrightarrow]\longrightarrow & \K[\OLDswarrow]\swarrow \\ \K[\OLDleftrightarrow]\leftrightarrow & \K[\OLDmapsfrom]\mapsfrom$^*$ & \K[\OLDuparrow]\uparrow \\ \K[\OLDlonghookrightarrow]\longhookrightarrow & \K[\OLDmapsto]\mapsto & \K[\OLDupdownarrow]\updownarrow \\ \K[\OLDlongleftarrow]\longleftarrow & \K[\OLDnearrow]\nearrow & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{OLDARR}{old-arrows}. \end{tablenote} \bigskip \begin{tablenote}[*] Requires \ST. \end{tablenote} \end{symtable} \begin{symtable}[OLDARR]{\OLDARR\ Harpoons} \index{harpoons} \label{old-arrows-harpoons} \begin{tabular}{*2{ll}} \K[\OLDlongleftharpoondown]\longleftharpoondown & \K[\OLDlongrightharpoondown]\longrightharpoondown \\ \K[\OLDlongleftharpoonup]\longleftharpoonup & \K[\OLDlongrightharpoonup]\longrightharpoonup \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{OLDARR}{old-arrows}. \end{tablenote} \end{symtable} \begin{longsymtable}[LOGIX]{\LOGIX\ Arrows} \ltindex{arrows} \ltidxboth{logic}{symbols} \label{logix-arrows} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K\DashArrowLeft & \K\LMtImpl & \K\RplcFree \\ \K\DashArrowRight & \K\LoopArrowLeft & \K\RplcFreeLeft \\ \K\Entail & \K\LoopArrowRight & \K\RplcFreeRight \\ \K\EntailEquv & \K\LParFunc & \K\SEntail \\ \K\Equv & \K\LWkEntail & \K\SEntailEquv \\ \K\FishArrowLeft & \K\LWkEntailEquv & \K\SEquv \\ \K\FishArrowRight & \K\MapParInGndMul & \K\SFunc \\ \K\FlatArrowLeft & \K\MapParInGndOne & \K\ShftAccent \\ \K\FlatArrowRight & \K\MapParInGndSng & \K\ShftSubscr \\ \K\ForkArrowLeft & \K\MapParInMul & \K\ShftSuper \\ \K\ForkArrowRight & \K\MapParInOne & \K\SImpl \\ \K\Func & \K\MapParInSng & \K\SMapTo \\ \K\FunParInGndMul & \K\MapParOnGndMul & \K\SMtEquv \\ \K\FunParInGndOne & \K\MapParOnGndOne & \K\SMtImpl \\ \K\FunParInGndSng & \K\MapParOnGndSng & \K\SParFunc \\ \K\FunParInMul & \K\MapParOnMul & \K\SWkEntail \\ \K\FunParInOne & \K\MapParOnOne & \K\SWkEntailEquv \\ \K\FunParInSng & \K\MapParOnSng & \K\VEntail \\ \K\FunParOnGndMul & \K\MapTo & \K\VEntailEquv \\ \K\FunParOnGndOne & \K\MapTotInGndMul & \K\VEquv \\ \K\FunParOnGndSng & \K\MapTotInGndOne & \K\VFunc \\ \K\FunParOnMul & \K\MapTotInGndSng & \K\VImpl \\ \K\FunParOnOne & \K\MapTotInMul & \K\VMapTo \\ \K\FunParOnSng & \K\MapTotInOne & \K\VMtEquv \\ \K\FunTotInGndMul & \K\MapTotInSng & \K\VMtImpl \\ \K\FunTotInGndOne & \K\MapTotOnGndMul & \K\VParFunc \\ \K\FunTotInGndSng & \K\MapTotOnGndOne & \K\VWkEntail \\ \K\FunTotInMul & \K\MapTotOnGndSng & \K\VWkEntailEquv \\ \K\FunTotInOne & \K\MapTotOnMul & \K\WavyArrowLeft \\ \K\FunTotInSng & \K\MapTotOnOne & \K\WavyArrowRight \\ \K\FunTotOnGndMul & \K\MapTotOnSng & \K\WkEntail \\ \K\FunTotOnGndOne & \K\MtEquv & \K\WkEntailEquv \\ \K\FunTotOnGndSng & \K\MtImpl & \K\XEntail \\ \K\FunTotOnMul & \K\ParFunc & \K\XEntailEquv \\ \K\FunTotOnOne & \K\RplcAll & \K\XEquv \\ \K\FunTotOnSng & \K\RplcAllBnd & \K\XFunc \\ \K\HookArrowLeft & \K\RplcAllBndLeft & \K\XImpl \\ \K\HookArrowRight & \K\RplcAllBndRight & \K\XMapTo \\ \K\Impl & \K\RplcAllLeft & \K\XMtEquv \\ \K\LEntail & \K\RplcAllRight & \K\XMtImpl \\ \K\LEntailEquv & \K\RplcAny & \K\XParFunc \\ \K\LEquv & \K\RplcAnyLeft & \K\XWkEntail \\ \K\LFunc & \K\RplcAnyRight & \K\XWkEntailEquv \\ \K\LImpl & \K\RplcEquv & \K\ZigArrowLeft \\ \K\LMapTo & \K\RplcEquvLeft & \K\ZigArrowRight \\ \K\LMtEquv & \K\RplcEquvRight & \\ \end{longtable} \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{longsymtable} \begin{symtable}[LOGIX]{\LOGIX\ Negated Arrows} \subindex{arrows}{negated} \idxboth{logic}{symbols} \label{logix-narrows} \begin{tabular}{*3{ll}} \K\NotEntail & \K\NotSEntail & \K\NotVWkEntail \\ \K\NotEntailEquv & \K\NotSEntailEquv & \K\NotVWkEntailEquv \\ \K\NotEquv & \K\NotSEquv & \K\NotWkEntail \\ \K\NotImpl & \K\NotSImpl & \K\NotWkEntailEquv \\ \K\NotLEntail & \K\NotSMtEquv & \K\NotXEntail \\ \K\NotLEntailEquv & \K\NotSMtImpl & \K\NotXEntailEquv \\ \K\NotLEquv & \K\NotSWkEntail & \K\NotXEquv \\ \K\NotLImpl & \K\NotSWkEntailEquv & \K\NotXImpl \\ \K\NotLMtEquv & \K\NotVEntail & \K\NotXMtEquv \\ \K\NotLMtImpl & \K\NotVEntailEquv & \K\NotXMtImpl \\ \K\NotLWkEntail & \K\NotVEquv & \K\NotXWkEntail \\ \K\NotLWkEntailEquv & \K\NotVImpl & \K\NotXWkEntailEquv \\ \K\NotMtEquv & \K\NotVMtEquv & \\ \K\NotMtImpl & \K\NotVMtImpl & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Harpoons} \index{harpoons} \label{logix-harpoons} \begin{tabular}{*2{ll}} \K\HarpoonDnLeft & \K\HarpoonUpLeft \\ \K\HarpoonDnRight & \K\HarpoonUpRight \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Implications and Equivalences} \idxboth{logic}{symbols} \label{logix-impl} \begin{tabular}{*4{ll}} \K\InEquv & \K\SInEquv & \K\VWkEquv & \K\XInEquv \\ \K\InImpl & \K\SInImpl & \K\VWkImpl & \K\XInImpl \\ \K\LInEquv & \K\SWkEquv & \K\VWkMtEquv & \K\XWkEquv \\ \K\LInImpl & \K\SWkImpl & \K\VWkMtImpl & \K\XWkImpl \\ \K\LWkEquv & \K\SWkMtEquv & \K\WkEquv & \K\XWkMtEquv \\ \K\LWkImpl & \K\SWkMtImpl & \K\WkImpl & \K\XWkMtImpl \\ \K\LWkMtEquv & \K\VInEquv & \K\WkMtEquv & \\ \K\LWkMtImpl & \K\VInImpl & \K\WkMtImpl & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Negated Implications and Equivalences} \idxboth{logic}{symbols} \label{logix-nimpl} \begin{tabular}{*3{ll}} \K\NotInEquv & \K\NotSWkEquv & \K\NotWkEquv \\ \K\NotInImpl & \K\NotSWkImpl & \K\NotWkImpl \\ \K\NotLInEquv & \K\NotSWkMtEquv & \K\NotWkMtEquv \\ \K\NotLInImpl & \K\NotSWkMtImpl & \K\NotWkMtImpl \\ \K\NotLWkEquv & \K\NotVInEquv & \K\NotXInEquv \\ \K\NotLWkImpl & \K\NotVInImpl & \K\NotXInImpl \\ \K\NotLWkMtEquv & \K\NotVWkEquv & \K\NotXWkEquv \\ \K\NotLWkMtImpl & \K\NotVWkImpl & \K\NotXWkImpl \\ \K\NotSInEquv & \K\NotVWkMtEquv & \K\NotXWkMtEquv \\ \K\NotSInImpl & \K\NotVWkMtImpl & \K\NotXWkMtImpl \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[ESR]{\ESR\ Restrictions} \index{restrictions} \label{esrelations} \begin{tabular}{*3{ll}} \K\restrictbarb & \K\restrictmallet & \K\restrictwand \\ \K\restrictbarbup & \K\restrictmalletup & \K\restrictwandup \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Spoons} \index{binary relations} \index{relational symbols>binary} \index{spoon symbols (mathematics)} \index{symbols>spoon (mathematics)} \label{mns-spoons} \begin{tabular}{*3{ll}} \K[\MNSdownfilledspoon]\downfilledspoon & \K[\MNSnnespoon]\nnespoon & \K[\MNSnwfilledspoon]\nwfilledspoon \\ \K[\MNSdownspoon]\downspoon & \K[\MNSnnwfilledspoon]\nnwfilledspoon & \K[\MNSnwspoon]\nwspoon \\ \K[\MNSleftfilledspoon]\leftfilledspoon & \K[\MNSnnwspoon]\nnwspoon & \K[\MNSrightfilledspoon]\rightfilledspoon \\ \K[\MNSleftspoon]\leftspoon & \K[\MNSnrightfilledspoon]\nrightfilledspoon & \K[\MNSrightspoon]\rightspoon$^*$ \\ \K[\MNSndownfilledspoon]\ndownfilledspoon & \K[\MNSnrightspoon]\nrightspoon$^*$ & \K[\MNSsefilledspoon]\sefilledspoon \\ \K[\MNSndownspoon]\ndownspoon & \K[\MNSnsefilledspoon]\nsefilledspoon & \K[\MNSsespoon]\sespoon \\ \K[\MNSnefilledspoon]\nefilledspoon & \K[\MNSnsespoon]\nsespoon & \K[\MNSswfilledspoon]\swfilledspoon \\ \K[\MNSnespoon]\nespoon & \K[\MNSnswfilledspoon]\nswfilledspoon & \K[\MNSswspoon]\swspoon \\ \K[\MNSnleftfilledspoon]\nleftfilledspoon & \K[\MNSnswspoon]\nswspoon & \K[\MNSupfilledspoon]\upfilledspoon \\ \K[\MNSnleftspoon]\nleftspoon & \K[\MNSnupfilledspoon]\nupfilledspoon & \K[\MNSupspoon]\upspoon \\ \K[\MNSnnefilledspoon]\nnefilledspoon & \K[\MNSnupspoon]\nupspoon & \\ \end{tabular} \bigskip \begin{tablenote}[*] \MNS\ defines \cmdI[\MNSrightspoon]{\multimap} as a synonym for \cmdI[\MNSrightspoon]{\rightspoon} and \cmdI[\MNSnrightspoon]{\nmultimap} as a synonym for \cmdI[\MNSnrightspoon]{\nrightspoon}. \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Pitchforks} \index{binary relations} \index{relational symbols>binary} \index{pitchforks} \label{mns-pitchforks} \begin{tabular}{*3{ll}} \K[\MNSdownpitchfork]\downpitchfork & \K[\MNSnnwpitchfork]\nnwpitchfork & \K[\MNSrightpitchfork]\rightpitchfork \\ \K[\MNSleftpitchfork]\leftpitchfork & \K[\MNSnrightpitchfork]\nrightpitchfork & \K[\MNSsepitchfork]\sepitchfork \\ \K[\MNSndownpitchfork]\ndownpitchfork & \K[\MNSnsepitchfork]\nsepitchfork & \K[\MNSswpitchfork]\swpitchfork \\ \K[\MNSnepitchfork]\nepitchfork & \K[\MNSnswpitchfork]\nswpitchfork & \K[\MNSuppitchfork]\uppitchfork \\ \K[\MNSnleftpitchfork]\nleftpitchfork & \K[\MNSnuppitchfork]\nuppitchfork & \\ \K[\MNSnnepitchfork]\nnepitchfork & \K[\MNSnwpitchfork]\nwpitchfork & \\ \end{tabular} \bigskip \begin{tablenote}[*] \MNS\ defines \cmdI[\MNSuppitchfork]{\pitchfork} as a synonym for \cmdI[\MNSuppitchfork]{\uppitchfork} and \cmdI[\MNSnuppitchfork]{\npitchfork} as a synonym for \cmdI[\MNSnuppitchfork]{\nuppitchfork}. \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Smiles and Frowns} \index{binary relations} \index{relational symbols>binary} \idxboth{smile}{symbols} \idxboth{frown}{symbols} \label{mns-smile-frown} \begin{tabular}{*3{ll}} \K[\MNSdoublefrown]\doublefrown & \K[\MNSnsmileeq]\nsmileeq & \K[\MNSsmileeq]\smileeq \\ \K[\MNSdoublefrowneq]\doublefrowneq & \K[\MNSnsmileeqfrown]\nsmileeqfrown & \K[\MNSsmileeqfrown]\smileeqfrown \\ \K[\MNSdoublesmile]\doublesmile & \K[\MNSnsmilefrown]\nsmilefrown & \K[\MNSsmilefrown]\smilefrown \\ \K[\MNSdoublesmileeq]\doublesmileeq & \K[\MNSnsmilefrowneq]\nsmilefrowneq & \K[\MNSsmilefrowneq]\smilefrowneq \\ \K[\MNSeqfrown]\eqfrown & \K[\MNSnsqdoublefrown]\nsqdoublefrown & \K[\MNSsqdoublefrown]\sqdoublefrown \\ \K[\MNSeqsmile]\eqsmile & \K[\MNSnsqdoublefrowneq]\nsqdoublefrowneq & \K[\MNSsqdoublefrowneq]\sqdoublefrowneq \\ \K[\MNSfrown]\frown & \K[\MNSnsqdoublesmile]\nsqdoublesmile & \K[\MNSsqdoublesmile]\sqdoublesmile \\ \K[\MNSfrowneq]\frowneq & \K[\MNSnsqdoublesmileeq]\nsqdoublesmileeq & \K[\MNSsqdoublesmileeq]\sqdoublesmileeq \\ \K[\MNSfrowneqsmile]\frowneqsmile & \K[\MNSnsqeqfrown]\nsqeqfrown & \K[\MNSsqeqfrown]\sqeqfrown \\ \K[\MNSfrownsmile]\frownsmile & \K[\MNSnsqeqsmile]\nsqeqsmile & \K[\MNSsqeqsmile]\sqeqsmile \\ \K[\MNSfrownsmileeq]\frownsmileeq & \K[\MNSnsqfrown]\nsqfrown & \K[\MNSsqfrown]\sqfrown \\ \K[\MNSndoublefrown]\ndoublefrown & \K[\MNSnsqfrowneq]\nsqfrowneq & \K[\MNSsqfrowneq]\sqfrowneq \\ \K[\MNSndoublefrowneq]\ndoublefrowneq & \K[\MNSnsqfrowneqsmile]\nsqfrowneqsmile & \K[\MNSsqfrowneqsmile]\sqfrowneqsmile \\ \K[\MNSndoublesmile]\ndoublesmile & \K[\MNSnsqfrownsmile]\nsqfrownsmile & \K[\MNSsqfrownsmile]\sqfrownsmile \\ \K[\MNSndoublesmileeq]\ndoublesmileeq & \K[\MNSnsqsmile]\nsqsmile & \K[\MNSsqsmile]\sqsmile \\ \K[\MNSneqfrown]\neqfrown & \K[\MNSnsqsmileeq]\nsqsmileeq & \K[\MNSsqsmileeq]\sqsmileeq \\ \K[\MNSneqsmile]\neqsmile & \K[\MNSnsqsmileeqfrown]\nsqsmileeqfrown & \K[\MNSsqsmileeqfrown]\sqsmileeqfrown \\ \K[\MNSnfrown]\nfrown & \K[\MNSnsqsmilefrown]\nsqsmilefrown & \K[\MNSsqsmilefrown]\sqsmilefrown \\ \K[\MNSnfrowneq]\nfrowneq & \K[\MNSnsqtriplefrown]\nsqtriplefrown & \K[\MNSsqtriplefrown]\sqtriplefrown \\ \K[\MNSnfrowneqsmile]\nfrowneqsmile & \K[\MNSnsqtriplesmile]\nsqtriplesmile & \K[\MNSsqtriplesmile]\sqtriplesmile \\ \K[\MNSnfrownsmile]\nfrownsmile & \K[\MNSntriplefrown]\ntriplefrown & \K[\MNStriplefrown]\triplefrown \\ \K[\MNSnfrownsmileeq]\nfrownsmileeq & \K[\MNSntriplesmile]\ntriplesmile & \K[\MNStriplesmile]\triplesmile \\ \K[\MNSnsmile]\nsmile & \K[\MNSsmile]\smile & \\ \end{tabular} \bigskip \begin{tablenote}[*] \MNS\ defines \cmdI[\MNSsmile]{\smallsmile} as a synonym for \cmdI[\MNSsmile]{\smile}, \cmdI[\MNSfrown]{\smallfrown} as a synonym for \cmdI[\MNSfrown]{\frown}, \cmdI[\MNSsmilefrown]{\asymp} as a synonym for \cmdI[\MNSsmilefrown]{\smilefrown}, and \cmdI[\MNSnsmilefrown]{\nasymp} as a synonym for \cmdI[\MNSnsmilefrown]{\nsmilefrown}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Spoons} \index{binary relations} \index{relational symbols>binary} \index{spoon symbols (mathematics)} \index{symbols>spoon (mathematics)} \label{fdsym-spoons} \begin{tabular}{*3{ll}} \K[\FDSYMblackwhitespoon]\blackwhitespoon & \K[\FDSYMndownblackspoon]\ndownblackspoon & \K[\FDSYMnupblackspoon]\nupblackspoon \\ \K[\FDSYMdownblackspoon]\downblackspoon & \K[\FDSYMndownspoon]\ndownspoon & \K[\FDSYMnupspoon]\nupspoon \\ \K[\FDSYMdownspoon]\downspoon & \K[\FDSYMnleftblackspoon]\nleftblackspoon & \K[\FDSYMnwhiteblackspoon]\nwhiteblackspoon \\ \K[\FDSYMleftblackspoon]\leftblackspoon & \K[\FDSYMnleftrightblackspoon]\nleftrightblackspoon & \K[\FDSYMrightblackspoon]\rightblackspoon \\ \K[\FDSYMleftrightblackspoon]\leftrightblackspoon & \K[\FDSYMnleftrightspoon]\nleftrightspoon & \K[\FDSYMrightspoon]\rightspoon \\ \K[\FDSYMleftrightspoon]\leftrightspoon & \K[\FDSYMnleftspoon]\nleftspoon & \K[\FDSYMupblackspoon]\upblackspoon \\ \K[\FDSYMleftspoon]\leftspoon & \K[\FDSYMnrightblackspoon]\nrightblackspoon & \K[\FDSYMupspoon]\upspoon \\ \K[\FDSYMnblackwhitespoon]\nblackwhitespoon & \K[\FDSYMnrightspoon]\nrightspoon & \K[\FDSYMwhiteblackspoon]\whiteblackspoon \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines synonyms for many of the preceding symbols: \begin{center} \begin{tabular}{*3{ll}} \K[\FDSYMcirmid]{\cirmid} & \K[\FDSYMmultimapinv]{\multimapinv} & \K[\FDSYMnmultimap]{\nmultimap} \\ \K[\FDSYMdualmap]{\dualmap} & \K[\FDSYMncirmid]{\ncirmid} & \K[\FDSYMnmultimapinv]{\nmultimapinv} \\ \K[\FDSYMimageof]{\imageof} & \K[\FDSYMndualmap]{\ndualmap} & \K[\FDSYMnorigof]{\norigof} \\ \K[\FDSYMmidcir]{\midcir} & \K[\FDSYMnimageof]{\nimageof} & \K[\FDSYMorigof]{\origof} \\ \K[\FDSYMmultimap]{\multimap} & \K[\FDSYMnmidcir]{\nmidcir} & \\ \end{tabular} \end{center} \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Pitchforks} \index{binary relations} \index{relational symbols>binary} \index{pitchforks} \label{fdsym-pitchforks} \begin{tabular}{*3{ll}} \K[\FDSYMdownpitchfork]\downpitchfork & \K[\FDSYMnleftpitchfork]\nleftpitchfork & \K[\FDSYMrightpitchfork]\rightpitchfork \\ \K[\FDSYMleftpitchfork]\leftpitchfork & \K[\FDSYMnrightpitchfork]\nrightpitchfork & \K[\FDSYMuppitchfork]\uppitchfork \\ \K[\FDSYMndownpitchfork]\ndownpitchfork & \K[\FDSYMnuppitchfork]\nuppitchfork & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMnpitchfork]{\npitchfork} as a synonym for \cmdI[\string\FDSYMnuppitchfork]{\nuppitchfork} and \cmdI[\string\FDSYMpitchfork]{\pitchfork} as a synonym for \cmdI[\string\FDSYMuppitchfork]{\uppitchfork}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Smiles and Frowns} \index{binary relations} \index{relational symbols>binary} \idxboth{smile}{symbols} \idxboth{frown}{symbols} \label{fdsym-smile-frown} \begin{tabular}{*3{ll}} \K[\FDSYMfrown]\frown & \K[\FDSYMnfrowneq]\nfrowneq & \K[\FDSYMnsmilefrown]\nsmilefrown \\ \K[\FDSYMfrowneq]\frowneq & \K[\FDSYMnfrownsmile]\nfrownsmile & \K[\FDSYMsmile]\smile \\ \K[\FDSYMfrownsmile]\frownsmile & \K[\FDSYMnsmile]\nsmile & \K[\FDSYMsmileeq]\smileeq \\ \K[\FDSYMnfrown]\nfrown & \K[\FDSYMnsmileeq]\nsmileeq & \K[\FDSYMsmilefrown]\smilefrown \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMarceq]{\arceq} as a synonym for \cmdI[\string\FDSYMfrowneq]{\frowneq}, \cmdI[\string\FDSYMasymp]{\asymp} as a synonym for \cmdI[\string\FDSYMsmilefrown]{\smilefrown}, \cmdI[\string\FDSYMclosure]{\closure} as a synonym for \cmdI[\string\FDSYMfrownsmile]{\frownsmile}, \cmdI[\string\FDSYMnarceq]{\narceq} as a synonym for \cmdI[\string\FDSYMnfrowneq]{\nfrowneq}, \cmdI[\string\FDSYMnasymp]{\nasymp} as a synonym for \cmdI[\string\FDSYMnsmilefrown]{\nsmilefrown}, \cmdI[\string\FDSYMnclosure]{\nclosure} as a synonym for \cmdI[\string\FDSYMnfrownsmile]{\nfrownsmile}, \cmdI[\string\FDSYMsmallfrown]{\smallfrown} as a synonym for \cmdI[\string\FDSYMfrown]{\frown}, and \cmdI[\string\FDSYMsmallsmile]{\smallsmile} as a synonym for \cmdI[\string\FDSYMsmile]{\smile}. \end{tablenote} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Brooms and Pitchforks} \index{brooms} \index{pitchforks} \label{hwmath-brooms} \begin{tabular}{llll} \X\hmleftpitchfork & \X\leftbroom \\ \X\hmrightpitchfork & \X\rightbroom \\ \end{tabular} \end{symtable} \begin{symtable}[ULSY]{\ULSY\ Contradiction Symbols} \idxboth{contradiction}{symbols} \index{lightning} \label{ulsy} \medskip \begin{tabular}{*6{ll}} \K\blitza & \K\blitzb & \K\blitzc & \K\blitzd & \K\blitze \\ \end{tabular} \end{symtable} \begin{symtable}{Extension Characters} \index{extension characters} \label{ext} \begin{indexingoff} \begin{tabular}{*2{ll}} \X\relbar & \X\Relbar \\ \end{tabular} \end{indexingoff} \end{symtable} \begin{symtable}[ST]{\ST\ Extension Characters} \index{extension characters} \label{st-ext} \begin{indexingoff} \begin{tabular}{*3{ll}} \X\Arrownot &\X\Mapsfromchar &\X\Mapstochar \\ \X\arrownot &\X\mapsfromchar \end{tabular} \end{indexingoff} \end{symtable} \begin{symtable}[TX]{\TXPX\ Extension Characters} \index{extension characters} \label{txpx-ext} \begin{indexingoff} \begin{tabular}{*3{ll}} \X\Mappedfromchar & \X\Mmappedfromchar & \X\Mmapstochar \\ \X\mappedfromchar & \X\mmappedfromchar & \X\mmapstochar \\ \end{tabular} \end{indexingoff} \end{symtable} \begin{symtable}[ABX]{\ABX\ Extension Characters} \index{extension characters} \label{abx-ext} \begin{indexingoff} \begin{tabular}{*3{ll}} \X[\ABXmapsfromchar]\mapsfromchar & \X[\ABXmapstochar]\mapstochar \\ \X[\ABXMapsfromchar]\Mapsfromchar & \X[\ABXMapstochar]\Mapstochar \\ \end{tabular} \end{indexingoff} \end{symtable} \begin{symtable}[STIX]{\STIX\ Extension Characters} \index{extension characters} \label{stix-ext} \begin{indexingoff} \begin{tabular}{*3{ll}} \K[\STIXlhook]\lhook & \K[\STIXrelbar]\relbar & \K[\STIXRRelbar]\RRelbar \\ \K[\STIXmapsfromchar]\mapsfromchar & \K[\STIXRelbar]\Relbar & \K[\STIXRrelbar]\Rrelbar \\ \K[\STIXmapstochar]\mapstochar & \K[\STIXrhook]\rhook & \\ \end{tabular} \end{indexingoff} \end{symtable} \begin{symtable}{Log-like Symbols} \idxboth{log-like}{symbols} \index{atomic math objects} \index{limits} \index{trigonometric functions} \label{log} \begin{indexingoff} \begin{tabular}{*8l} \Z\arccos & \Z\cos & \Z\csc & \Z\exp & \Z\ker & \Z\limsup & \Z\min & \Z\sinh \\ \Z\arcsin & \Z\cosh & \Z\deg & \Z\gcd & \Z\lg & \Z\ln & \Z\Pr & \Z\sup \\ \Z\arctan & \Z\cot & \Z\det & \Z\hom & \Z\lim & \Z\log & \Z\sec & \Z\tan \\ \Z\arg & \Z\coth & \Z\dim & \Z\inf & \Z\liminf & \Z\max & \Z\sin & \Z\tanh \end{tabular} \bigskip \begin{tablenote} See the note about base \latex symbols \vpageref{note-latex}. \end{tablenote} \end{indexingoff} \end{symtable} \begin{symtable}[AMS]{\AMS\ Log-like Symbols} \idxboth{log-like}{symbols} \index{atomic math objects} \index{limits} \index{inverse limit=inverse limit ($\varprojlim$)} \label{ams-log} \begin{indexingoff} \renewcommand{\arraystretch}{1.5} % Keep tall symbols from touching. \begin{tabular}{*2{ll@{\qquad}}ll} \X\injlim & \X\varinjlim & \X\varlimsup \\ \X\projlim & \X\varliminf & \X\varprojlim \end{tabular} \bigskip \begin{tablenote} Load the \pkgname{amsmath} package to get these symbols. See the note about base \latex symbols \vpageref{note-latex} for some additional comments regarding log-like symbols. \end{tablenote} \end{indexingoff} \end{symtable} \begin{symtable}[MISMATH]{\MISMATH\ Log-like Symbols} \idxboth{log-like}{symbols} \index{atomic math objects} \index{trigonometric functions} \label{mismath-log} \begin{indexingoff} \renewcommand{\arraystretch}{1.4} % Keep tall symbols from touching. \begin{tabular}{*3{ll@{\hspace*{3em}}}ll} \X[\MISMadj]\adj & \X[\MISMConv]\Conv & \X[\MISMid]\id & \X[\MISMsech]\sech \\ \X[\MISMarccot]\arccot & \X[\MISMCov]\Cov & \X[\MISMId]\Id & \X[\MISMsgn]\sgn \\ \X[\MISMarcosh]\arcosh & \X[\MISMcov]\cov & \X[\MISMim]\im & \X[\MISMspa]\spa \\ \X[\MISMarcoth]\arcoth & \X[\MISMcsch]\csch & \X[\MISMIm]\Im$^*$ & \X[\MISMtr]\tr \\ \X[\MISMarcsch]\arcsch & \X[\MISMcurl]\curl & \X[\MISMlb]\lb & \X[\MISMVar]\Var \\ \X[\MISMarsech]\arsech & \X[\MISMdivg]\divg & \X[\MISMlcm]\lcm & \X[\MISMZu]\Zu \\ \X[\MISMarsinh]\arsinh & \X[\MISMEnd]\End & \X[\MISMrank]\rank & \\ \X[\MISMartanh]\artanh & \X[\MISMerf]\erf & \X[\MISMRe]\Re$^*$ & \\ \X[\MISMAut]\Aut & \X[\MISMgrad]\grad & \X[\MISMrot]\rot & \\ \end{tabular} \end{indexingoff} \bigskip \begin{tablenote}[*] \MISMATH\ renames \LaTeX's \cmdX{\Re} and \cmdX{\Im} (\ref{letter-like}) to \cmdI[$\Re$]{\oldRe} and \cmdI[$\Im$]{\oldIm}. \end{tablenote} \end{symtable} \begin{symtable}[MISMATH]{\MISMATH\ Asymptotic Notation} \index{asymptotic complexity} \index{big O notation} \index{little o notation} \index{Bachmann-Landau notation} \label{mismath-asymp} \begin{tabular}{*2{ll@{\hspace*{3em}}}ll} \X[\MISMbigo]\bigo & \X[\MISMbigO]\bigO & \X[\MISMlito]\lito \\ \end{tabular} \end{symtable} \begin{symtable}[CHINA]{\CHINA\ Number Sets} \label{china-numsets} \begin{tabular}{*5{ll}} \K\Complex & \K\Integer & \K\Natural & \K\Rational & \K\Real \\ \K\COMPLEX & \K\INTEGER & \K\NATURAL & \K\RATIONAL & \K\REAL \\ \end{tabular} \end{symtable} \begin{symtable}{Greek Letters} \index{Greek>letters} \subindex{alphabets}{Greek} \index{pi=pi ($\pi$)} \label{greek} \begin{tabular}{*8l} \X\alpha &\X\theta &\X o &\X\tau \\ \X\beta &\X\vartheta &\X\pi &\X\upsilon \\ \X\gamma &\X\iota &\X\varpi &\X\phi \\ \X\delta &\X\kappa &\X\rho &\X\varphi \\ \X\epsilon &\X\lambda &\X\varrho &\X\chi \\ \X\varepsilon &\X\mu &\X\sigma &\X\psi \\ \X\zeta &\X\nu &\X\varsigma &\X\omega \\ \X\eta &\X\xi \\ \\ \X\Gamma &\X\Lambda &\X\Sigma &\X\Psi \\ \X\Delta &\X\Xi &\X\Upsilon &\X\Omega \\ \X\Theta &\X\Pi &\X\Phi \end{tabular} \bigskip \begin{tablenote} The remaining Greek majuscules\index{majuscules} can be produced with ordinary Latin letters. The symbol ``M'', for instance, is used for both an uppercase ``m'' and an uppercase ``$\mu$''. To make available commands for \emph{all} of the Greek majuscules\index{majuscules}, either use the \pkgname{mathspec} package, which requires \xelatex, or copy \hfilename{https://mirror.ctan.org/macros/xetex/latex/mathspec/mathspec.sty}{mathspec.sty}'s Greek-letter definitions to your document's preamble: \newcommand{\dms}[3]{% \ttfamily \string\DeclareMathSymbol\string{\cmdI[#2]{#1}\string}% \string{\string\mathalpha\string}\string{operators\string}\string{"#3\string}% }% \hspace*{\normalparindent}% \begin{tabular}{@{}l@{}} \dms{\Alpha}{A}{41} \\ \dms{\Beta}{B}{42} \\ \dms{\Epsilon}{E}{45} \\ \dms{\Zeta}{Z}{5A} \\ \dms{\Eta}{H}{48} \\ \dms{\Iota}{I}{49} \\ \dms{\Kappa}{K}{4B} \\ \dms{\Mu}{M}{4D} \\ \dms{\Nu}{N}{4E} \\ \dms{\Omicron}{O}{4F} \\ \dms{\Rho}{P}{50} \\ \dms{\Tau}{T}{54} \\ \dms{\Chi}{X}{58} \\ \ttfamily \string\DeclareMathSymbol\string{\cmdI[o]{\omicron}\string}% \string{\string\mathord\string}\string{letters\string}\string{"6F\string} \\ \end{tabular} See \ref{bold-math} for examples of how to produce bold Greek letters.\index{Greek>bold}\index{Greek>letters} The symbols in this table are intended to be used in mathematical typesetting. \greekfontmessage. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Greek Letters} \index{Greek>letters} \subindex{alphabets}{Greek} \label{ams-greek} \begin{tabular}{*4l} \X\digamma &\X\varkappa \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Upright Greek Letters} \subindex{alphabets}{Greek} \index{Greek>upright} \index{Greek>letters} \index{upright Greek letters} \label{txpx-greek} \begin{tabular}{*4{ll}} \X\alphaup & \X\thetaup & \X\piup & \X\phiup \\ \X\betaup & \X\varthetaup & \X\varpiup & \X\varphiup \\ \X\gammaup & \X\iotaup & \X\rhoup & \X\chiup \\ \X\deltaup & \X\kappaup & \X\varrhoup & \X\psiup \\ \X\epsilonup & \X\lambdaup & \X\sigmaup & \X\omegaup \\ \X\varepsilonup & \X\muup & \X\varsigmaup \\ \X\zetaup & \X\nuup & \X\tauup \\ \X\etaup & \X\xiup & \X\upsilonup \\ \end{tabular} \bigskip \begin{tablenote} The symbols in this table are intended to be used sporadically throughout a document (e.g.,~to represent mathematical units or numerical quantities---``$\piup$~{\usefont{OMS}{txsy}{m}{n}\char"19} {\usefont{OT1}{txr}{m}{n}3.14159}''). In contrast, \greekfontmessage. \end{tablenote} \end{symtable} \begin{symtable}[UPGR]{\UPGR\ Upright Greek Letters} \subindex{alphabets}{Greek} \index{Greek>upright} \index{Greek>letters} \index{upright Greek letters} \label{upgreek-greek} \begin{tabular}{*4{ll}} \K\upalpha & \K\uptheta & \K\uppi & \K\upphi \\ \K\upbeta & \K\upvartheta & \K\upvarpi & \K\upvarphi \\ \K\upgamma & \K\upiota & \K\uprho & \K\upchi \\ \K\updelta & \K\upkappa & \K\upvarrho & \K\uppsi \\ \K\upepsilon & \K\uplambda & \K\upsigma & \K\upomega \\ \K\upvarepsilon & \K\upmu & \K\upvarsigma \\ \K\upzeta & \K\upnu & \K\uptau \\ \K\upeta & \K\upxi & \K\upupsilon \\ \\ \K\Upgamma & \K\Uplambda & \K\Upsigma & \K\Uppsi \\ \K\Updelta & \K\Upxi & \K\Upupsilon & \K\Upomega \\ \K\Uptheta & \K\Uppi & \K\Upphi \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{UPGR}{upgreek}. \end{tablenote} \end{symtable} \begin{symtable}[FOUR]{\FOUR\ Variant Greek Letters} \index{Greek>letters} \subindex{alphabets}{Greek} \index{pi=pi (\FOURpi)} \label{fourier-greek} \begin{tabular}{*2{ll}} \K[\FOURpi]\pi & \K[\FOURrho]\rho \\ \K[\FOURvarpi]\varpi & \K[\FOURvarrho]\varrho \\ \K\varvarpi & \K\varvarrho \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Variant Latin Letters} \index{letters>variant Latin} \label{txpx-variant} \begin{tabular}{*3{ll@{\qquad}}ll} \X\varg & \X\varv & \X\varw & \X\vary \\ \end{tabular} \bigskip \begin{tablenote} \newcommand*{\txital}[1]{{\usefont{T1}{txr}{m}{it}#1}} Pass the \optname{txfonts/pxfonts}{varg} option to \TXPX\ to replace~\txital{g}, \txital{v}, \txital{w}, and~\txital{y} with~$\varg$, $\varv$, $\varw$, and~$\vary$ in every mathematical expression in your document. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Variant Greek Letters} \index{letters>variant Greek} \label{bsk-variant-greek} \begin{tabular}{*3{ll@{\qquad}}ll} \K[\BSKvarbeta]\varbeta & \K[\BSKvarkappa]\varkappa & \K[\BSKvarpi]\varpi & \K[\BSKvarsigma]\varsigma \\ \K[\BSKvarepsilon]\varepsilon & \K[\BSKvarphi]\varphi & \K[\BSKvarrho]\varrho & \K[\BSKvartheta]\vartheta \\ \end{tabular} \end{symtable} \begin{symtable}[BSK]{\BSK\ Variant Latin Letters} \index{letters>variant Latin} \label{bsk-variant-latin} \begin{tabular}{ll} \K[\BSKvarg]\varg \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Variant Greek Letters} \index{letters>variant Greek} \label{stix-variant-greek} \begin{tabular}{*3{ll@{\qquad}}ll} \K[\STIXvarepsilon]\varepsilon & \K[\STIXvarphi]\varphi & \K[\STIXvarrho]\varrho & \K[\STIXvartheta]\vartheta \\ \K[\STIXvarkappa]\varkappa & \K[\STIXvarpi]\varpi & \K[\STIXvarsigma]\varsigma & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Transformed Greek Letters} \label{stix-xform-greek} \begin{tabular}{*2{ll@{\qquad}}ll} \K[\STIXbackepsilon]\backepsilon & \K[\STIXturnediota]\turnediota \\ \K[\STIXmho]\mho & \K[\STIXupbackepsilon]\upbackepsilon \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Hebrew Letters} \index{Hebrew}\subindex{alphabets}{Hebrew} \label{ams-hebrew} \begin{tabular}{*6l} \X\beth & \X\gimel & \X\daleth \end{tabular} \bigskip \begin{tablenote} \cmdX{\aleph}~($\aleph$) appears in \vref{ord}. \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Hebrew Letters} \index{Hebrew}\subindex{alphabets}{Hebrew} \label{mns-hebrew} \begin{tabular}{*8l} \K[\MNSaleph]\aleph & \K[\MNSbeth]\beth & \K[\MNSgimel]\gimel & \K[\MNSdaleth]\daleth \\ \end{tabular} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Hebrew Letters} \index{Hebrew}\subindex{alphabets}{Hebrew} \label{fdsym-hebrew} \begin{tabular}{*8l} \K[\FDSYMaleph]\aleph & \K[\FDSYMbeth]\beth & \K[\FDSYMgimel]\gimel & \K[\FDSYMdaleth]\daleth \\ \end{tabular} \end{symtable} \begin{symtable}[BSK]{\BSK\ Hebrew Letters} \index{Hebrew}\subindex{alphabets}{Hebrew} \label{bsk-hebrew} \begin{tabular}{*8l} \K[\BSKbeth]\beth & \K[\BSKgimel]\gimel & \K[\BSKdaleth]\daleth \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Hebrew Letters} \index{Hebrew}\subindex{alphabets}{Hebrew} \label{stix-hebrew} \begin{tabular}{*4{ll}} \K[\STIXaleph]\aleph & \K[\STIXbeth]\beth & \K[\STIXgimel]\gimel & \K[\STIXdaleth]\daleth \\ \end{tabular} \end{symtable} \begin{symtable}{Letter-like Symbols} \idxboth{letter-like}{symbols} \index{tacks} \idxboth{logic}{symbols} \label{letter-like} \begin{tabular}{*5{ll}} \X\bot & \X\forall & \X\imath & \X\ni & \X\top \\ \X\ell & \X\hbar & \X\in & \X\partial & \X\wp \\ \X\exists & \X\Im & \X\jmath & \X\Re \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{ams-letter-like} \begin{tabular}{*3{ll}} \X\Bbbk & \X\complement & \X\hbar \\ \X\circledR & \X\Finv & \X\hslash \\ \X\circledS & \X\Game & \X\nexists \\ \end{tabular} \end{symtable} \begin{symtable}[TX]{\TXPX\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{txpx-letter-like} \begin{tabular}{*4{ll}} \X\mathcent & \X[\TXmathsterling]\mathsterling$^*$ & \X\notin & \X\notni \\ \end{tabular} \bigskip \usetextmathmessage[*] \end{symtable} \begin{symtable}[ABX]{\ABX\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{abx-letter-like} \begin{tabular}{*4{ll}} \X[\ABXbarin]\barin & \X[\ABXin]\in & \X[\ABXnottop]\nottop & \X[\ABXvarnotin]\varnotin \\ \X[\ABXcomplement]\complement & \X[\ABXnexists]\nexists & \X[\ABXowns]\owns & \X[\ABXvarnotowner]\varnotowner \\ \X[\ABXexists]\exists & \X[\ABXnotbot]\notbot & \X[\ABXownsbar]\ownsbar \\ \X[\ABXFinv]\Finv & \X[\ABXnotin]\notin & \X[\ABXpartial]\partial \\ \X[\ABXGame]\Game & \X[\ABXnotowner]\notowner & \X[\ABXpartialslash]\partialslash \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Letter-like Symbols} \idxboth{letter-like}{symbols} \idxboth{logic}{symbols} \label{mns-letter-like} \begin{tabular}{*4{ll}} \K[\MNSbot]\bot & \K[\MNSin]\in & \K[\MNSnowns]\nowns & \K[\MNStop]\top \\ \K[\MNSexists]\exists & \K[\MNSnexists]\nexists & \K[\MNSowns]\owns & \K[\MNSwp]\wp \\ \K[\MNSforall]\forall & \K[\MNSnin]\nin & \K[\MNSpowerset]\powerset & \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ provides synonyms \cmdI[\MNSnin]{\notin} for \cmdI[\MNSnin]{\nin}, \cmdI[\MNSowns]{\ni} for \cmdI[\MNSowns]{\owns}, and \cmdI[\MNStop]{\intercal} for \cmdI[\MNStop]{\top}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Letter-like Symbols} \idxboth{letter-like}{symbols} \idxboth{logic}{symbols} \label{fdsym-letter-like} \begin{tabular}{*4{ll}} \K[\FDSYMbot]\bot & \K[\FDSYMforall]\forall & \K[\FDSYMin]\in & \K[\FDSYMowns]\owns \\ \K[\FDSYMcomplement]\complement & \K[\FDSYMGame]\Game & \K[\FDSYMnexists]\nexists & \K[\FDSYMtop]\top \\ \K[\FDSYMexists]\exists & \K[\FDSYMhbar]\hbar & \K[\FDSYMnin]\nin & \K[\FDSYMwp]\wp \\ \K[\FDSYMFinv]\Finv & \K[\FDSYMhslash]\hslash & \K[\FDSYMnowns]\nowns & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ provides synonyms \cmdI[\FDSYMnin]{\notin} for \cmdI[\FDSYMnin]{\nin}, \cmdI[\FDSYMowns]{\ni} for \cmdI[\FDSYMowns]{\owns}, and \cmdI[\FDSYMnowns]{\nni} for \cmdI[\FDSYMnowns]{\nowns}. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Letter-like Symbols} \idxboth{letter-like}{symbols} \idxboth{logic}{symbols} \label{bsk-letter-like} \begin{tabular}{*4{ll}} \K[\BSKBbbk]\Bbbk & \K[\BSKGame]\Game & \K[\BSKimath]\imath & \K[\BSKnexists]\nexists \\ \K[\BSKcomplement]\complement & \K[\BSKhbar]\hbar & \K[\BSKintercal]\intercal & \K[\BSKwp]\wp \\ \K[\BSKFinv]\Finv & \K[\BSKhslash]\hslash & \K[\BSKjmath]\jmath & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Letter-like Symbols} \idxboth{letter-like}{symbols} \idxboth{logic}{symbols} \label{stix-letter-like} \begin{tabular}{*4{ll}} \K[\STIXAngstrom]\Angstrom & \K[\STIXEulerconst]\Eulerconst & \K[\STIXimath]\imath & \K[\STIXtop]\top \\ \K[\STIXBbbk]\Bbbk & \K[\STIXexists]\exists & \K[\STIXintercal]\intercal & \K[\STIXtopbot]\topbot \\ \K[\STIXbot]\bot & \K[\STIXFinv]\Finv & \K[\STIXjmath]\jmath & \K[\STIXwp]\wp \\ \K[\STIXcircledR]\circledR & \K[\STIXforall]\forall & \K[\STIXmathdollar]\mathdollar & \K[\STIXYup]\Yup \\ \K[\STIXcircledS]\circledS & \K[\STIXGame]\Game & \K[\STIXmathparagraph]\mathparagraph & \K[\STIXZbar]\Zbar \\ \K[\STIXcomplement]\complement & \K[\STIXhbar]\hbar & \K[\STIXmathsterling]\mathsterling & \\ \K[\STIXdigamma]\digamma & \K[\STIXhslash]\hslash & \K[\STIXnexists]\nexists & \\ \K[\STIXell]\ell & \K[\STIXIm]\Im & \K[\STIXRe]\Re & \\ \end{tabular} \end{symtable} \begin{symtable}[TRF]{\TRF\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{trf-letter-like} \begin{tabular}{ll@{\qqquad}ll} \X\e & \X\im \\ \end{tabular} \end{symtable} \begin{symtable}[MDES]{\MDES\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{mdes-letter-like} \begin{tabular}{*2{ll}} \K[\MDESin]\in & \K[\MDESowns]\owns \\ \K[\MDESnotin]\notin & \K[\MDESsmallin]\smallin \\ \K[\MDESnotsmallin]\notsmallin & \K[\MDESsmallowns]\smallowns \\ \K[\MDESnotsmallowns]\notsmallowns & \\ \end{tabular} \bigskip \begin{tablenote} \ifAMS The \MDES\ package additionally provides versions of each of the letter-like symbols shown in \vref{ams-letter-like}. \else The \MDES\ package additionally provides versions of each of the \AMS\ letter-like symbols. \fi \end{tablenote} \end{symtable} \begin{symtable}[FGE]{\FGE\ Letter-like Symbols} \idxboth{letter-like}{symbols} \idxboth{Frege logic}{symbols} \idxboth{rotated}{letters} \index{upside-down letters} \index{inverted letters} \label{fge-letter-like} \begin{tabular}{*3{ll@{\qqquad}}ll} \K\fgeA & \K\fgeeszett & \K\fgeleftB & \K\fges \\ \K\fgec & \K\fgeF & \K\fgeleftC & \\ \K\fged & \K\fgef & \K\fgemark$^*$ & \\ \K\fgee & \K\fgelb$^*$ & \K\fgerightB & \\ \end{tabular} \bigskip \begin{tablenote}[*] The \FGE\ package defines \cmdI[\fgelb]{\fgeeta}, \cmdI[\fgelb]{\fgeN}, and \cmdI[\fgelb]{\fgeoverU} as synonyms for \cmdI{\fgelb} and \cmdI[\fgemark]{\fgeU} as a synonym for \cmdI{\fgemark}. \end{tablenote} \end{symtable} \begin{symtable}[FOUR]{\FOUR\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{fourier-letter-like} \begin{tabular}{*2{ll}} \K[\FOURpartial]\partial & \K\varpartialdiff \\ \end{tabular} \end{symtable} \begin{symtable}[CMLL]{\CMLL\ Letter-like Symbols} \idxboth{letter-like}{symbols} \label{cmll-letter-like} \begin{tabular}{ll@{\qquad}ll} \K[\CMLLBot]\Bot & \K[\CMLLsimbot]\simbot \\ \end{tabular} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Proof Symbols} \index{quantifiers} \index{Q.E.D.} \index{end of proof} \index{proof, end of} \idxboth{logic}{symbols} \label{logix-proof} \begin{tabular}{*4{ll}} \K\BnchExists & \K[\LOGIXBot]\Bot & \K\HdnForAll & \K\TFBoth \\ \K\BnchForAll & \K\Defn & \K\NFalse & \K\TFNone \\ \K\BnchHdnExists & \K\End & \K\NtExists & \K[\LOGIXTop]\Top \\ \K\BnchHdnForAll & \K\Exists & \K\NTrue & \K\True \\ \K\BnchNtExists & \K\False & \K\Qed & \K\Unique \\ \K\BnchUnique & \K\ForAll & \K\QuantCon & \\ \K\BndMap & \K\HdnExists & \K\QuantDis & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[EOPROOF]{\EOPROOF\ End-of-Proof Symbols} \index{Q.E.D.} \index{end of proof} \index{proof, end of} \label{endofproof} \begin{tabular}{ll} \K\wasserdicht \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{EOPROOF}{endofproof}. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Delimiters} \index{delimiters} \label{ams-del} \begin{tabular}{*2{ll}} \X\ulcorner & \X\urcorner \\ \X\llcorner & \X\lrcorner \end{tabular} \end{symtable} \begin{symtable}[ST]{\ST\ Delimiters} \index{delimiters} \label{st-del} \begin{tabular}{*4{ll}} \X\Lbag &\X\Rbag &\X\lbag &\X\rbag \\ \X\llceil &\X\rrceil &\X\llfloor &\X\rrfloor \\ \X\llparenthesis &\X\rrparenthesis \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Delimiters} \index{delimiters} \label{abx-del} \begin{tabular}{ll@{\hspace*{2em}}ll} \X[\ABXlcorners]\lcorners & \X[\ABXrcorners]\rcorners \\[3ex] \X[\ABXulcorner]\ulcorner & \X[\ABXurcorner]\urcorner \\ \X[\ABXllcorner]\llcorner & \X[\ABXlrcorner]\lrcorner \\ \end{tabular} \end{symtable} \begin{symtable}[BSK]{\BSK\ Delimiters} \index{delimiters} \label{bsk-del} \begin{tabular}{*2{ll}} \K[\BSKulcorner]\ulcorner & \K[\BSKurcorner]\urcorner \\ \K[\BSKllcorner]\llcorner & \K[\BSKlrcorner]\lrcorner \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Delimiters} \index{delimiters} \label{stix-del} \begin{tabular}{llll@{\qqquad}llll} \K[\STIXlangledot]\langledot & \K[\STIXrangledot]\rangledot & \K[\STIXllangle]\llangle & \K[\STIXrrangle]\rrangle \\ \K[\STIXlbag]\lbag & \K[\STIXrbag]\rbag & \K[\STIXllcorner]\llcorner & \K[\STIXlrcorner]\lrcorner \\ \K[\STIXlblkbrbrak]\lblkbrbrak & \K[\STIXrblkbrbrak]\rblkbrbrak & \K[\STIXllparenthesis]\llparenthesis & \K[\STIXrrparenthesis]\rrparenthesis \\ \K[\STIXlbracklltick]\lbracklltick & \K[\STIXrbrackurtick]\rbrackurtick & \K[\STIXLparengtr]\Lparengtr & \K[\STIXRparenless]\Rparenless \\ \K[\STIXlbrackubar]\lbrackubar & \K[\STIXrbrackubar]\rbrackubar & \K[\STIXlparenless]\lparenless & \K[\STIXrparengtr]\rparengtr \\ \K[\STIXlbrackultick]\lbrackultick & \K[\STIXrbracklrtick]\rbracklrtick & \K[\STIXlvzigzag]\lvzigzag & \K[\STIXrvzigzag]\rvzigzag \\ \K[\STIXLbrbrak]\Lbrbrak & \K[\STIXRbrbrak]\Rbrbrak & \K[\STIXLvzigzag]\Lvzigzag & \K[\STIXRvzigzag]\Rvzigzag \\ \K[\STIXlcurvyangle]\lcurvyangle & \K[\STIXrcurvyangle]\rcurvyangle & \K[\STIXulcorner]\ulcorner & \K[\STIXurcorner]\urcorner \\ \end{tabular} \end{symtable} \begin{symtable}[NATH]{\NATH\ Delimiters} \index{delimiters} \label{nath-del} \begin{tabular}{ll@{\qqquad}ll} \X\niv & \X\vin \\ \end{tabular} \end{symtable} \begin{symtable}{Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \label{dels} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll@{\hspace*{1.5cm}}lll@{\qquad}lll} \N\downarrow & \N\Downarrow & \N{[} & \N[\magicrbrack]{]} \\ \N\langle & \N\rangle & \Np[\vert][\magicvertname]| & \Np[\Vert][\magicVertname]\| \\ \N\lceil & \N\rceil & \N\uparrow & \N\Uparrow \\ \N\lfloor & \N\rfloor & \N\updownarrow & \N\Updownarrow \\ \N( & \N) & \Np\{ & \Np\} \\ \N/ & \N\backslash \\ \end{tabular} \bigskip \begin{tablenote} When used with \cmd{\left} and \cmd{\right}, these symbols expand to the height of the enclosed math expression. Note that \cmdX{\vert} is a synonym for \verb+|+\index{_magicvertname=\magicvertname{} ($\vert$)}, and \cmdX{\Vert} is a synonym for \verb+\|+\index{_magicVertName=\magicVertname{} ($\Vert$)}. $\varepsilon$-\TeX{}\index{e-tex=$\varepsilon$-\TeX} provides a \cmd{\middle} analogue to \cmd{\left} and \cmd{\right}. \cmd{\middle} can be used, for example, to make an internal ``$|$'' expand to the height of the surrounding \cmd{\left} and \cmd{\right} symbols. (This capability is commonly needed when typesetting adjacent bras\index{bra} and kets\index{ket} in Dirac\index{Dirac notation} notation: ``$\langle\phi\vert\psi\rangle$''). This is exactly what the \QTIKZ\ package \ifQTIKZ does (see \vref{quantikz}). \else does. \fi A similar effect can be achieved in conventional \latex using the \pkgname{braket} package. \end{tablenote} \end{symtable} \begin{symtable}{Large, Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \index{braces} \label{ldels} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{*3{lll@{\qquad}}lll} \Y\lmoustache & \Y\rmoustache & \Y\lgroup & \Y\rgroup \\ \Y\arrowvert & \Y\Arrowvert & \Y\bracevert \end{tabular} \bigskip \begin{tablenote} These symbols \emph{must} be used with \cmd{\left} and \cmd{\right}. The \ABX\ package, however, redefines \cmdI[$\string\big\string\lgroup$]{\lgroup} and \cmdI[$\string\big\string\rgroup$]{\rgroup} so that those symbols can work without \cmd{\left} and \cmd{\right}. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \label{ams-var-del} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \N\lvert & \N\rvert \\ \N\lVert & \N\rVert \\ \end{tabular} \bigskip \begin{tablenote} According to the \texttt{amsmath} documentation~\cite{AMS1999:amsmath}, the preceding symbols are intended to be used as delimiters (e.g.,~as in ``$\lvert -z \rvert$'') while the \cmdX{\vert} and \cmdX{\Vert} symbols (\vref*{dels}) are intended to be used as operators (e.g.,~as in ``$p \vert q$''). \end{tablenote} \end{symtable} \begin{symtable}[ST]{\ST\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \index{semantic valuation} \label{st-var-del} \begin{tabular}{lll@{\qquad}lll} \N\llbracket & \N\rrbracket \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \idxboth{wavy line}{delimiters} \index{semantic valuation} \label{abx-var-dels} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \N[\ABXldbrack]\ldbrack & \N[\ABXrdbrack]\rdbrack \\ \Nbig[\ABXlfilet]\lfilet & \Nbig[\ABXrfilet]\rfilet \\ \N[\ABXthickvert]\thickvert & \N[\ABXvvvert]\vvvert \\ \end{tabular} \end{symtable} \begin{longsymtable}[MNS]{\MNS\ Variable-sized Delimiters} \ltindex{delimiters} \ltindex{delimiters>variable-sized} \ltindex{braces} \ltidxboth{wavy line}{delimiters} \label{mns-var-dels} \renewcommand{\arraystretch}{3} % Keep tall symbols from touching. \begin{longtable}{lll*2{@{\qquad}lll}} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[1ex] \endhead \endfirsthead \\[0ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KNbig[\MNStArrowvert][\MNSdArrowvert]\Arrowvert & \KNbig[\MNStlbrace][\MNSdlbrace]\lbrace & \KNbig[\MNStrceil][\MNSdrceil]\rceil \\ \KNbig[\MNStarrowvert][\MNSdarrowvert]\arrowvert & \KNbig[\MNStlceil][\MNSdlceil]\lceil & \KNbig[\MNStrfloor][\MNSdrfloor]\rfloor \\ \KNbig[\MNStbackslash][\MNSdbackslash]\backslash & \KNbig[\MNStlfloor][\MNSdlfloor]\lfloor & \KNbig[\MNStrgroup][\MNSdrgroup]\rgroup \\ \KNbig[\MNStbracevert][\MNSdbracevert]\bracevert & \KNbig[\MNStlgroup][\MNSdlgroup]\lgroup & \KNbig[\MNStrmoustache][\MNSdrmoustache]\rmoustache \\ \KNbig[\MNStlbracket][\MNSdlbracket]{[} & \KNbig[\MNStllangle][\MNSdllangle]\llangle & \KNbig[\MNStrrangle][\MNSdrrangle]\rrangle \\ \KNbig[\MNStrbracket][\MNSdrbracket]{]} & \KNbig[\MNStllcorner][\MNSdllcorner]\llcorner & \KNbig[\MNStrsem][\MNSdrsem]\rsem \\ \KNbig[\MNStlparen][\MNSdlparen]( & \KNbig[\MNStlmoustache][\MNSdlmoustache]\lmoustache & \KNbig[\MNStrWavy][\MNSdrWavy]\rWavy \\ \KNbig[\MNStrparen][\MNSdrparen]) & \KNbig[\MNStlrcorner][\MNSdlrcorner]\lrcorner & \KNbig[\MNStrwavy][\MNSdrwavy]\rwavy \\ \KNbig[\MNStslash][\MNSdslash]/ & \KNbig[\MNStlsem][\MNSdlsem]\lsem & \KNbig[\MNStulcorner][\MNSdulcorner]\ulcorner \\ \KNbig[\MNStless][\MNSdless]< & \KNbig[\MNStlwavy][\MNSdlwavy]\lwavy & \KNbig[\MNStullcorner][\MNSdullcorner]\ullcorner \\ \KNbig[\MNStgreater][\MNSdgreater]> & \KNbig[\MNStlWavy][\MNSdlWavy]\lWavy & \KNbig[\MNStulrcorner][\MNSdulrcorner]\ulrcorner \\ \let\indexcommand=\indexpunct % Hack to make the "|" symbol index properly \KNbig[\MNStvert][\MNSdvert]| & \KNbig[\MNStrangle][\MNSdrangle]\rangle & \KNbig[\MNSturcorner][\MNSdurcorner]\urcorner \\ \KNbig[\MNStlangle][\MNSdlangle]\langle & \KNbig[\MNStranglebar][\MNSdranglebar]\ranglebar & \let\indexcommand=\indexpunct % Hack to make the "|" symbol index properly \KNbig[\MNStVert][\MNSdVert]\| \\ \KNbig[\MNStlanglebar][\MNSdlanglebar]\langlebar & \KNbig[\MNStrbrace][\MNSdrbrace]\rbrace & \\ \end{longtable} \bigskip \begin{tablenote} \cmdX{\vert} is a synonym for \verb+|+\index{_magicvertname=\magicvertname{} ($\vert$)}. \cmdX{\Vert} is a synonym for \verb+\|+\index{_magicVertname=\magicVertname{} ($\Vert$)}. \cmdX{\mid} and \verb|\mvert| produce the same symbol as \cmdX{\vert} but designated as math relations instead of ordinals. \verb|\divides| produces the same symbol as \cmdX{\vert} but designated as a binary operator instead of an ordinal. \cmdX{\parallel} and \verb|\mVert| produce the same symbol as \cmdX{\Vert} but designated as math relations instead of ordinals. \end{tablenote} \end{longsymtable} \begin{longsymtable}[FDSYM]{\FDSYM\ Variable-sized Delimiters} \ltindex{delimiters} \ltindex{delimiters>variable-sized} \ltindex{braces} \ltidxboth{wavy line}{delimiters} \label{fdsym-var-dels} \renewcommand{\arraystretch}{3} % Keep tall symbols from touching. \begin{longtable}{lll*2{@{\qquad}lll}} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[1ex] \endhead \endfirsthead \\[0ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KNbig[\FDSYMtbackslash][\FDSYMdbackslash]\backslash & \KNbig[\FDSYMtlrcorner][\FDSYMdlrcorner]\lrcorner & \KNbig[\FDSYMtrparen][\FDSYMdrparen]\rparen \\ \KNbig[\FDSYMtdownarrow][\FDSYMddownarrow]\downarrow & \KNbig[\FDSYMtlvert][\FDSYMdlvert]\lvert & \KNbig[\FDSYMtrvert][\FDSYMdrvert]\rvert \\ \KNbig[\FDSYMtDownarrow][\FDSYMdDownarrow]\Downarrow & \KNbig[\FDSYMtlVert][\FDSYMdlVert]\lVert & \KNbig[\FDSYMtrVert][\FDSYMdrVert]\rVert \\ \KNbig[\FDSYMtlAngle][\FDSYMdlAngle]\lAngle & \KNbig[\FDSYMtlVvert][\FDSYMdlVvert]\lVvert & \KNbig[\FDSYMtrVvert][\FDSYMdrVvert]\rVvert \\ \KNbig[\FDSYMtlangle][\FDSYMdlangle]\langle & \KNbig[\FDSYMtmathslash][\FDSYMdmathslash]\mathslash & \KNbig[\FDSYMtulcorner][\FDSYMdulcorner]\ulcorner \\ \KNbig[\FDSYMtlangledot][\FDSYMdlangledot]\langledot & \KNbig[\FDSYMtrangle][\FDSYMdrangle]\rangle & \KNbig[\FDSYMtullcorner][\FDSYMdullcorner]\ullcorner \\ \KNbig[\FDSYMtlbrace][\FDSYMdlbrace]\lbrace & \KNbig[\FDSYMtrAngle][\FDSYMdrAngle]\rAngle & \KNbig[\FDSYMtulrcorner][\FDSYMdulrcorner]\ulrcorner \\ \KNbig[\FDSYMtlbrack][\FDSYMdlbrack]\lbrack & \KNbig[\FDSYMtrangledot][\FDSYMdrangledot]\rangledot & \KNbig[\FDSYMtuparrow][\FDSYMduparrow]\uparrow \\ \KNbig[\FDSYMtlBrack][\FDSYMdlBrack]\lBrack & \KNbig[\FDSYMtrbrace][\FDSYMdrbrace]\rbrace & \KNbig[\FDSYMtUparrow][\FDSYMdUparrow]\Uparrow \\ \KNbig[\FDSYMtlceil][\FDSYMdlceil]\lceil & \KNbig[\FDSYMtrBrack][\FDSYMdrBrack]\rBrack & \KNbig[\FDSYMtupdownarrow][\FDSYMdupdownarrow]\updownarrow \\ \KNbig[\FDSYMtlfloor][\FDSYMdlfloor]\lfloor & \KNbig[\FDSYMtrbrack][\FDSYMdrbrack]\rbrack & \KNbig[\FDSYMtUpdownarrow][\FDSYMdUpdownarrow]\Updownarrow \\ \KNbig[\FDSYMtlgroup][\FDSYMdlgroup]\lgroup & \KNbig[\FDSYMtrceil][\FDSYMdrceil]\rceil & \KNbig[\FDSYMturcorner][\FDSYMdurcorner]\urcorner \\ \KNbig[\FDSYMtllcorner][\FDSYMdllcorner]\llcorner & \KNbig[\FDSYMtrfloor][\FDSYMdrfloor]\rfloor & \KNbig[\FDSYMtvert][\FDSYMdvert]\vert \\ \KNbig[\FDSYMtlmoustache][\FDSYMdlmoustache]\lmoustache & \KNbig[\FDSYMtrgroup][\FDSYMdrgroup]\rgroup & \KNbig[\FDSYMtVert][\FDSYMdVert]\Vert \\ \KNbig[\FDSYMtlparen][\FDSYMdlparen]\lparen & \KNbig[\FDSYMtrmoustache][\FDSYMdrmoustache]\rmoustache & \KNbig[\FDSYMtVvert][\FDSYMdVvert]\Vvert \\ \end{longtable} \bigskip \begin{tablenote} \FDSYM\ defines ``\cmdI[\string\FDSYMtlparen]('' as a synonym for \cmdI[\string\FDSYMtlparen]{\lparen}, ``\cmdI[\string\FDSYMtrparen])'' as a synonym for \cmdI[\string\FDSYMtrparen]{\rparen}, ``\cmdI[\string\FDSYMtlbrack]['' as a synonym for \cmdI[\string\FDSYMtlbrack]{\lbrack}, ``\cmdI[\string\FDSYMtrbrack]]'' as a synonym for \cmdI[\string\FDSYMtrbrack]{\rbrack}, ``\verb|{|'' as a synonym for \cmdI[\string\FDSYMtlbrace]{\lbrace}, ``\verb|}|'' as a synonym for \cmdI[\string\FDSYMtrbrace]{\rbrace}, ``\cmdIp[\string\FDSYMtmathslash]/'' as a synonym for \cmdI[\string\FDSYMtmathslash]\mathslash, ``\cmdIp[\string\FDSYMtvert]|'' as a synonym for \cmdI[\string\FDSYMtvert]\vert, ``\cmdIp[\string\FDSYMtVert]\|'' as a synonym for \cmdI[\string\FDSYMtVert]\Vert, \cmdI[\string\FDSYMtlBrack]{\lsem} as a synonym for \cmdI[\string\FDSYMtlBrack]{\lBrack}, and \cmdI[\string\FDSYMtrBrack]{\rsem} as a synonym for \cmdI[\string\FDSYMtrBrack]{\rBrack}. \end{tablenote} \end{longsymtable} \begin{longsymtable}[STIX]{\STIX\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \index{braces} \idxboth{wavy line}{delimiters} \label{stix-var-dels} \renewcommand{\arraystretch}{3} % Keep tall symbols from touching. \begin{longtable}{lll*2{@{\qquad}lll}} \multicolumn{9}{l}{\small\textit{(continued from previous page)}} \\[1ex] \endhead \endfirsthead \\[0ex] \multicolumn{9}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \KNbig[\STIXtArrowvert][\STIXdArrowvert]\Arrowvert & \KNbig[\STIXtlAngle][\STIXdlAngle]\lAngle & \KNbig[\STIXtrceil][\STIXdrceil]\rceil \\ \KNbig[\STIXtarrowvert][\STIXdarrowvert]\arrowvert & \KNbig[\STIXtlbrace][\STIXdlbrace]\lbrace & \KNbig[\STIXtrfloor][\STIXdrfloor]\rfloor \\ \KNbig[\STIXtbackslash][\STIXdbackslash]\backslash & \KNbig[\STIXtlBrace][\STIXdlBrace]\lBrace & \KNbig[\STIXtrgroup][\STIXdrgroup]\rgroup \\ \KNbig[\STIXtDdownarrow][\STIXdDdownarrow]\Ddownarrow & \KNbig[\STIXtlBrack][\STIXdlBrack]\lBrack & \KNbig[\STIXtrmoustache][\STIXdrmoustache]\rmoustache \\ \KNbig[\STIXtDDownarrow][\STIXdDDownarrow]\DDownarrow & \KNbig[\STIXtlbrbrak][\STIXdlbrbrak]\lbrbrak & \KNbig[\STIXtrParen][\STIXdrParen]\rParen \\ \KNbig[\STIXtdownarrow][\STIXddownarrow]\downarrow & \KNbig[\STIXtlceil][\STIXdlceil]\lceil & \KNbig[\STIXtuparrow][\STIXduparrow]\uparrow \\ \KNbig[\STIXtDownarrow][\STIXdDownarrow]\Downarrow & \KNbig[\STIXtlfloor][\STIXdlfloor]\lfloor & \KNbig[\STIXtUparrow][\STIXdUparrow]\Uparrow \\ \KNbig[\STIXtlbracket][\STIXdlbracket]{[} & \KNbig[\STIXtlgroup][\STIXdlgroup]\lgroup & \KNbig[\STIXtUpdownarrow][\STIXdUpdownarrow]\Updownarrow \\ \KNbig[\STIXtrbracket][\STIXdrbracket]{]} & \KNbig[\STIXtlmoustache][\STIXdlmoustache]\lmoustache & \KNbig[\STIXtupdownarrow][\STIXdupdownarrow]\updownarrow \\ \KNbig[\STIXtlparen][\STIXdlparen]( & \KNbig[\STIXtlParen][\STIXdlParen]\lParen & \KNbig[\STIXtUuparrow][\STIXdUuparrow]\Uuparrow \\ \KNbig[\STIXtrparen][\STIXdrparen]) & \KNbig[\STIXtrAngle][\STIXdrAngle]\rAngle & \KNbig[\STIXtUUparrow][\STIXdUUparrow]\UUparrow \\ \KNbig[\STIXtslash][\STIXdslash]/ & \KNbig[\STIXtrangle][\STIXdrangle]\rangle & \KNbig[\STIXtVert][\STIXdVert]\Vert \\ \KNbig[\STIXtless][\STIXdless]< & \KNbig[\STIXtrbrace][\STIXdrbrace]\rbrace & \KNbig[\STIXtvert][\STIXdvert]\vert \\ \KNbig[\STIXtgreater][\STIXdgreater]> & \KNbig[\STIXtrBrace][\STIXdrBrace]\rBrace & \KNbig[\STIXtVvert][\STIXdVvert]\Vvert \\ \let\indexcommand=\indexpunct % Hack to make the "|" symbol index properly \KNbig[\STIXtbar][\STIXdbar]| & \KNbig[\STIXtrBrack][\STIXdrBrack]\rBrack & \\ \KNbig[\STIXtlangle][\STIXdlangle]\langle & \KNbig[\STIXtrbrbrak][\STIXdrbrbrak]\rbrbrak & \\ \end{longtable} \end{longsymtable} \begin{symtable}[MDES]{\MDES\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \idxboth{wavy line}{delimiters} \label{mdes-var-dels} \renewcommand{\arraystretch}{2.75} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \KNbig[\MDESleftwavelet][\MDESleftwave]\leftwave & \KNbig[\MDESleftwavelet][\MDESleftwave]\rightwave \\ \KNbig[\MDESleftevawlet][\MDESleftevaw]\leftevaw & \KNbig[\MDESleftevawlet][\MDESleftevaw]\rightevaw \\ \end{tabular} \bigskip \begin{tablenote} The definitions of these symbols include a preceding \cmd{\left} or \cmd{\right}. It is therefore an error to specify \cmd{\left} or \cmd{\right} explicitly. The internal, ``primitive'' versions of these symbols are called \cmdI[\MDESleftwave]{\lwave}, \cmdI[\MDESleftwave]{\rwave}, \cmdI[\MDESleftevaw]{\levaw}, and \cmdI[\MDESleftevaw]{\revaw}. \end{tablenote} \end{symtable} \begin{symtable}[NATH]{\NATH\ Variable-sized Delimiters (Double)} \index{delimiters} \index{delimiters>variable-sized} \index{semantic valuation} \label{nath-var-dels-double} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \Nn[\langle]\lAngle & \Nn[\rangle]\rAngle \\ \Nn[{[}]\lBrack & \Nn[\magicrbrack]\rBrack \\ \Nn[\lceil]\lCeil & \Nn[\rceil]\rCeil \\ \Nn[\lfloor]\lFloor & \Nn[\rfloor]\rFloor \\ \Nn[\vert]\lVert$^*$ & \Nn[\vert]\rVert$^*$ \\ \end{tabular} \bigskip \begin{tablenote} All of the symbols in this table also can be expressed using the \cmd{\double} macro. See the \NATH\ documentation for examples and additional information. \end{tablenote} \bigskip \begin{tablenote}[*] Separate \verb+\lVert+ and \verb+\rVert+ commands exist to disambiguate whether ``\verb+|+\index{_magicvertname=\magicvertname{} ($\vert$)}'' is a left or right delimiter. This is because \NATH\ defines all of the symbols shown in this table to include implicit \cmd{\left} and \cmd{\right} commands. \end{tablenote} \end{symtable} \begin{symtable}[NATH]{\NATH\ Variable-sized Delimiters (Triple)} \index{delimiters} \index{delimiters>variable-sized} \index{triple<=\verb+\triple<+ ($\nathtriple\langle$)} \index{triple!>=\verb+\triple!>+ ($\nathtriple\rangle$)} \index{triple[=\verb+\triple[+ ($\nathtriple[$)} \index{triple]=\verb+\triple]+ ($\nathtriple]$)} \index{ltriplevert=\verb+\ltriple\vert+ ($\nathtriple\vert$)} \index{rtriplevert=\verb+\rtriple\vert+ ($\nathtriple\vert$)} \label{nath-var-dels-triple} \renewcommand{\arraystretch}{2.5} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \Nnt{}[\langle]< & \Nnt{}[\rangle]> \\ \Nnt{}[{[}]{[} & \Nnt{}[\magicrbrack]{]} \\ \Nnt{l}[\vert]|$^*$ & \Nnt{r}[\vert]|$^*$ \\ \end{tabular} \bigskip \begin{tablenote} Note that \cmd{\triple}---and the corresponding \cmd{\double}---is actually a macro that takes a delimiter as an argument. \end{tablenote} \bigskip \begin{tablenote}[*] Similar to \verb+\lVert+ and \verb+\rVert+ in \vref{nath-var-dels-double}, \cmd{\ltriple} and \cmd{\rtriple} must be used instead of \cmd{\triple} to disambiguate whether ``\verb+|+\index{_magicvertname=\magicvertname{} ($\vert$)}'' is a left or right delimiter. \end{tablenote} \end{symtable} \begin{symtable}[FOUR]{\FOUR\ Variable-sized Delimiters} \index{delimiters} \index{delimiters>variable-sized} \index{semantic valuation} \label{fourier-var-dels} \renewcommand{\arraystretch}{2.75} % Keep tall symbols from touching. \begin{tabular}{lll@{\qquad}lll} \KNbig[\FOURtllbracket][\FOURdllbracket]\llbracket & \KNbig[\FOURtrrbracket][\FOURdrrbracket]\rrbracket \\ \KNbig[\FOURtVERT][\FOURdVERT]\VERT \\ \end{tabular} \end{symtable} \begin{longsymtable}[LOGIX]{\LOGIX\ Variable-sized Delimiters} \ltindex{delimiters} \ltindex{delimiters>variable-sized} \label{logix-dels} \renewcommand{\arraystretch}{1.75} % Keep tall symbols from touching. \begin{longtable}{lll@{\qquad}lll} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \Nlogix{BndBar} \\ \Nlogixii{Angl} \\ \Nlogixii{AnglBar} \\ \Nlogixii{ArrwBrac} \\ \Nlogixii{Bar} \\ \Nlogixii{Brac} \\ \Nlogixii{BracBar} \\ \Nlogixii{BrknBrac} \\ \Nlogixii{BrknBracBar} \\ \Nlogixii{BrknBrkt} \\ \Nlogixii{BrknBrktBar} \\ \Nlogixii{Brkt} \\ \Nlogixii{BrktBar} \\ \Nlogixii{Ceil} \\ \Nlogixii{CircBrac} \\ \Nlogixii{CircBracBar} \\ \Nlogixii{CircBrkt} \\ \Nlogixii{CircBrktBar} \\ \Nlogixii{CrlyBrkt} \\ \Nlogixii{CrlyBrktBar} \\ \Nlogixii{CurvAngl} \\ \Nlogixii{DblAngl} \\ \Nlogixii{DblBar} \\ \Nlogixii{DblBrac} \\ \Nlogixii{DblCeil} \\ \Nlogixii{DblFloor} \\ \Nlogixii{DblGrp} \\ \Nlogixii{DblParn} \\ \Nlogixii{Floor} \\ \Nlogixii{Grp} \\ \Nlogixii{Parn} \\ \Nlogixii{ParnBar} \\ \Nlogixii{SqrParn} \\ \Nlogixii{Tortoise} \\ \Nlogixii{TortoiseBar} \\ \Nlogixii{TrpBar} \\ \Nlogixii{Turn} \\ \end{longtable} \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{longsymtable} \begin{symtable}{\TC\ Text-mode Delimiters} \index{delimiters} \index{delimiters>text-mode} \label{tc-delimiters} \begin{tabular}{*2{ll}} \K\textlangle & \K\textrangle \\ \K\textlbrackdbl & \K\textrbrackdbl \\ \K\textlquill & \K\textrquill \\ \end{tabular} \end{symtable} \begin{symtable}[METRE]{\METRE\ Text-mode Delimiters} \index{delimiters} \index{delimiters>text-mode} \label{metre-delimiters} \begin{tabular}{*2{ll}@{\qqquad}*2{ll}} \K\alad & \K\Alad & \K\crux & \K\Crux \\ \K\alas & \K\Alas & \K\quadrad & \K\Quadrad \\ \K\angud & \K\Angud & \K\quadras & \K\Quadras \\ \K\angus & \K\Angus \\ \end{tabular} \end{symtable} \begin{symtable}{Math-mode Accents} \index{accents} \index{accents>acute=acute (\blackacchack\')} % "Generic" \index{accents>breve=breve (\blackacchack\u)} % "Generic" \index{accents>caron=caron (\blackacchack\v)} % "Generic" \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>diaeresis=di\ae{}resis (\blackacchack\")} % "Generic" \index{accents>dot=dot (\blackacchack\. or \blackacc\d)} % "Generic" \index{accents>grave=grave (\blackacchack\`)} % "Generic" \index{accents>macron=macron (\showmacron)} % "Generic" \index{accents>ring=ring (\blackacchack\r)} % "Generic" \index{accents>hat} \index{tilde} \label{math-accents} \begin{tabular}{*4{ll}} \W\acute{a} & \W\check{a} & \W\grave{a} & \W\tilde{a} \\ \W\bar{a}$^*$ & \W\ddot{a} & \W\hat{a} & \W\vec{a} \\ \W\breve{a} & \W\dot{a} & \W\mathring{a} \\ \end{tabular} \bigskip \begin{tablenote} \subindex{dotless i=dotless $i~(\imath)$}{math mode} \subindex{dotless j=dotless $j~(\jmath)$}{math mode} Note also the existence of \cmdX{\imath} and \cmdX{\jmath}, which produce dotless versions of ``\textit{i}'' and ``\textit{j}''. (See \vref{ord}.) These are useful when the accent is supposed to replace the dot. For example, ``\verb|\hat{\imath}|'' produces a correct ``$\,\hat{\imath}\,$'', while ``\verb|\hat{i}|'' would yield the rather odd-looking ``\,$\hat{i}\,$''. \end{tablenote} \bigskip \begin{tablenote}[*] The \cmdI[$\string\blackacc{\string\overline}$]{\overline} command (\vref*{extensible-accents}) produces a wider accent than \verb|\bar|: ``$\overline{A}$''~vs.~``$\bar{A}$''. However, unlike adjacent \verb|\bar|s, adjacent \verb|\overline|s run together, which is often not desired: ``$\overline{A}\overline{B}$''~vs.~``$\bar{A}\bar{B}$''. If wider bars than \verb|\bar| are needed, the following code from \person{Enrico}{Gregorio} can be used to add the requisite inter-symbol spacing~\cite{Gregorio2009:latex-book}: \vspace{-\baselineskip} \begin{verbatim} \newcommand{\closure}[2][3]{% {}\mkern#1mu\overline{\mkern-#1mu#2}} \end{verbatim} \vspace{-\baselineskip} With that definition, ``\cmdI[$\string\blackacc{\string\closure}$]{\closure}\verb|{A}\closure{B}|'' produces ``$\closure{A}\closure{B}$'', with a visible gap between the two accents. The optional argument can be used to fine-tune the spacing. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Math-mode Accents} \index{accents} \label{ams-math-accents} \begin{tabular}{ll@{\hspace*{2em}}ll} \W\dddot{a} & \W\ddddot{a} \\ \end{tabular} \bigskip \begin{tablenote} These accents are also provided by the \ABX\ and \pkgname{accents} packages and are redefined by the \MDOTS\ package if the \pkgname{amsmath} and \pkgname{amssymb} packages have previously been loaded. All of the variations except for the original \AMS\ ones tighten the space between the dots% \ifMDOTS ~(from~$\dddot{a}$ to~$\MDOTSdddot{a}$)% \else \ifABX ~(from~$\dddot{a}$ to~$\ABXdddot{a}$)% \else \ifACCENTS ~(from~$\dddot{a}$ to~$\ACCENTSdddot{a}$)% \fi \fi \fi . The \ABX\ and \MDOTS\ versions also function properly within subscripts and superscripts% \ifMDOTS ~($x^{\MDOTSdddot{a}}$ instead of~$x^{\dddot{a}}$) \else \ifABX ~($x^{\ABXdddot{a}}$ instead of~$x^{\dddot{a}}$) \fi \fi . \end{tablenote} \end{symtable} \begin{symtable}[MNS]{\MNS\ Math-mode Accents} \index{accents} \label{mns-math-accents} \begin{tabular}{ll} \W[\MNSvec]\vec{a} \\ \end{tabular} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Math-mode Accents} \index{accents} \label{fdsym-math-accents} \renewcommand{\arraystretch}{1.1} \begin{tabular}{ll@{\quad}ll} \W[\FDSYMmiddlebar]\middlebar{a} & \W[\FDSYMstrokethrough]\strokethrough{a} \\ \W[\FDSYMmiddleslash]\middleslash{a} & \W[\FDSYMvec]\vec{a} \\ \end{tabular} \bigskip \begin{tablenote} \verb|\middlebar| and \verb|\middleslash| are applied here to ``$a$'' for consistency with the rest of the document, but they generally look better when applied to taller lowercase characters. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Math-mode Accents} \index{accents} \label{bsk-math-accents} \begin{tabular}{ll} \W[\BSKvec]\vec{a} \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Math-mode Accents} \index{accents} \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>hat} \label{stix-math-accents} \renewcommand{\arraystretch}{1.1} \begin{tabular}{ll@{\quad}ll} \W[\STIXacute]\acute{a} & \W[\STIXhat]\hat{a} \\ \W[\STIXannuity]\annuity{a} & \W[\STIXleftarrowaccent]\leftarrowaccent{a} \\ \W[\STIXasteraccent]\asteraccent{a} & \W[\STIXleftharpoonaccent]\leftharpoonaccent{a} \\ \W[\STIXbar]\bar{a} & \W[\STIXleftrightarrowaccent]\leftrightarrowaccent{a} \\ \W[\STIXbreve]\breve{a} & \W[\STIXmathring]\mathring{a} \\ \W[\STIXcandra]\candra{a} & \W[\STIXocommatopright]\ocommatopright{a} \\ \W[\STIXcheck]\check{a} & \W[\STIXoturnedcomma]\oturnedcomma{a} \\ \W[\STIXddddot]\ddddot{a} & \W[\STIXovhook]\ovhook{a} \\ \W[\STIXdddot]\dddot{a} & \W[\STIXrightharpoonaccent]\rightharpoonaccent{a} \\ \W[\STIXddot]\ddot{a} & \W[\STIXtilde]\tilde{a} \\ \W[\STIXdot]\dot{a} & \W[\STIXvec]\vec{a} \\ \W[\STIXdroang]\droang{a} & \W[\STIXwidebridgeabove]\widebridgeabove{a} \\ \W[\STIXgrave]\grave{a} & \\ \end{tabular} \end{symtable} \begin{symtable}[FGE]{\FGE\ Math-mode Accents} \index{accents} \label{fge-math-accents} \begin{tabular}{ll} \Q\spiritusasper \\ \Q\spirituslenis \\ \end{tabular} \bigskip \begin{tablenote} When \FGE\ is passed the \optname{fge}{crescent} option, these symbols instead uses a crescent accent as in ``\,\spiritusasperB{a}\,'' and ``\,\spirituslenisB{a}\,''. \end{tablenote} \end{symtable} \begin{symtable}[YH]{\YH\ Math-mode Accents} \index{accents} \index{accents>ring=ring (\blackacchack\r)} % "Generic" \label{yhmath-accents} \begin{tabular}{ll} \W\ring{a} \end{tabular} \bigskip \begin{tablenote} This symbol is largely obsolete, as standard \latexE has supported \cmdI[$\string\blackacc{\string\mathring}$]{\mathring} (\vref{math-accents}) since June~1998~\cite{ltnews09}. \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Math-mode Accents} \index{accents} \label{pdfmsym-accents} \renewcommand{\arraystretch}{1.2} \begin{tabular}{ll@{\qquad}ll} \W\shortlvecc{a} & \W\shortunderleftrightharp{a} \\ \W\shortoverleftharp{a} & \W\shortunderleftrightvecc{a} \\ \W\shortoverleftrightharp{a} & \W\shortunderlvecc{a} \\ \W\shortoverleftrightvecc{a} & \W\shortunderrightharp{a} \\ \W\shortoverrightharp{a} & \W\shortunderrightleftharp{a} \\ \W\shortoverrightleftharp{a} & \W\shortunderstraightlvecc{a} \\ \W\shortstraightlvecc{a} & \W\shortunderstraightvecc{a} \\ \W\shortstraightvecc{a} & \W\shortundervecc{a} \\ \W\shortunderleftharp{a} & \W\shortvecc{a} \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Halloween-Themed Math-mode Accents} \index{accents} \label{hwmath-accents} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{tabular}{llll} \W\overbat{a} & \W\underbat{a} \\ \Wstar\overbat{a} & \Wstar\underbat{a} \\ \end{tabular} \end{symtable} \begin{symtable}[RHATS]{\RHATS\ Math-mode Hat Accents} \index{accents} \index{accents>hat, literal} \index{Ash Ketchum's hat=Ash Ketchum's hat ($\blackacc{\RHATash}$)} \index{beret=beret ($\blackacc{\RHATberet}$)} \index{birthday hat=birthday hat ($\blackacc{\RHATbirthday}$)} \index{cowboy hat=cowboy hat ($\blackacc{\RHATcowboy}$)} \index{crown=crown ($\blackacc{\RHATcrown}$)} \index{dunce cap=dunce cap ($\blackacc{\RHATdunce}$)} \index{fez=fez ($\blackacc{\RHATfez}$)} \index{mortarboard=mortarboard ($\blackacc{\RHATmortarboard}$)} \index{policeman's hat=policeman's hat ($\blackacc{\RHATpoliceman}$)} \index{Santa Claus's hat=Santa Claus's hat ($\blackacc{\RHATsanta}$)} \index{Scottish hat=Scottish hat ($\blackacc{\RHATscottish}$)} \index{sombrero=sombrero ($\blackacc{\RHATsombrero}$)} \index{top hat=top hat ($\blackacc{\RHATtophat}$)} \index{witch's hat=witch's hat ($\blackacc{\RHATwitch}$)} \label{realhats} \renewcommand{\arraystretch}{1.2} % Keep tall symbols from touching. \begin{tabular}{ll@{\qquad}ll} \W[\RHATash]{\hat[ash]}{a} & \W[\RHATsanta]{\hat[santa]}{a} \\ \W[\RHATberet]{\hat[beret]}{a} & \W[\RHATscottish]{\hat[scottish]}{a} \\ \W[\RHATbirthday]{\hat[birthday]}{a} & \W[\RHATsombrero]{\hat[sombrero]}{a} \\ \W[\RHATcowboy]{\hat[cowboy]}{a} & \W[\RHATtileblue]{\hat[tile-blue]}{a} \\ \W[\RHATcrown]{\hat[crown]}{a} & \W[\RHATtilegray]{\hat[tile-gray]}{a} \\ \W[\RHATdunce]{\hat[dunce]}{a} & \W[\RHATtilelightblue]{\hat[tile-light-blue]}{a} \\ \W[\RHATfez]{\hat[fez]}{a} & \W[\RHATtilewhite]{\hat[tile-white]}{a} \\ \W[\RHATmortarboard]{\hat[mortarboard]}{a} & \W[\RHATtophat]{\hat[tophat]}{a} \\ \W[\RHATpoliceman]{\hat[policeman]}{a} & \W[\RHATwitch]{\hat[witch]}{a} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{RHATS}{realhats}. \end{tablenote} \end{symtable} \begin{symtable}{Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{braces} \index{underline} \index{tilde} \index{tilde>extensible} \index{extensible tildes} \idxboth{extensible}{symbols} \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>macron=macron (\showmacron)} % "Generic" \index{accents>hat} \label{extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{*4l} \W\widetilde{abc}$^*$ & \W\widehat{abc}$^*$ \\ \W\overleftarrow{abc}$^\dag$ & \W\overrightarrow{abc}$^\dag$ \\ \W\overline{abc} & \W\underline{abc} \\ \W\overbrace{abc} & \W\underbrace{abc} \\[5pt] \W\sqrt{abc}$^\ddag$ \\ \end{tabular} \bigskip \begin{tablenote} \def\longdivsign{% \ensuremath{\overline{\vphantom{)}% \hbox{\smash{\raise3.5\fontdimen8\textfont3\hbox{$)$}}}% abc}}} \idxbothbegin{long}{division} \idxbothbegin{polynomial}{division} As demonstrated in a 1997 \TUGboat article about typesetting long-division problems~\cite{Gibbons:longdiv}, an extensible long-division sign (``\,\longdivsign\,'') can be faked by putting a ``\verb|\big)|'' in a \texttt{tabular} environment with an \verb|\hline| or \verb|\cline| in the preceding row. The article also presents a piece of code (uploaded to \CTAN as \hfilename{https://mirror.ctan.org/macros/generic/misc/longdiv.tex}{longdiv.tex}% \index{longdiv=\textsf{longdiv} (package)}% \index{packages>longdiv=\textsf{longdiv}}) that automatically solves and typesets---by putting an \cmdW{\overline} atop ``\verb|\big)|'' and the desired text---long-division problems. \ifSTIX More recently, the \STIX\ fonts include a true long-division sign. See \incsyms\indexaccent[$\string\blackacc{\string\STIXlongdivision}$]{\longdivision}\verb|\longdivision| in \ref{stix-extensible-accents} for a sample of this symbol. \fi See also the \pkgname{polynom} package, which automatically solves and typesets polynomial-division problems in a similar manner. \idxbothend{long}{division} \idxbothend{polynomial}{division} \end{tablenote} \bigskip \begin{tablenote}[*] \def\reftextafter{on the following page} % Don't use randomness within a sentence. These symbols are made more extensible by the \MNS\ package \ifMNS (\vref*{mns-extensible-accents}). \fi % MNS test and even more extensible by the \YH\ \ifYH package (\vref*{yhmath-extensible-accents}). \else package. \fi % YH test \end{tablenote} \bigskip \begin{tablenote}[\dag] If you're looking for an extensible \emph{diagonal} line or arrow to be used for canceling or reducing mathematical subexpressions\subindex{arrows}{diagonal, for reducing subexpressions} \ifhavecancel (e.g.,~``$\cancel{x + -x}$'' or ``$\cancelto{5}{3+2}\quad$'') \fi then consider using the \pkgname{cancel} package. \end{tablenote} \bigskip \begin{tablenote}[\ddag] With an optional argument, \verb|\sqrt| typesets nth roots. For example, ``\verb|\sqrt[3]{abc}|'' produces~``$\sqrt[3]{abc}\,$'' and ``\verb|\sqrt[n]{abc}|'' produces~``$\,\sqrt[n]{abc}$\,''. \end{tablenote} \end{symtable} \begin{symtable}[ORA]{\ORA\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{ora-extensible-accents} \begin{tabular}{ll} \W\Overrightarrow{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[YH]{\YH\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \index{accents>hat} \label{yhmath-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\YHwidehat]\widehat{abc} & \W[\YHwidetilde]\widetilde{abc} \\ \W[\YHwideparen]\wideparen{abc} & \W[\YHwidetriangle]\widetriangle{abc} \\ \W[\YHwidering]\widering{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \label{ams-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W\overleftrightarrow{abc} & \W\underleftrightarrow{abc} \\ \W\underleftarrow{abc} & \W\underrightarrow{abc} \\[2ex] \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{braces} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>hat} \label{mns-extensible-accents} \renewcommand{\arraystretch}{1.75} \begin{tabular}{ll@{\qquad}ll} \W[\MNSoverbrace]\overbrace{abc} & \W[\MNSundergroup]\undergroup{abc} \\ \W[\MNSovergroup]\overgroup{abc} & \W[\MNSunderlinesegment]\underlinesegment{abc} \\ \W[\MNSoverleftharpoon]\overleftharpoon{abc} & \W[\MNSwidehat]\widehat{abc} \\ \W[\MNSoverlinesegment]\overlinesegment{abc} & \W[\MNSwideparen]\wideparen{abc} \\ \W[\MNSoverrightharpoon]\overrightharpoon{abc} & \W[\MNSwidetilde]\widetilde{abc} \\ \W[\MNSunderbrace]\underbrace{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>hat} \label{fdsym-extensible-accents} \renewcommand{\arraystretch}{1.75} \begin{tabular}{ll@{\qquad}ll} \W[\FDSYMoverbrace]\overbrace{abc} & \W[\FDSYMundergroup]\undergroup{abc} \\ \W[\FDSYMovergroup]\overgroup{abc} & \W[\FDSYMunderlinesegment]\underlinesegment{abc} \\ \W[\FDSYMoverleftharpoon]\overleftharpoon{abc} & \W[\FDSYMwidehat]\widehat{abc} \\ \W[\FDSYMoverlinesegment]\overlinesegment{abc} & \W[\FDSYMwideparen]\wideparen{abc} \\ \W[\FDSYMoverrightharpoon]\overrightharpoon{abc} & \W[\FDSYMwidetilde]\widetilde{abc} \\ \W[\FDSYMunderbrace]\underbrace{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>hat} \idxboth{long}{division} \label{stix-extensible-accents} \renewcommand{\arraystretch}{1.75} \begin{tabular}{ll@{\qquad}ll} \W[\STIXlongdivision]\longdivision{abc} & \W[\STIXunderbracket]\underbracket{abc} \\ \W[\STIXoverbrace]\overbrace{abc} & \W[\STIXunderleftarrow]\underleftarrow{abc} \\ \W[\STIXoverbracket]\overbracket{abc} & \W[\STIXunderleftharpoon]\underleftharpoon{abc} \\ \W[\STIXoverleftarrow]\overleftarrow{abc} & \W[\STIXunderleftrightarrow]\underleftrightarrow{abc} \\ \W[\STIXoverleftharpoon]\overleftharpoon{abc} & \W[\STIXunderparen]\underparen{abc} \\ \W[\STIXoverleftrightarrow]\overleftrightarrow{abc} & \W[\STIXunderrightarrow]\underrightarrow{abc} \\ \W[\STIXoverparen]\overparen{abc} & \W[\STIXunderrightharpoon]\underrightharpoon{abc} \\ \W[\STIXoverrightarrow]\overrightarrow{abc} & \W[\STIXwidecheck]\widecheck{abc} \\ \W[\STIXoverrightharpoon]\overrightharpoon{abc} & \W[\STIXwidehat]\widehat{abc} \\ \W[\STIXsqrt]\sqrt{abc} & \W[\STIXwidetilde]\widetilde{abc} \\ \W[\STIXunderbrace]\underbrace{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[MTOOLS]{\MTOOLS\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{braces} \idxboth{extensible}{symbols} \label{mathtools-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\MTOOLSoverbrace]\overbrace{abc} & \W[\MTOOLSunderbrace]\underbrace{abc} \\ \W[\MTOOLSoverbracket]\overbracket{abc}$^*$ & \W[\MTOOLSunderbracket]\underbracket{abc}$^*$ \\ \end{tabular} \bigskip \begin{tablenote}[*] \verb|\overbracket| and \verb|\underbracket| accept optional arguments that specify the bracket height and thickness. \seedocs{\MTOOLS}. \end{tablenote} \end{symtable} \begin{symtable}[ABX]{\ABX\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{braces} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \index{accents>caron=caron (\blackacchack\v)} % "Generic" \index{accents>macron=macron (\showmacron)} % "Generic" \label{abx-extensible-accents} \renewcommand{\arraystretch}{1.75} \begin{tabular}{ll@{\qquad}ll} \W[\ABXoverbrace]\overbrace{abc} & \W[\ABXwidebar]\widebar{abc} \\ \W[\ABXovergroup]\overgroup{abc} & \W[\ABXwidecheck]\widecheck{abc} \\ \W[\ABXunderbrace]\underbrace{abc} & \W[\ABXwideparen]\wideparen{abc} \\ \W[\ABXundergroup]\undergroup{abc} & \W[\ABXwidering]\widering{abc} \\ \W[\ABXwidearrow]\widearrow{abc} \\ \end{tabular} \bigskip \begin{tablenote} The braces shown for \verb|\overbrace| and \verb|\underbrace| appear in their minimum size. They can expand arbitrarily wide, however. \end{tablenote} \end{symtable} \begin{symtable}[FOUR]{\FOUR\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \index{accents>arc=arc (\blackacchack\newtie)} % "Generic" \label{four-extensible-accents} \renewcommand{\arraystretch}{1.75} \begin{tabular}{ll@{\qquad}ll} \W[\FOURwidearc]\widearc{abc} & \W[\FOURwideparen]\wideparen{abc} \\ \W[\FOURwideOarc]\wideOarc{abc} & \W[\FOURwidering]\widering{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[ESV]{\ESV\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{esv-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll} \VV{a}{abc} \\ \VV{b}{abc} \\ \VV{c}{abc} \\ \VV{d}{abc} \\ \VV{e}{abc} \\ \VV{f}{abc} \\ \VV{g}{abc} \\ \VV{h}{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{ESV}{esvect}. \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Extensible Accents} \index{accents} \index{accents>circumflex=circumflex (\blackacchack\^)} % "Generic" \index{accents>hat} \label{pdfmsym-ext-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W\lvecc{abc}$^*$ & \W\underlvecc{abc} \\ \W\overleftharp{abc}$^*$ & \W\underrightharp{abc} \\ \W\overleftrightharp{abc}$^*$ & \W\underrightleftharp{abc} \\ \W\overleftrightvecc{abc}$^*$ & \W\understraightlvecc{abc} \\ \W\overrightharp{abc}$^*$ & \W\understraightvecc{abc} \\ \W\overrightleftharp{abc}$^*$ & \W\undervecc{abc} \\ \W\straightlvecc{abc}$^*$ & \W\varwidecheck{abc} \\ \W\straightvecc{abc}$^*$ & \W\varwidehat{abc} \\ \W\underleftharp{abc} & \W\varwidetilde{abc} \\ \W\underleftrightharp{abc} & \W\vecc{abc}$^*$ \\ \W\underleftrightvecc{abc} & \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \bigskip \begin{tablenote}[*] The \cmd{\constvec} command takes one of these vector commands and its argument and typesets the accent at $x$~height, truncating everything above it. Hence, while \verb|\overleftharp{abcMxyz}| produces ``$\overleftharp{abcMxyz}$'', \verb|\constvec{\overleftharp}{abcMxyz}| produces ``$\constvec{\overleftharp}{abcMxyz}$''. \end{tablenote} \end{symtable} \begin{symtable}[OVARS]{\OVARS\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{overarrows-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\OVARSoverbar]\overbar{abc} & \W[\OVARSunderbar]\underbar{abc} \\ \W[\OVARSoverleftarrow]\overleftarrow{abc} & \W[\OVARSunderleftarrow]\underleftarrow{abc} \\ \W[\OVARSoverleftharpoondown]\overleftharpoondown{abc} & \W[\OVARSunderleftharpoondown]\underleftharpoondown{abc} \\ \W[\OVARSoverleftharpoonup]\overleftharpoonup{abc} & \W[\OVARSunderleftharpoonup]\underleftharpoonup{abc} \\ \W[\OVARSoverleftrightarrow]\overleftrightarrow{abc} & \W[\OVARSunderleftrightarrow]\underleftrightarrow{abc} \\ \W[\OVARSoverrightarrow]\overrightarrow{abc} & \W[\OVARSunderrightarrow]\underrightarrow{abc} \\ \W[\OVARSoverrightharpoondown]\overrightharpoondown{abc} & \W[\OVARSunderrightharpoondown]\underrightharpoondown{abc} \\ \W[\OVARSoverrightharpoonup]\overrightharpoonup{abc} & \W[\OVARSunderrightharpoonup]\underrightharpoonup{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{OVARS}{overarrows}. \end{tablenote} \end{symtable} \begin{symtable}[ABRACES]{\ABRACES\ Extensible Accents} \idxboth{extensible}{accents} \idxboth{extensible}{braces} \idxboth{multiline}{braces} \idxboth{asymmetric}{braces} \idxboth{extensible}{symbols} \label{abraces-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W\aoverbrace{abc} & \W\aunderbrace{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{ABRACES}{abraces}. \end{tablenote} \end{symtable} \begin{symtable}[UTILD]{\UTILD\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \index{tilde>extensible} \index{extensible tildes} \index{tilde} \idxboth{extensible}{symbols} \label{utild-extensible-accents} \begin{tabular}{ll} \W\utilde{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{UTILD}{undertilde}. \end{tablenote} \end{symtable} \begin{symtable}[USHORT]{\USHORT\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \index{underline} \label{ushort-extensible-accents} \begin{tabular}{ll@{\qquad}ll} \W\ushortdw{abc} & \W\ushortw{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{USHORT}{ushort}. \end{tablenote} \end{symtable} \begin{symtable}[MDW]{\MDW\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \label{mdw-extensible-accents} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll} \W[\MDWsqrt]{\sqrt*}{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[ACTANG]{\ACTANG\ Extensible Accents} \index{accents} \idxboth{extensible}{accents} \idxboth{extensible}{symbols} \index{symbols>actuarial} \index{actuarial symbols} \index{symbols>annuity} \index{annuity symbols} \index{symbols>life insurance} \index{life-insurance symbols} \index{symbols>present value} \index{present-value symbols} \label{actuarialangle} \begin{tabular}{ll} \W\actuarialangle{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{ACTANG}{actuarialangle}. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{ams-extensible-arrows} \begin{tabular}{ll@{\qquad}ll} \W\xleftarrow{abc} & \W\xrightarrow{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[MTOOLS]{\MTOOLS\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{mathtools-extensible-arrows} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\MTOOLSxhookleftarrow]\xhookleftarrow{abc} & \W[\MTOOLSxleftrightharpoons]\xleftrightharpoons{abc} \\ \W[\MTOOLSxhookrightarrow]\xhookrightarrow{abc} & \W[\MTOOLSxmapsto]\xmapsto{abc} \\ \W[\MTOOLSxLeftarrow]\xLeftarrow{abc} & \W[\MTOOLSxRightarrow]\xRightarrow{abc} \\ \W[\MTOOLSxleftharpoondown]\xleftharpoondown{abc} & \W[\MTOOLSxrightharpoondown]\xrightharpoondown{abc} \\ \W[\MTOOLSxleftharpoonup]\xleftharpoonup{abc} & \W[\MTOOLSxrightharpoonup]\xrightharpoonup{abc} \\ \W[\MTOOLSxleftrightarrow]\xleftrightarrow{abc} & \W[\MTOOLSxrightleftharpoons]\xrightleftharpoons{abc} \\ \W[\MTOOLSxLeftrightarrow]\xLeftrightarrow{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[CHEMA]{\CHEMA\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{chemarr-extensible-arrows} \begin{tabular}{ll} \W\xrightleftharpoons{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[CHEMB]{\CHEMB\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{chemarrow-extensible-arrows} \renewcommand{\arraystretch}{4} % Keep upper and lower strings from touching. \begin{tabular}{ll@{\qquad}ll} \Wul\autoleftarrow{abc}{def} & \Wul\autorightarrow{abc}{def} \\ \Wul\autoleftrightharpoons{abc}{def} & \Wul\autorightleftharpoons{abc}{def} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{CHEMB}{chemarrow}. \end{tablenote} \end{symtable} \begin{symtable}[EXTAR]{\EXTAR\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{extarrows-extensible-arrows} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\EXTARxLeftrightarrow]\xLeftrightarrow{abc} & \W\xLongleftrightarrow{abc} \\ \W[\EXTARxleftrightarrow]\xleftrightarrow{abc} & \W\xlongleftrightarrow{abc} \\ \W\xlongequal{abc} & \W\xLongrightarrow{abc} \\ \W\xLongleftarrow{abc} & \W\xlongrightarrow{abc} \\ \W\xlongleftarrow{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{pdfmsym-extensible-arrows} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W\xvarCircleleftarrow{abc} & \W\xvarLleftRrightarrow{abc} \\ \W\xvarcircleleftarrow{abc} & \W\xvarmapsfrom{abc} \\ \W\xvarCirclerightarrow{abc} & \W\xvarmapsto{abc} \\ \W\xvarcirclerightarrow{abc} & \W\xvarRibbonleftarrow{abc} \\ \W\xvardoubleleftarrow{abc} & \W\xvarRibbonrightarrow{abc} \\ \W\xvardoublerightarrow{abc} & \W\xvarRightarrow{abc} \\ \W\xvardownhookleftarrow{abc} & \W\xvarrightarrow{abc} \\ \W\xvardownhookrightarrow{abc} & \W\xvarrightarrows{abc} \\ \W\xvarleftarrow{abc} & \W\xvarrightleftarrows{abc} \\ \W\xvarLeftarrow{abc} & \W\xvarRrightarrow{abc} \\ \W\xvarleftarrows{abc} & \W\xvarSquareleftarrow{abc} \\ \W\xvarleftrightarrow{abc} & \W\xvarSquarerightarrow{abc} \\ \W\xvarleftrightarrows{abc} & \W\xvaruphookleftarrow{abc} \\ \W\xvarLleftarrow{abc} & \W\xvaruphookrightarrow{abc} \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[XPFEIL]{\XPFEIL\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{extpfeil-extensible-arrows} \renewcommand{\arraystretch}{1.5} \begin{tabular}{ll@{\qquad}ll} \W[\XPFEILxlongequal]\xlongequal{abc} & \W\xtwoheadleftarrow{abc} \\ \W[\XPFEILxmapsto]\xmapsto{abc} & \W\xtwoheadrightarrow{abc} \\ \W\xtofrom{abc} \end{tabular} \bigskip \begin{tablenote} \seepackagenote{XPFEIL}{extpfeil}. \end{tablenote} \end{symtable} \begin{symtable}[DOTARR]{\DOTARR\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{dotted}{arrows} \idxboth{extensible}{symbols} \label{dot-arrows} \begin{tabular}{ll} \W\dotarrow{a} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{DOTARR}{DotArrow}. \end{tablenote} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Extensible Arrows} \index{arrows} \idxboth{extensible}{arrows} \idxboth{extensible}{symbols} \label{hwmath-arrows} \renewcommand{\arraystretch}{1.5} % Keep high and low accents from touching. \begin{tabular}{ll*2{@{\qquad}ll}} \W\overscriptleftarrow{abc} & \W\underscriptleftarrow{abc} \\ \W\overscriptleftrightarrow{abc} & \W\underscriptleftrightarrow{abc} \\ \W\overscriptrightarrow{abc} & \W\underscriptrightarrow{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{HWMATH}{halloweenmath}. \end{tablenote} \end{symtable} \begin{symtable}[PDFMSYM]{\PDFMSYM\ Extensible Harpoons} \index{harpoons} \idxboth{extensible}{symbols} \label{pdfmsym-ext-harpoons} \renewcommand{\arraystretch}{1.5} % Keep accents from touching. \begin{tabular}{*2{ll}} \W\xvarleftharp{abc} & \W\xvarrightharp{abc} \\ \W\xvarleftrightharp{abc} & \W\xvarrightleftharp{abc} \\ \end{tabular} \bigskip \begin{tablenote} \pdfmsymmessage. \end{tablenote} \end{symtable} \begin{symtable}[HARP]{\HARP\ Extensible Harpoons} \index{harpoons} \idxboth{extensible}{symbols} \label{harp-harpoons} \renewcommand{\arraystretch}{1.5} % Keep high and low accents from touching. \begin{tabular}{*2{ll}} \W\overleftharp{abc} & \W\underleftharp{abc} \\ \W\overleftharpdown{abc} & \W\underleftharpdown{abc} \\ \W\overrightharp{abc} & \W\underrightharp{abc} \\ \W\overrightharpdown{abc} & \W\underrightharpdown{abc} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{HARP}{harpoon}. \end{tablenote} \end{symtable} \begin{symtable}[TRF]{\TRF\ Extensible Transform Symbols} \index{transforms} \idxboth{extensible}{symbols} \label{trf-extend} \begin{tabular}{ll@{\hspace*{2em}}ll} \W\dft{abc} & \W\DFT{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[ESR]{\ESR\ Extensible Relations} \index{relations} \idxboth{extensible}{symbols} \label{esr-extend} \renewcommand{\arraystretch}{1.5} % Keep tall symbols from touching. \begin{tabular}{ll@{\hspace*{2em}}ll} \W[\ESRrelationleftproject]\relationleftproject{abc} & \W[\ESRrelationrightproject]\relationrightproject{abc} \\ \W[\ESRrelationlifting]\relationlifting{abc} & \\ \end{tabular} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Extensible Brooms and Pitchforks} \index{brooms} \index{pitchforks} \idxboth{extensible}{symbols} \label{hwmath-unwitched} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{tabular}{ll@{\hspace*{2em}}ll} \W\overleftbroom{abc} & \W\underrightbroom{abc} \\ \W\overleftpitchfork{abc} & \W\underrightpitchfork{abc} \\ \W\overrightbroom{abc} & \W\xleftbroom{abc} \\ \W\overrightpitchfork{abc} & \W\xleftpitchfork{abc} \\ \W\underleftbroom{abc} & \W\xrightbroom{abc} \\ \W\underleftpitchfork{abc} & \W\xrightpitchfork{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Extensible Witches} \index{witches} \index{brooms} \index{pitchforks} \idxboth{extensible}{symbols} \idxboth{Halloween}{symbols} \label{hwmath-witches} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{tabular}{ll@{\hspace*{2em}}ll} \W\overleftwitchonbroom{abc} & \W\underrightwitchonbroom{abc} \\ \Wstar\overleftwitchonbroom{abc} & \Wstar\underrightwitchonbroom{abc} \\ \Wstar\overleftwitchonpitchfork{abc} & \Wstar\underrightwitchonpitchfork{abc} \\ \W\overleftwitchonpitchfork{abc} & \W\underrightwitchonpitchfork{abc} \\ \Wstar\overrightwitchonbroom{abc} & \Wstar\xleftwitchonbroom{abc} \\ \W\overrightwitchonbroom{abc} & \W\xleftwitchonbroom{abc} \\ \Wstar\overrightwitchonpitchfork{abc} & \Wstar\xleftwitchonpitchfork{abc} \\ \W\overrightwitchonpitchfork{abc} & \W\xleftwitchonpitchfork{abc} \\ \W\underleftwitchonbroom{abc} & \W\xrightwitchonbroom{abc} \\ \Wstar\underleftwitchonbroom{abc} & \Wstar\xrightwitchonbroom{abc} \\ \Wstar\underleftwitchonpitchfork{abc} & \W\xrightwitchonpitchfork{abc} \\ \W\underleftwitchonpitchfork{abc} & \Wstar\xrightwitchonpitchfork{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Extensible Ghosts} \index{ghosts} \idxboth{extensible}{symbols} \idxboth{Halloween}{symbols} \label{hwmath-ghosts} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{tabular}{ll@{\hspace*{2em}}ll} \W\overleftswishingghost{abc} & \W\overrightswishingghost{abc} \\ \W\underleftswishingghost{abc} & \W\underrightswishingghost{abc} \\ \W\xleftswishingghost{abc} & \W\xrightswishingghost{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[HWMATH]{\HWMATH\ Extensible Bats} \index{bats} \idxboth{extensible}{symbols} \idxboth{Halloween}{symbols} \label{hwmath-bats} \renewcommand{\arraystretch}{2} % Keep tall symbols from touching. \begin{tabular}{ll@{\hspace*{2em}}ll} \W\overleftflutteringbat{abc} & \W\overrightflutteringbat{abc} \\ \W\underleftflutteringbat{abc} & \W\underrightflutteringbat{abc} \\ \W\xleftflutteringbat{abc} & \W\xrightflutteringbat{abc} \\ \end{tabular} \end{symtable} \begin{symtable}[HOPO]{\HOPO\ Non-commutative Division Symbols} \idxboth{extensible}{accents} \idxboth{non-commutative}{division} \index{symbols>non-commutative division} \label{holtpolt} \begin{tabular}{ll@{\qquad}ll} \Wul\holter{abc}{def} & \Wul\polter{abc}{def} \\ \end{tabular} \end{symtable} \begin{symtable}{Dots} \idxboth{dot}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \label{dots} \begin{tabular}{*{3}{ll@{\hspace*{1.5cm}}}ll} \X\cdotp & \X\colon$^*$ & \X\ldotp & \X\vdots$^\dag$ \\ \X\cdots & \X\ddots$^\dag$ & \X\ldots \\ \end{tabular} \bigskip \begin{tablenote}[*] While ``\texttt{:}'' is valid in math mode, \cmd{\colon} uses different surrounding spacing. See \ref{math-spacing} and the Short Math Guide for \latex~\cite{Downes:smg} for more information on math-mode spacing. \end{tablenote} \bigskip \begin{tablenote}[\dag] \ifMDOTS \let\mdcmdX=\cmdX \else \let\mdcmdX=\cmd \fi The \MDOTS\ package redefines \cmdX{\ddots} and \cmdX{\vdots} \ifMDOTS (\ref{mathdots-dots}) \fi to make them scale properly with font size. (They normally scale horizontally but not vertically.) \mdcmdX{\fixedddots} and \mdcmdX{\fixedvdots} provide the original, fixed-height functionality of \latexE's \cmdX{\ddots} and \cmdX{\vdots} macros. \end{tablenote} \end{symtable} \begin{symtable}[AMS]{\AMS\ Dots} \idxboth{dot}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \label{ams-dots} \begin{tabular}{*{2}{ll@{\hspace*{1.5cm}}}ll} \X\because$^*$ & \X[\cdots]\dotsi & \X\therefore$^*$ \\ \X[\cdots]\dotsb & \X[\cdots]\dotsm & \\ \X[\ldots]\dotsc & \X[\ldots]\dotso & \\ \end{tabular} \bigskip \begin{tablenote} The \AMS\ \verb|\dots|\rule{1em}{1pt} symbols are named according to their intended usage: \cmdI[$\string\cdots$]{\dotsb} between pairs of binary operators/relations, \cmdI[$\string\ldots$]{\dotsc} between pairs of commas, \cmdI[$\string\cdots$]{\dotsi} between pairs of integrals, \cmdI[$\string\cdots$]{\dotsm} between pairs of multiplication signs, and \cmdI[$\string\ldots$]{\dotso} between other symbol pairs. \end{tablenote} \bigskip \begin{tablenote}[*] \cmdX{\because} and \cmdX{\therefore} are defined as binary relations and therefore also appear in \vref{ams-rel}. \end{tablenote} \end{symtable} \begin{symtable}[WASY]{\WASY\ Dots} \idxboth{dot}{symbols} \label{wasy-dots} \begin{tabular}{ll} \K\wasytherefore \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Dots} \idxboth{dot}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \label{mns-dots} \begin{tabular}{*{2}{ll@{\hspace*{1.5cm}}}ll} \K[\MNScdot]\cdot & \K[\MNShdotdot]\hdotdot & \K[\MNSudots]\udots \\ \K[\MNSddotdot]\ddotdot & \K[\MNShdots]\hdots & \K[\MNSuptherefore]\uptherefore \\ \K[\MNSddots]\ddots & \K[\MNSlefttherefore]\lefttherefore & \K[\MNSvdotdot]\vdotdot \\ \K[\MNSdiamonddots]\diamonddots & \K[\MNSrighttherefore]\righttherefore & \K[\MNSvdots]\vdots \\ \K[\MNSdowntherefore]\downtherefore & \K[\MNSsquaredots]\squaredots & \\ \K[\MNSfivedots]\fivedots & \K[\MNSudotdot]\udotdot & \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ defines \cmdI[\MNSuptherefore]{\therefore} as \cmdI[\MNSuptherefore]{\uptherefore} and \cmdI[\MNSdowntherefore]{\because} as \cmdI[\MNSdowntherefore]{\downtherefore}. Furthermore, \cmdI[\MNScdot]{\cdotp} and \cmdI[\MNSvdotdot]{\colon} produce the same glyphs as \cmdI[\MNScdot]{\cdot} and \cmdI[\MNSvdotdot]{\vdotdot} respectively but serve as \tex\ math punctuation (class~6 symbols) instead of \tex\ binary operators (class~2). \end{tablenote} \bigskip \begin{tablenote} All of the above except \cmdI[\MNShdots]\hdots\ and \cmdI[\MNSvdots]\vdots\ are defined as binary operators and therefore also appear in \vref{mns-bin}. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Dots} \idxboth{dot}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \label{fdsym-dots} \begin{tabular}{*2{ll@{\hspace*{1.5cm}}}ll} \K[\FDSYMcdot]\cdot & \K[\FDSYMhdots]\hdots & \K[\FDSYMudots]\udots \\ \K[\FDSYMddotdot]\ddotdot & \K[\FDSYMlefttherefore]\lefttherefore & \K[\FDSYMuptherefore]\uptherefore \\ \K[\FDSYMddots]\ddots & \K[\FDSYMrighttherefore]\righttherefore & \K[\FDSYMvdotdot]\vdotdot \\ \K[\FDSYMdowntherefore]\downtherefore & \K[\FDSYMsquaredots]\squaredots & \\ \K[\FDSYMhdotdot]\hdotdot & \K[\FDSYMudotdot]\udotdot & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMadots]{\adots} as a synonym for \cmdI[\string\FDSYMudots]{\udots}; \cmdI[\string\FDSYMbecause]{\because} as a synonym for \cmdI[\string\FDSYMdowntherefore]{\downtherefore}; \cmdI[\string\FDSYMcdot]{\cdotp} as a synonym for \cmdI[\string\FDSYMcdot]{\cdot}; \cmdI[\string\FDSYMcdots]{\cdots} as a synonym for \cmdI[\string\FDSYMhdots]{\hdots}; \cmdI[\string\FDSYMColon]{\Colon} as a synonym for \cmdI[\string\FDSYMsquaredots]{\squaredots}; \cmdI[\string\FDSYMcolon]{\colon}, \cmdI[\string\FDSYMmathcolon]{\mathcolon}, and \cmdI[\string\FDSYMmathratio]{\mathratio} as synonyms for \cmdI[\string\FDSYMvdotdot]{\vdotdot}; and \cmdI[\string\FDSYMtherefore]{\therefore} as a synonym for \cmdI[\string\FDSYMuptherefore]{\uptherefore}. (Some of these serve different mathematical roles, such as relations versus binary operators.) \end{tablenote} \end{symtable} \begin{symtable}[STIX]{\STIX\ Dots} \idxboth{dot}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \label{stix-dots} \begin{tabular}{*2{ll@{\hspace*{1.5cm}}}ll} \K[\STIXadots]\adots & \K[\STIXcdots]\cdots & \K[\STIXfourvdots]\fourvdots \\ \K[\STIXbecause]\because & \K[\STIXColon]\Colon & \K[\STIXldotp]\ldotp \\ \K[\STIXcdot]\cdot & \K[\STIXddots]\ddots & \K[\STIXmathellipsis]\mathellipsis \\ \K[\STIXcdotp]\cdotp & \K[\STIXenleadertwodots]\enleadertwodots & \K[\STIXtherefore]\therefore \\ \end{tabular} \bigskip \begin{tablenote} \STIX\ defines \cmdI[\string\STIXcenterdot]{\centerdot} as a synonym for \cmdI[\string\STIXcdotp]{\cdotp} and \cmdI[\string\STIXdotsb]{\dotsb} and \cmdI[\string\STIXdotsm]{\dotsm} as synonyms for \cmdI[\string\STIXcdots]{\cdots}. \end{tablenote} \end{symtable} \begin{symtable}[MDOTS]{\MDOTS\ Dots} \index{dots (ellipses)} \index{ellipses (dots)} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \idxboth{dot}{symbols} \label{mathdots-dots} \begin{tabular}{ll*2{@{\quad}ll}} \X[\MDOTSddots]\ddots & \X[\MDOTSiddots]\iddots & \X[\MDOTSvdots]\vdots \\ \end{tabular} \bigskip \begin{tablenote} Unlike the default definitions of the above (\vref{dots}), \MDOTS's commands are designed to scale properly with the surrounding font size. \end{tablenote} \end{symtable} \begin{symtable}[YH]{\YH\ Dots} \index{dots (ellipses)} \index{ellipses (dots)} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \idxboth{dot}{symbols} \label{yhmath-dots} \begin{tabular}{ll} \X\adots \end{tabular} \end{symtable} \begin{symtable}[TEUB]{\TEUB\ Dots} \index{dots (ellipses)} \index{ellipses (dots)} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \idxboth{dot}{symbols} \label{teubner-dots} \begin{tabular}{*3{ll@{\qquad}}ll} \K[\TEUBtwodots]\: & \K[\TEUBthreedots]\; & \K[\TEUBfourdots]\? & \K\antilabe \\ \end{tabular} \end{symtable} \begin{symtable}[LOGIX]{\LOGIX\ Dots} \index{dots (ellipses)} \index{ellipses (dots)} \index{dots (ellipses)>math mode} \index{ellipses (dots)>math mode} \idxboth{dot}{symbols} \label{logix-dots} \begin{tabular}{*4{ll}} \K\BndDot & \K\Cln & \K\LDots & \K\Thus \\ \K\CDots & \K\Dt & \K\Since & \K\VDots \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} \begin{symtable}[BEGRIFF]{\BEGRIFF\ Begriffsschrift Symbols} \idxboth{Frege logic}{symbols} \idxboth{Begriffsschrift}{symbols} \label{begriff} \begin{tabular}{*3{ll}} \X\BGassert & \X\BGcontent & \X\BGnot \\ \end{tabular} \par\bigskip \begin{tabular}{*2{ll}} \Wul\BGconditional{a\strut}{b\strut} & \W\BGquant{a} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{BEGRIFF}{begriff}. \end{tablenote} \end{symtable} \begin{symtable}[FREGE]{\FREGE\ Begriffsschrift Symbols} \idxboth{Frege logic}{symbols} \idxboth{Begriffsschrift}{symbols} \label{frege} \begin{tabular}{*3{ll}} \K\Facontent & \K\Fanncontent & \K\Fncontent \\ \K\Fancontent & \K\Fcontent & \K\Fnncontent \\ \end{tabular} \par\bigskip \begin{tabular}{*3{ll}} \W\Fannquant{a} & \W\Faquant{a} & \W\Fnquant{a} \\ \W\Fannquantn{a} & \W\Faquantn{a} & \W\Fnquantn{a} \\ \W\Fannquantnn{a} & \W\Faquantnn{a} & \W\Fnquantnn{a} \\ \W\Fanquant{a} & \W\Fnnquant{a} & \W\Fquantn{a} \\ \W\Fanquantn{a} & \W\Fnnquantn{a} & \W\Fquantnn{a} \\ \W\Fanquantnn{a} & \W\Fnnquantnn{a} & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{BEGRIFF}{frege}. \end{tablenote} \end{symtable} \begin{symtable}{\MC\ Math Symbols} \label{mc-math} \begin{tabular}{*3{ll}} \K[\textcelsius]\tccentigrade & \K[\textohm]\tcohm & \K[\textperthousand]\tcperthousand \\ \K[\textmu]\tcmu & \K[\textpertenthousand]\tcpertenthousand & \\ \end{tabular} \end{symtable} \begin{symtable}[MARV]{\MARV\ Math Symbols} \index{angles} \label{marv-math} \begin{tabular}{*3{ll}ll} \K\AngleSign & \K\LargerOrEqual & \K\MVMultiplication \\ \K\Conclusion & \K\LessOrEqual & \K\MVPeriod \\ \K\Congruent & \K\MultiplicationDot & \K\MVPlus \\ \K\Corresponds & \K\MVComma & \K\MVRightArrow \\ \K\Divides & \K\MVDivision & \K\MVRightBracket \\ \K\DividesNot & \K\MVLeftBracket & \K\NotCongruent \\ \K\Equivalence & \K\MVMinus & \\ \end{tabular} \end{symtable} \begin{symtable}[MARV]{\MARV\ Digits} \index{numerals} \label{marv-digits} \begin{tabular}{*4{ll@{\qquad}}ll} \K\MVZero & \K\MVTwo & \K\MVFour & \K\MVSix & \K\MVEight \\ \K\MVOne & \K\MVThree & \K\MVFive & \K\MVSeven & \K\MVNine \\ \end{tabular} \end{symtable} \begin{symtable}[FGE]{\FGE\ Digits} \subindex{numerals}{rotated} \subindex{numerals}{slashed} \idxboth{Frege logic}{symbols} \label{fge-digits} \begin{tabular}{*2{ll@{\qqquad}}ll} \K\fgeleftthree & \K\fgerighttwo & \K\fgestruckzero \\ \K\fgelefttwo & \K\fgestruckone & \\ \end{tabular} \end{symtable} \begin{symtable}[DOZ]{\DOZ\ Base-12 Digits} \index{numerals} \subindex{dozenal (base 12)}{numerals} \subindex{base twelve}{numerals} \subindex{duodecimal (base 12)}{numerals} \idxboth{Pitman's base 12}{symbols} \label{dozenal-digits} \begin{tabular}{ll@{\qquad}ll} \K[\DOZx]\x & \K[\DOZe]\e \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{\ABX\ Mayan Digits} \idxboth{Mayan}{numerals} \label{abx-mayan} \begin{tabular}{*2{ll@{\qquad}}ll} \Tm{0} & \Tm{2} & \Tm{4} \\ \Tm{1} & \Tm{3} & \Tm{5} \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Infinities} \index{infinity} \label{stix-infinity} \begin{tabular}{*3{ll}} \K[\STIXacidfree]\acidfree & \K[\STIXinfty]\infty & \K[\STIXtieinfty]\tieinfty \\ \K[\STIXiinfin]\iinfin & \K[\STIXnvinfty]\nvinfty & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Primes} \index{primes} \label{stix-prime} \begin{tabular}{ll@{\qquad}ll} \K[\STIXprime]\prime & \K[\STIXbackprime]\backprime \\ \K[\STIXdprime]\dprime & \K[\STIXbackdprime]\backdprime \\ \K[\STIXtrprime]\trprime & \K[\STIXbacktrprime]\backtrprime \\ \K[\STIXqprime]\qprime \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Empty Sets} \index{null set} \index{empty set} \label{stix-empty} \begin{tabular}{*3{ll}} \K[\STIXemptyset]\emptyset & \K[\STIXemptysetobar]\emptysetobar & \K[\STIXvarnothing]\varnothing \\ \K[\STIXemptysetoarr]\emptysetoarr & \K[\STIXemptysetocirc]\emptysetocirc & \\ \K[\STIXemptysetoarrl]\emptysetoarrl & \K[\STIXrevemptyset]\revemptyset & \\ \end{tabular} \end{symtable} \begin{symtable}[AMS]{\AMS\ Angles} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \label{ams-angles} \begin{tabular}{*3{ll}} \X[\AMSangle]\angle & \X\measuredangle & \X\sphericalangle \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{\MNS\ Angles} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \label{mns-angles} \begin{tabular}{*3{ll}} \K[\MNSangle]\angle & \K[\MNSmeasuredangle]\measuredangle & \K[\MNSsphericalangle]\sphericalangle \\ \end{tabular} \end{symtable} \begin{symtable}[FDSYM]{\FDSYM\ Angles} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \idxboth{right}{angles} \label{fdsym-angles} \begin{tabular}{*3{ll}} \K[\FDSYMangle]\angle & \K[\FDSYMrevangle]\revangle & \K[\FDSYMsphericalangle]\sphericalangle \\ \K[\FDSYMmeasuredangle]\measuredangle & \K[\FDSYMrevmeasuredangle]\revmeasuredangle & \K[\FDSYMsphericalangledown]\sphericalangledown \\ \K[\FDSYMmeasuredrightangle]\measuredrightangle & \K[\FDSYMrightangle]\rightangle & \K[\FDSYMsphericalangleleft]\sphericalangleleft \\ \K[\FDSYMmeasuredrightangledot]\measuredrightangledot & \K[\FDSYMrightanglesquare]\rightanglesquare & \K[\FDSYMsphericalangleup]\sphericalangleup \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMmeasuredangleleft]{\measuredangleleft} as a synonym for \cmdI[\string\FDSYMrevmeasuredangle]{\revmeasuredangle}; \cmdI[\string\FDSYMrevsphericalangle]{\revsphericalangle} and \cmdI[\string\FDSYMgtlpar]{\gtlpar} as synonyms for \cmdI[\string\FDSYMsphericalangleleft]{\sphericalangleleft}; \cmdI[\string\FDSYMrightanglesqr]{\rightanglesqr} as a synonym for \cmdI[\string\FDSYMrightanglesquare]{\rightanglesquare}; and \cmdI[\string\FDSYMrightanglemdot]{\rightanglemdot} as a synonym for \cmdI[\string\FDSYMmeasuredrightangledot]{\measuredrightangledot}. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{\BSK\ Angles} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \idxboth{right}{angles} \label{bsk-angles} \begin{tabular}{*3{ll}} \K[\BSKangle]\angle & \K[\BSKrightangle]\rightangle & \K[\BSKsphericalangle]\sphericalangle \\ \K[\BSKmeasuredangle]\measuredangle & \K[\BSKrightanglemdot]\rightanglemdot & \\ \K[\BSKmeasuredrightangle]\measuredrightangle & \K[\BSKrightanglesqr]\rightanglesqr & \\ \end{tabular} \end{symtable} \begin{symtable}[STIX]{\STIX\ Angles} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \idxboth{right}{angles} \index{axes=axes (\STIXthreedangle)} \label{stix-angles} \begin{tabular}{*3{ll}} \K[\STIXangdnr]\angdnr & \K[\STIXmeasanglerutone]\measanglerutone & \K[\STIXrightanglemdot]\rightanglemdot \\ \K[\STIXangle]\angle & \K[\STIXmeasangleultonw]\measangleultonw & \K[\STIXrightanglesqr]\rightanglesqr \\ \K[\STIXangles]\angles & \K[\STIXmeasangleurtone]\measangleurtone & \K[\STIXsphericalangle]\sphericalangle \\ \K[\STIXangleubar]\angleubar & \K[\STIXmeasuredangle]\measuredangle & \K[\STIXsphericalangleup]\sphericalangleup \\ \K[\STIXgtlpar]\gtlpar & \K[\STIXmeasuredangleleft]\measuredangleleft & \K[\STIXthreedangle]\threedangle \\ \K[\STIXmeasangledltosw]\measangledltosw & \K[\STIXmeasuredrightangle]\measuredrightangle & \K[\STIXturnangle]\turnangle \\ \K[\STIXmeasangledrtose]\measangledrtose & \K[\STIXrangledownzigzagarrow]\rangledownzigzagarrow & \K[\STIXwideangledown]\wideangledown \\ \K[\STIXmeasangleldtosw]\measangleldtosw & \K[\STIXrevangle]\revangle & \K[\STIXwideangleup]\wideangleup \\ \K[\STIXmeasanglelutonw]\measanglelutonw & \K[\STIXrevangleubar]\revangleubar & \\ \K[\STIXmeasanglerdtose]\measanglerdtose & \K[\STIXrightangle]\rightangle & \\ \end{tabular} \end{symtable} \begin{symtable}[LUCICOS]{\LUCICOS\ Decorative Geometry Symbols} \index{tangent=tangent (\lucideicon{tangent})} \index{radius=radius (\lucideicon{radius})} \index{ratio=ratio (\lucideicon{ratio})} \index{diameter=diameter (\lucideicon{diameter})} \index{axes=axes (\lucideicon{axis-3d})} \label{lucide-icons-geometry} \begin{tabular}{ll@{\qquad}ll} \TLUC{axis-3d} & \TLUC{ratio} \\ \TLUC{diameter} & \TLUC{tangent} \\ \TLUC{radius} & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LUCICOS}{lucide-icons}. \end{tablenote} \end{symtable} \begin{symtable}[TYPICOS]{\TYPICOS\ Decorative Mathematical Symbols} \index{division=division (\tiDivideOutline)} \index{division=division (\tiDivide)} \index{equals=equals (\tiEqualsOutline)} \index{equals=equals (\tiEquals)} \index{infinity=infinity (\tiInfinityOutline)} \index{infinity=infinity (\tiInfinity)} \index{minus=minus (\tiMinusOutline)} \index{minus=minus (\tiMinus)} \index{pi=pi (\tiPi)} \index{plus=plus (\tiPlusOutline)} \index{plus=plus (\tiPlus)} \label{typicons-math} \begin{tabular}{*3{ll}} \K\tiDivide & \K\tiInfinity & \K\tiPi \\ \K\tiDivideOutline & \K\tiInfinityOutline & \K\tiPlus \\ \K\tiEquals & \K\tiMinus & \K\tiPlusOutline \\ \K\tiEqualsOutline & \K\tiMinusOutline & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{TYPICOS}{typicons}. See also \cmdI[\protect\tiTimes]{\tiTimes}~(\tiTimes) and \cmdI[\protect\tiTimesOutline]{\tiTimesOutline}~(\tiTimesOutline) in \ref{typicons-check-marks}. All \TYPICOS\ symbols are intended to be used in text mode, not math mode. \end{tablenote} \end{symtable} \begin{symtable}[FNTAWE]{\FNTAWE\ Decorative Mathematical Symbols} \index{division=division (\faDivide)} \index{equals=equals (\faEquals)} \index{greater than or equal to=greater than or equal to (\faGreaterThanEqual)} \index{greater than=greater than (\faGreaterThan)} \index{infinity=infinity (\faInfinity)} \index{less than or equal to=less than or equal to (\faLessThanEqual)} \index{less than=less than (\faLessThan)} \index{minus=minus (\faMinus)} \index{not equal=not equal (\faNotEqual)} \index{percent=percent (\faPercent)} \index{plus=plus (\faPlus)} \index{plus or minus=plus or minus (\faPlusMinus)} \index{question mark=question mark (\faQuestion)} \label{fontawesome-math} \begin{tabular}{*3{ll}} \K\faDivide & \K\faLessThan & \K\faPlus \\ \K\faEquals & \K\faLessThanEqual & \K\faPlusMinus \\ \K\faGreaterThan & \K\faMinus & \K\faQuestion \\ \K\faGreaterThanEqual & \K\faNotEqual & \\ \K\faInfinity & \K\faPercent$^*$ & \\ \end{tabular} \bigskip \begin{tablenote}[*] In \FNTAWEv, \cmdI{\faPercent} was called \cmdI[\faPercent]{\faPercentage}, and \FNTAWEv\ additionally defined a \cmd{\faPercent}, which used hollow circles instead of solid dots. \end{tablenote} \begin{tablenote} See also \cmdI{\faXmark}~(\faXmark) in \ref{fontawesome-check-marks}. All \FNTAWE\ symbols are intended to be used in text mode, not math mode. \end{tablenote} \end{symtable} \begin{symtable}[LUCICOS]{\LUCICOS\ Decorative Mathematical Symbols} \index{approximately equal to=approximately equal to (\lucideicon{equal-approximately})} \index{division=division (\lucideicon{divide})} \index{equals=equals (\lucideicon{equal})} \index{infinity=infinity (\lucideicon{infinity})} \index{minus=minus (\lucideicon{minus})} \index{multiplication=multiplication (\lucideicon{x})} \index{not equal=not equal (\lucideicon{equal-not})} \index{omega=omega (\lucideicon{omega})} \index{parentheses=parentheses (\lucideicon{parentheses})} \index{percent=percent (\lucideicon{percent})} \index{pi=pi (\lucideicon{pi})} \index{plus or minus=plus or minus (\lucideicon{diff})} \index{plus=plus (\lucideicon{plus})} \index{radical=radical (\lucideicon{radical})} \index{sigma=sigma (\lucideicon{sigma})} \index{variable=variable (\lucideicon{variable})} \label{lucide-icons-math} \begin{tabular}{ll@{\qquad}ll} \TLUC{diff} & \TLUC{parentheses} \\ \TLUC{divide} & \TLUC{percent} \\ \TLUC{equal} & \TLUC{pi} \\ \TLUC{equal-approximately} & \TLUC{plus} \\ \TLUC{equal-not} & \TLUC{radical} \\ \TLUC{infinity} & \TLUC{sigma} \\ \TLUC{minus} & \TLUC{variable} \\ \TLUC{omega} & \TLUC{x} \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LUCICOS}{lucide-icons}. \end{tablenote} \end{symtable} \begin{longsymtable}[CASIO]{\CASIO\ Casio Calculator Keys} \ltindex{Casio calculator keys} \ltindex{calculator keys} \ltindex{symbols>calculator key} \label{casiofont} \begin{longtable}{lll@{\qquad}lll} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\CASIOAbs]\Abs & \K[\CASIOCJKOn]\CJKOn & \K[\CASIOMenu]\Menu \\ \K[\CASIOAlpha]\Alpha & \K[\CASIOCommaParen]\CommaParen & \K[\CASIOMinus]\Minus \\ \K[\CASIOangleParen]\angleParen & \K[\CASIOCube]\Cube & \K[\CASIOminusParen]\minusParen \\ \K[\CASIOAns]\Ans & \K[\CASIOCubeParen]\CubeParen & \K[\CASIOMixedFrac]\MixedFrac \\ \K[\CASIOBackArrow]\BackArrow & \K[\CASIOCubeRoot]\CubeRoot & \K[\CASIOMminus]\Mminus \\ \K[\CASIOCalc]\Calc & \K[\CASIODegRadGrad]\DegRadGrad & \K[\CASIOMplus]\Mplus \\ \K[\CASIOcasioAbs]\casioAbs & \K[\CASIODel]\Del & \K[\CASIOnExp]\nExp \\ \K[\CASIOcasioAC]\casioAC & \K[\CASIODivide]\Divide & \K[\CASIOnLog]\nLog \\ \K[\CASIOcasioComma]\casioComma & \K[\CASIOdivR]\divR & \K[\CASIOnRoot]\nRoot \\ \K[\CASIOcasioCos]\casioCos & \K[\CASIODownArrow]\DownArrow & \K[\CASIOnTen]\nTen \\ \K[\CASIOcasioDblParen]\casioDblParen & \K[\CASIOdydx]\dydx & \K[\CASIOOptn]\Optn \\ \K[\CASIOcasioDot]\casioDot & \K[\CASIOeExp]\eExp & \K[\CASIOPercent]\Percent \\ \K[\CASIOcasioIntegral]\casioIntegral & \K[\CASIOEng]\Eng & \K[\CASIOPlus]\Plus \\ \K[\CASIOcasioLn]\casioLn & \K[\CASIOEqual]\Equal & \K[\CASIORightArrow]\RightArrow \\ \K[\CASIOcasioLog]\casioLog & \K[\CASIOExe]\Exe & \K[\CASIOSen]\Sen \\ \K[\CASIOcasioLParen]\casioLParen & \K[\CASIOFactorial]\Factorial & \K[\CASIOSetup]\Setup \\ \K[\CASIOcasioObar]\casioObar & \K[\CASIOFrac]\Frac & \K[\CASIOShift]\Shift \\ \K[\CASIOcasioOdot]\casioOdot & \K[\CASIOFracMult]\FracMult & \K[\CASIOSim]\Sim \\ \K[\CASIOcasioPi]\casioPi & \K[\CASIOInverse]\Inverse & \K[\CASIOSimp]\Simp \\ \K[\CASIOcasioProd]\casioProd & \K[\CASIOInverseCos]\InverseCos & \K[\CASIOSquareRoot]\SquareRoot \\ \K[\CASIOcasioRParen]\casioRParen & \K[\CASIOInverseParen]\InverseParen & \K[\CASIOSto]\Sto \\ \K[\CASIOcasioSin]\casioSin & \K[\CASIOInverseSin]\InverseSin & \K[\CASIOswitchMixedFrac]\switchMixedFrac \\ \K[\CASIOcasioSum]\casioSum & \K[\CASIOInverseTan]\InverseTan & \K[\CASIOTimes]\Times \\ \K[\CASIOcasioTan]\casioTan & \K[\CASIOiParen]\iParen & \K[\CASIOUpArrow]\UpArrow \\ \K[\CASIOcasioX]\casioX & \K[\CASIOLeftArrow]\LeftArrow & \K[\CASIOxTenx]\xTenx \\ \K[\CASIOcasioY]\casioY & \K[\CASIOLineFrac]\LineFrac & \\ \K[\CASIOCJKMenu]\CJKMenu & \K[\CASIOlogParen]\logParen & \\[3ex] \K[\CASIOZero]\Zero & \K[\CASIOFour]\Four & \K[\CASIOEight]\Eight \\ \K[\CASIOOne]\One & \K[\CASIOFive]\Five & \K[\CASIONine]\Nine \\ \K[\CASIOTwo]\Two & \K[\CASIOSix]\Six & \\ \K[\CASIOThree]\Three & \K[\CASIOSeven]\Seven & \\ \end{longtable} \begin{tablenote} \seepackagenote{CASIO}{casiofont}. \end{tablenote} \end{longsymtable} \begin{symtable}{Miscellaneous \latexE\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{dots (ellipses)} \index{ellipses (dots)} \index{null set} \index{empty set} \subindex{dotless i=dotless $i~(\imath)$}{math mode} \subindex{dotless j=dotless $j~(\jmath)$}{math mode} \index{angles} \index{rhombuses} \index{infinity} \index{primes} \label{ord} \ifAMS \def\AMSfn{$^\ddag$} \else \def\AMSfn{} \fi \begin{tabular}{*4{ll}} \X\aleph & \X\Box$^{*,\dag}$ & \X\nabla & \X\triangle \\ \X\emptyset\AMSfn & \X\Diamond$^*$ & \X\neg & \\ \X\angle & \X\infty & \X\prime & \\ \X\backslash & \X\mho$^*$ & \X\surd & \\ \end{tabular} \bigskip \begin{tablenote}[*] Not predefined in \latexE. Use one of the packages \pkgname{latexsym}, \pkgname{amsfonts}, \pkgname{amssymb}, \pkgname{txfonts}, \pkgname{pxfonts}, or \pkgname{wasysym}. Note, however, that \pkgname{amsfonts} and \pkgname{amssymb} define \cmdX{\Diamond} to produce the same glyph as \ifAMS \cmdX{\lozenge}~(``$\lozenge$'');\index{rhombuses} \else \cmd{\lozenge};\index{rhombuses} \fi the other packages produce a squarer \cmdX{\Diamond} as depicted above. \end{tablenote} \bigskip \begin{tablenote}[\dag] To use \cmdX{\Box}---or any other symbol---as an end-of-proof (Q.E.D\@.)\index{Q.E.D.}\index{end of proof}\index{proof, end of} marker, consider using the \pkgname{ntheorem} package, which properly juxtaposes a symbol with the end of the proof text. \end{tablenote} \ifAMS \bigskip \begin{tablenote}[\ddag] Many people prefer the look of \AMS's \cmdX{\varnothing} (``$\varnothing$'', \ref{ams-misc}) to that of \latex's \cmdX{\emptyset}. \end{tablenote} \fi % AMS test \end{symtable} \begin{symtable}[AMS]{Miscellaneous \AMS\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{stars} \index{triangles} \index{null set} \index{empty set} \index{rhombuses} \index{primes} \label{ams-misc} \begin{tabular}{*3{ll}} \X\backprime & \X\blacktriangledown & \X\mho \\ \X\bigstar & \X\diagdown & \X\square \\ \X\blacklozenge & \X\diagup & \X\triangledown \\ \X\blacksquare & \X\eth & \X\varnothing \\ \X\blacktriangle & \X\lozenge & \X\vartriangle \\ \end{tabular} \end{symtable} \begin{symtable}[WASY]{Miscellaneous \WASY\ Math Symbols} \index{angles} \index{rhombuses} \index{upside-down letters} \label{wasy-math} \begin{tabular}{*4{ll}} \X[\WASYBox]\Box & \X[\WASYDiamond]\Diamond & \X\mho$^*$ & \K\varangle \\ \end{tabular} \bigskip \begin{tablenote}[*] \WASY\ also defines an \cmdI{\agemO} symbol, which is the same glyph as \cmdX{\mho} but is intended for use in text mode. \end{tablenote} \end{symtable} \begin{symtable}[TX]{Miscellaneous \TXPX\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{rhombuses} \label{txpx-misc} \begin{tabular}{*2{ll}} \X\Diamondblack & \X\lambdabar \\ \X\Diamonddot & \X\lambdaslash \\ \end{tabular} \end{symtable} \begin{symtable}[ABX]{Miscellaneous \ABX\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{null set} \index{semidirect products} \index{angles} \idxboth{measured}{angles} \idxboth{spherical}{angles} \index{pitchforks} \index{infinity} \label{abx-misc} \begin{tabular}{*4{ll}} \X[\ABXdegree]\degree & \X[\ABXfourth]\fourth & \X[\ABXmeasuredangle]\measuredangle & \X[\ABXsecond]\second \\ \X[\ABXdiagdown]\diagdown & \X[\ABXhash]\hash & \X[\ABXpitchfork]\pitchfork & \X[\ABXsphericalangle]\sphericalangle \\ \X[\ABXdiagup]\diagup & \X[\ABXinfty]\infty & \X[\ABXpropto]\propto & \X[\ABXthird]\third \\ \X[\ABXdiameter]\diameter & \X[\ABXleftthreetimes]\leftthreetimes & \X[\ABXrightthreetimes]\rightthreetimes & \X[\ABXvarhash]\varhash \\ \end{tabular} \end{symtable} \begin{symtable}[MNS]{Miscellaneous \MNS\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{null set} \index{empty set} \index{integrals} \index{check marks} \index{infinity} \index{primes} \label{mns-misc} \begin{tabular}{*4{ll}} \K[\MNSbackneg]\backneg & \K[\MNSdiameter]\diameter & \K[\MNSinvneg]\invneg & \K[\MNSneg]\neg \\ \K[\MNSbackprime]\backprime & \K[\MNSinfty]\infty & \K[\MNSmaltese]\maltese & \K[\MNSprime]\prime \\ \K[\MNScheckmark]\checkmark & \K[\MNSinvbackneg]\invbackneg & \K[\MNSnabla]\nabla & \K[\MNSsmallint]\smallint \\ \end{tabular} \bigskip \begin{tablenote} \MNS\ defines \cmdI[\MNSdiameter]{\emptyset} and \cmdI[\MNSdiameter]{\varnothing} as synonyms for \cmdI[\MNSdiameter]{\diameter}; \cmdI[\MNSneg]{\lnot} and \cmdI[\MNSneg]{\minushookdown} as synonyms for \cmdI[\MNSneg]{\neg}; \cmdI[\MNSinvneg]{\minushookup} as a synonym for \cmdI[\MNSinvneg]{\invneg}; \cmdI[\MNSbackneg]{\hookdownminus} as a synonym for \cmdI[\MNSbackneg]{\backneg}; and, \cmdI[\MNSinvbackneg]{\hookupminus} as a synonym for \cmdI[\MNSinvbackneg]{\invbackneg}. \end{tablenote} \end{symtable} \begin{symtable}[MNS]{Miscellaneous Internal \MNS\ Math Symbols} \idxboth{miscellaneous}{symbols} \label{mns-misc-internal} \begin{tabular}{*2{ll}} \K[\smash\MNSpartialvardint]\partialvardint & \K[\smash\MNSpartialvartint]\partialvartint \\ \K[\smash\MNSpartialvardlanddownint]\partialvardlanddownint & \K[\smash\MNSpartialvartlanddownint]\partialvartlanddownint \\ \K[\smash\MNSpartialvardlandupint]\partialvardlandupint & \K[\smash\MNSpartialvartlandupint]\partialvartlandupint \\ \K[\smash\MNSpartialvardlcircleleftint]\partialvardlcircleleftint & \K[\smash\MNSpartialvartlcircleleftint]\partialvartlcircleleftint \\ \K[\smash\MNSpartialvardlcirclerightint]\partialvardlcirclerightint & \K[\smash\MNSpartialvartlcirclerightint]\partialvartlcirclerightint \\ \K[\smash\MNSpartialvardoiint]\partialvardoiint & \K[\smash\MNSpartialvartoiint]\partialvartoiint \\ \K[\smash\MNSpartialvardoint]\partialvardoint & \K[\smash\MNSpartialvartoint]\partialvartoint \\ \K[\smash\MNSpartialvardrcircleleftint]\partialvardrcircleleftint & \K[\smash\MNSpartialvartrcircleleftint]\partialvartrcircleleftint \\ \K[\smash\MNSpartialvardrcirclerightint]\partialvardrcirclerightint & \K[\smash\MNSpartialvartrcirclerightint]\partialvartrcirclerightint \\ \K[\smash\MNSpartialvardstrokedint]\partialvardstrokedint & \K[\smash\MNSpartialvartstrokedint]\partialvartstrokedint \\ \K[\smash\MNSpartialvardsumint]\partialvardsumint & \K[\smash\MNSpartialvartsumint]\partialvartsumint \\ \end{tabular} \bigskip \begin{tablenote} These symbols are intended to be used internally by \MNS\ to construct the integrals appearing in \vref{mns-large} but nevertheless can be used in isolation. \end{tablenote} \end{symtable} \begin{symtable}[FDSYM]{Miscellaneous \FDSYM\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{null set} \index{empty set} \index{integrals} \index{check marks} \index{infinity} \index{primes} \label{fdsym-misc} \begin{tabular}{*3{ll}} \K[\FDSYMbackneg]\backneg & \K[\FDSYMintprod]\intprod & \K[\FDSYMprime]\prime \\ \K[\FDSYMbackprime]\backprime & \K[\FDSYMintprodr]\intprodr & \K[\FDSYMrevemptyset]\revemptyset \\ \K[\FDSYMcheckmark]\checkmark & \K[\FDSYMinvneg]\invneg & \K[\FDSYMsector]\sector \\ \K[\FDSYMemptyset]\emptyset & \K[\FDSYMmaltese]\maltese & \K[\FDSYMsmallint]\smallint \\ \K[\FDSYMinfty]\infty & \K[\FDSYMneg]\neg & \\ \end{tabular} \bigskip \begin{tablenote} \FDSYM\ defines \cmdI[\string\FDSYMhookdownminus]{\hookdownminus}, \cmdI[\string\FDSYMinvneg]{\invneg}, and \cmdI[\string\FDSYMinvnot]{\invnot} as synonyms for \cmdI[\string\FDSYMbackneg]{\backneg}; \cmdI[\string\FDSYMlnot]{\lnot} and \cmdI[\string\FDSYMminushookdown]{\minushookdown} as synonyms for \cmdI[\string\FDSYMneg]{\neg}; \cmdI[\string\FDSYMhookupminus]{\hookupminus} and \cmdI[\string\FDSYMturnedbackneg]{\turnedbackneg} as synonyms for \cmdI[\string\FDSYMintprodr]{\intprodr}; \cmdI[\string\FDSYMminushookup]{\minushookup}, \cmdI[\string\FDSYMturnedneg]{\turnedneg}, and \cmdI[\string\FDSYMturnednot]{\turnednot} as synonyms for \cmdI[\string\FDSYMintprod]{\intprod}; and \cmdI[\string\FDSYMdiameter]{\diameter} and \cmdI[\string\FDSYMvarnothing]{\varnothing} as synonyms for \cmdI[\string\FDSYMemptyset]{\emptyset}. \end{tablenote} \end{symtable} \begin{symtable}[BSK]{Miscellaneous \BSK\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{null set} \index{empty set} \index{check marks} \index{primes} \label{bsk-misc} \begin{tabular}{*3{ll}} \K[\BSKbackepsilon]\backepsilon & \K[\BSKhermitmatrix]\hermitmatrix & \K[\BSKnotbot]\notbot \\ \K[\BSKbackprime]\backprime & \K[\BSKiinfin]\iinfin & \K[\BSKnottop]\nottop \\ \K[\BSKcheckmark]\checkmark & \K[\BSKinvnot]\invnot & \K[\BSKriota]\riota \\ \K[\BSKdalambert]\dalambert & \K[\BSKlambdabar]\lambdabar & \K[\BSKsinewave]\sinewave \\ \K[\BSKdiagdown]\diagdown & \K[\BSKlambdaslash]\lambdaslash & \K[\BSKvarnothing]\varnothing \\ \K[\BSKdiagup]\diagup & \K[\BSKmaltese]\maltese & \\ \end{tabular} \end{symtable} \begin{longsymtable}[STIX]{Miscellaneous \STIX\ Math Symbols} \ltidxboth{currency}{symbols} \ltidxboth{database}{symbols} \ltidxboth{engineering}{symbols} \ltindex{asterisks} \ltindex{check marks} \ltindex{circles} \ltindex{end of proof} \ltindex{faces} \ltindex{outer joins} \ltindex{proof, end of} \ltindex{Q.E.D.} \ltindex{smiley faces} \ltindex{squares} \ltindex{triangles} \ltindex{Xs} \label{stix-misc} \begin{longtable}{*3{ll}} \multicolumn{6}{l}{\small\textit{(continued from previous page)}} \\[3ex] \endhead \endfirsthead \\[3ex] \multicolumn{6}{r}{\small\textit{(continued on next page)}} \endfoot \endlastfoot \K[\STIXaccurrent]\accurrent & \K[\STIXhermitmatrix]\hermitmatrix & \K[\STIXPropertyLine]\PropertyLine \\ \K[\STIXbackslash]\backslash & \K[\STIXhyphenbullet]\hyphenbullet & \K[\STIXQED]\QED \\ \K[\STIXbbrktbrk]\bbrktbrk & \K[\STIXhzigzag]\hzigzag & \K[\STIXQuestion]\Question \\ \K[\STIXbigbot]\bigbot & \K[\STIXincrement]\increment & \K[\STIXrdiagovfdiag]\rdiagovfdiag \\ \K[\STIXbiginterleave]\biginterleave & \K[\STIXinversebullet]\inversebullet & \K[\STIXrightouterjoin]\rightouterjoin \\ \K[\STIXbigtop]\bigtop & \K[\STIXinvnot]\invnot & \K[\STIXsansLmirrored]\sansLmirrored \\ \K[\STIXblacksmiley]\blacksmiley & \K[\STIXJoin]\Join & \K[\STIXsansLturned]\sansLturned \\ \K[\STIXbracevert]\bracevert & \K[\STIXlaplac]\laplac & \K[\STIXsinewave]\sinewave \\ \K[\STIXcaretinsert]\caretinsert & \K[\STIXleftouterjoin]\leftouterjoin & \K[\STIXstrns]\strns \\ \K[\STIXcheckmark]\checkmark & \K[\STIXllarc]\llarc & \K[\STIXthermod]\thermod \\ \K[\STIXconictaper]\conictaper & \K[\STIXlrarc]\lrarc & \K[\STIXtopcir]\topcir \\ \K[\STIXdanger]\danger & \K[\STIXmaltese]\maltese & \K[\STIXturnednot]\turnednot \\ \K[\STIXdiagdown]\diagdown & \K[\STIXmathsection]\mathsection & \K[\STIXubrbrak]\ubrbrak \\ \K[\STIXdiagup]\diagup & \K[\STIXmathvisiblespace]\mathvisiblespace & \K[\STIXularc]\ularc \\ \K[\STIXdiameter]\diameter & \K[\STIXnabla]\nabla & \K[\STIXurarc]\urarc \\ \K[\STIXdingasterisk]\dingasterisk & \K[\STIXneg]\neg$^*$ & \K[\STIXviewdata]\viewdata \\ \K[\STIXelinters]\elinters & \K[\STIXobrbrak]\obrbrak & \K[\STIXvzigzag]\vzigzag \\ \K[\STIXeth]\eth & \K[\STIXperps]\perps & \K[\STIXyen]\yen \\ \K[\STIXExclam]\Exclam & \K[\STIXpostalmark]\postalmark & \K[\STIXzcmp]\zcmp \\ \K[\STIXfdiagovrdiag]\fdiagovrdiag & \K[\STIXprofline]\profline & \K[\STIXzpipe]\zpipe \\ \K[\STIXfullouterjoin]\fullouterjoin & \K[\STIXprofsurf]\profsurf & \K[\STIXzproject]\zproject \\ \end{longtable} \begin{tablenote}[*] \STIX\ defines \cmdI[\string\STIXlnot]{\lnot} as a synonym for \cmdI[\string\STIXneg]{\neg}. \end{tablenote} \end{longsymtable} \begin{symtable}{Miscellaneous \TC\ Text-mode Math Symbols} \index{fractions} \label{tc-math} \ifFRAC \def\FRACfn{$^\dag$} \else \def\FRACfn{} \fi \begin{tabular}{*3{ll}} \K\textdegree$^*$ & \K\textonehalf\FRACfn & \K\textthreequarters\FRACfn \\ \K\textdiv & \K\textonequarter\FRACfn & \K\textthreesuperior \\ \K\textfractionsolidus & \K\textonesuperior & \K\texttimes \\ \K\textlnot & \K\textpm & \K\texttwosuperior \\ \K\textminus & \K\textsurd \\ \end{tabular} \bigskip \begin{tablenote}[*] If you prefer a larger degree symbol you might consider defining one as ``\verb|\ensuremath{^\circ}|''~(``$^\circ$'')% \indexcommand[$\string\circ$]{\circ}. \end{tablenote} \ifFRAC \bigskip \begin{tablenote}[\dag] \pkgname{nicefrac} (part of the \pkgname{units} package) or the newer \pkgname{xfrac} package can be used to construct vulgar\index{fractions>vulgar} fractions like ``\nicefrac{1}{2}'', ``\nicefrac{1}{4}'', ``\nicefrac{3}{4}'', and even ``\nicefrac{c}{o}''\index{care of=care of (\nicefrac{c}{o})}. \end{tablenote} \fi % FRAC test \end{symtable} \begin{symtable}[FGE]{Miscellaneous \FGE\ Math Symbols} \index{angles} \index{infinity} \idxboth{Frege logic}{symbols} \label{fge-misc} \begin{tabular}{*3{ll@{\qquad}}ll} \K\fgebackslash & \K\fgecap & \K\fgecupacute & \K\fgelangle \\ \K\fgebaracute & \K\fgecapbar & \K\fgecupbar & \K\fgeupbracket \\ \K\fgebarcap & \K\fgecup & \K\fgeinfty & \\ \end{tabular} \end{symtable} \begin{symtable}[MDES]{Miscellaneous \MDES\ Math Symbols} \idxboth{miscellaneous}{symbols} \index{angles} \idxboth{right}{angles} \label{mdes-misc} \begin{tabular}{ll} \K[\MDESrightangle]\rightangle \end{tabular} \end{symtable} \begin{symtable}[LOGIX]{Miscellaneous \LOGIX\ Math Symbols} \idxboth{miscellaneous}{symbols} \idxboth{logic}{symbols} \label{logix-misc} \begin{tabular}{*4{ll}} \K\Aor & \K\FncCnvrs & \K\MapJoin & \K\SetJoin \\ \K\Append & \K\FncComp & \K\MapMeet & \K\SetMeet \\ \K\BncBistab & \K\ForComp & \K\Mnd & \K\SetSymDiff \\ \K\BnchJoin & \K\FrstOrd & \K\Mor & \K\SimPerp \\ \K\BnchMeet & \K\GrtFix & \K\Normal & \K\SInCoh \\ \K\Catenate & \K\InCoh & \K\OfCrse & \K\SmCircPlus \\ \K\Choice & \K\Infin & \K\QuantAAnd & \K\SmCircStar \\ \K\Choices & \K\LcgBistab & \K\QuantBnchJoin & \K\SmCircTimes \\ \K\Coh & \K\LgCircPlus & \K\QuantBnchMeet & \K\VeeJoin \\ \K\Concat & \K\LgCircStar & \K\QuantMor & \K\VeeMeet \\ \K\Cover & \K\LgCircTimes & \K\QuantSetJoin & \K\WhyNot \\ \K\ExGrtFix & \K\LstFix & \K\QuantSetMeet & \\ \K\ExLstFix & \K\MapComp & \K\SCoh & \\ \end{tabular} \bigskip \begin{tablenote} \seepackagenote{LOGIX}{logix}. \end{tablenote} \end{symtable} % Because the Math Alphabets table is a bit different from the symbol % tables in this document we start it on its own page to emphasize it % and to include enough room for some of the table notes. \clearpage \begin{symtable}{Math Alphabets} \idxboth{math}{alphabets} \label{alphabets} \begin{tabular}{@{}ll>{\ttfamily}ll@{}} \toprule Font sample & Generating command & \normalfont \tex\ font & Required package \\ \midrule \Wf\mathrm{ABCdef123} & cmr10 & \textit{none} \\ \Ww\textit\mathit{ABCdef123} & cmmi10 & \textit{none} \\ \Wf\mathnormal{ABCdef123}& cmmi10 & \textit{none} \\ \Ww\CMcal\mathcal{ABC} & cmsy10 & \textit{none} \\ \ifx\mathscr\undefined\else \Wf\mathscr{ABC} & rsfs10 & \pkgname{mathrsfs} \\ \multicolumn{1}{r@{}}{\emph{or}} & \verb|\mathcal{ABC}| & rsfs10 & \pkgname{calrsfs} \\ \fi \ifEU \Wf\mathcal{ABC} & eusm10 & \pkgname[pkg=amsfonts]{euscript} with the \optname{euscript}{mathcal} option \\ \multicolumn{1}{r@{}}{\emph{or}} & \verb|\mathscr{ABC}| & eusm10 & \pkgname[pkg=amsfonts]{euscript} with the \optname{euscript}{mathscr} option \\ \fi \ifRSFSO \Ww\RSFSmathcal\mathcal{ABC} & rsfso10 & \pkgname{rsfso} \\ \multicolumn{1}{r@{}}{\emph{or}} & \verb|\mathscr{ABC}| & rsfso10 & \pkgname{rsfso} with the \optname{rsfso}{scr} option \\ \fi \ifCHAN \Ww\CHANmathcal\mathcal{ABC} & urwchancal & \pkgname{urwchancal}$^*$ \\ \multicolumn{1}{r@{}}{\emph{or}} & \verb|\mathscr{ABC}| & urwchancal & \pkgname{urwchancal}$^*$ with the \optname{urwchancal}{mathscr} option \\ \fi \ifx\mathbb\undefined\else \Wf\mathbb{ABC} & msbm10 & \pkgname{amsfonts},% \ifx\MSYMmathbb\undefined\else$^\S$~\fi \pkgname{amssymb}, \pkgname{txfonts}, or \pkgname{pxfonts} \\ \fi \ifx\varmathbb\undefined\else \Wf\varmathbb{ABC} & txmia & \pkgname{txfonts} or \pkgname{pxfonts} \\ \fi \ifx\BBmathbb\undefined\else \Ww\BBmathbb\mathbb{ABCdef123} & bbold10 & \pkgname{bbold} or \pkgname{mathbbol}$^\dag$ \\ \fi \ifx\MBBmathbb\undefined\else \Ww\MBBmathbb\mathbb{ABCdef123} & mbb10 & \pkgname{mbboard}$^\dag$ \\ \fi \ifx\mathbbm\undefined\else \Wf\mathbbm{ABCdef12} & bbm10 & \pkgname{bbm} \\ \Wf\mathbbmss{ABCdef12} & bbmss10 & \pkgname{bbm} \\ \Wf\mathbbmtt{ABCdef12} & bbmtt10 & \pkgname{bbm} \\ \fi \ifx\mathds\undefined\else \Wf\mathds{ABC1} & dsrom10 & \pkgname[pkg=doublestroke]{dsfont} \\ \Ww\mathdsss\mathds{ABC1} & dsss10 & \pkgname[pkg=doublestroke]{dsfont} with the \optname{dsfont}{sans} option \\ \fi \ifx\dsserifbb\undefined\else \Ww\dsserifbb\mathbb{ABCdef123} & DSSerif & \pkgname{dsserif} \\ \Ww\dsserifbbb\mathbbb{ABCdef123} & DSSerif-Bold & \pkgname{dsserif} \\ \fi \ifx\symA\undefined\else \symA\symB\symC & \cmdI{\symA}\cmdI{\symB}\cmdI{\symC} & china10 & \pkgname{china2e}$^\ddag$ \\ \fi \ifx\mathfrak\undefined\else \Wf\mathfrak{ABCdef123} & eufm10 & \pkgname[pkg=amsfonts]{eufrak} \\ \fi \ifx\textfrak\undefined\else \Wf\textfrak{ABCdef123} & yfrak & \pkgname{yfonts}$^\P$ \\ \Wf\textswab{ABCdef123} & yswab & \pkgname{yfonts}$^\P$ \\ \Wf\textgoth{ABCdef123} & ygoth & \pkgname{yfonts}$^\P$ \\ \fi \bottomrule \end{tabular} \end{symtable} \unskip % Because we have so much text and because we're at the end of the % chapter, we put all of the table notes after the symtable to give % LaTeX the opportunity to split them across pages. \begin{center} \bigskip \begin{tablenote} The ``\tex\ font'' column lists the underlying \TeX\ font (or, more accurately, the \fileext{tfm} file) that provides the math alphabet. See the corresponding table in the associated \rawtables\ document for the math alphabet's complete character set. \end{tablenote} \ifCHAN \ifx\mathpzc\undefined\else \bigskip \begin{tablenote}[*] \CHAN\ redefines \cmd{\mathcal} or \cmd{\mathscr} to use \PSfont{Zapf Chancery} as the caligraphic or script font. However, like all \cmd{\mathcal} and \cmd{\mathscr} commands shown in \ref{alphabets}, these support only uppercase letters. An alternative is to put ``\verb|\DeclareMathAlphabet{\mathpzc}{T1}{pzc}{m}{it}|'' in your document's preamble to make \verb|\mathpzc| typeset a wider set of characters in \PSfont{Zapf Chancery}. Unfortunately, with this technique accents, superscripts, and subscripts don't align as well as they do with \CHAN. \ifx\textcalligra\undefined\else As a similar trick, you can typeset the \PSfont{Calligra} font's script ``{\Large\textcalligra{r}\,}''\index{r=r (\textcalligra{r})}\index{Griffith's separation vector=Griffith's separation vector (\textcalligra{r})}\index{separation vector=separation vector (\textcalligra{r})} (or other calligraphic symbols) in math mode by loading the \pkgname{calligra} package and putting ``\verb|\DeclareMathAlphabet{\mathcalligra}{T1}{calligra}{m}{n}|'' in your document's preamble to make \verb|\mathcalligra| typeset its argument in the \PSfont{Calligra} font. You may also want to specify ``\verb|\DeclareFontShape{T1}{calligra}{m}{n}{<->s*[2.2]callig15}{}|'' to set \PSfont{Calligra} at 2.2~times its design size for a better blend with typical body fonts. \fi % textcalligra test \end{tablenote} \fi % mathpzc test \fi % CHAN test \ifx\BBmathbb\undefined\else \bigskip \begin{tablenote}[\dag] The \pkgname{mathbbol} package defines some additional blackboard bold characters: parentheses, square brackets, angle brackets, and---if the \optname{mathbbol}{bbgreekl} option is passed to \pkgname{mathbbol}---Greek\index{Greek>blackboard bold}\index{Greek>letters} letters. For instance, ``$\BBmathbb{\char`<\char`[\char`(\char"0B\char"0C\char"0D\char`)\char`]\char`>}$'' is produced by ``\cmd{\mathbb}\verb|{|\cmdI{\Langle}\linebreak[1]% \cmdI{\Lbrack}\linebreak[1]\cmdI{\Lparen}\linebreak[1]% \cmdI{\bbalpha}\linebreak[1]\cmdI{\bbbeta}\linebreak[1]% \cmdI{\bbgamma}\linebreak[1]\cmdI{\Rparen}\linebreak[1]% \cmdI{\Rbrack}\linebreak[1]\cmdI{\Rangle}\verb|}|''. \ifx\MBBmathbb\undefined \pkgname{mbboard} extends the blackboard bold symbol set significantly further. It supports not only the Greek\index{Greek>blackboard bold}\subindex{alphabets}{Greek}\index{Greek>letters} alphabet---including ``Greek-like'' symbols such as \cmd{\bbnabla}---but also \emph{all} punctuation marks, various currency\idxboth{currency}{symbols}\idxboth{monetary}{symbols} symbols such as \cmd{\bbdollar} and \cmd{\bbeuro},\index{euro>blackboard bold} and the Hebrew\index{Hebrew}\subindex{alphabets}{Hebrew} alphabet. \else \pkgname{mbboard} extends the blackboard bold symbol set significantly further. It supports not only the Greek\index{Greek>blackboard bold}\subindex{alphabets}{Greek}\index{Greek>letters} alphabet---including ``Greek-like'' symbols such as \cmdI{\bbnabla}~(``\bbnabla'')---but also \emph{all} punctuation marks, various currency\idxboth{currency}{symbols}\idxboth{monetary}{symbols} symbols such as \cmdI{\bbdollar}~(``\bbdollar'') and \cmdI{\bbeuro}~(``\bbeuro''),\index{euro>blackboard bold} and the Hebrew\index{Hebrew}\subindex{alphabets}{Hebrew} alphabet~(e.g.,~``\cmdI{\bbfinalnun}\linebreak[1]\cmdI{\bbyod}% \linebreak[1]\cmdI{\bbqof}\linebreak[1]\cmdI{\bbpe}''~$\rightarrow$ ``\bbfinalnun\bbyod\bbqof\bbpe''). \fi % MBBmathbb test \end{tablenote} \fi \ifx\symA\undefined\else \bigskip \begin{tablenote}[\ddag] The \verb|\sym|\rule{2em}{1pt} commands provided by the \CHINA\ package are actually text-mode commands. They are included in \ref{alphabets} because they resemble the blackboard-bold symbols that appear in the rest of the table. In addition to the 26 letters of the English alphabet, \CHINA\ provides three umlauted% \index{accents>diaeresis=di\ae{}resis (\blackacchack\")} % "Generic" blackboard-bold letters: \cmdI{\symAE}~(``\symAE''), \cmdI{\symOE}~(``\symOE''), and \cmdI{\symUE}~(``\symUE''). Note that \CHINA\ does provide math-mode commands for the most common number-set symbols. These are presented in \vref{china-numsets}. \end{tablenote} \fi \ifx\textfrak\undefined\else \bigskip \begin{tablenote}[\P] As their \verb|\text|\dots{} names imply, the fonts provided by the \pkgname{yfonts} package are actually text fonts. They are included in \ref{alphabets} because they are frequently used in a mathematical context. \end{tablenote} \fi \ifx\MSYMmathbb\undefined\else \bigskip \begin{tablenote}[\S] An older (i.e.,~prior to~1991) version of the \AMS's fonts rendered $\mathbb{C}$, $\mathbb{N}$, $\mathbb{R}$, $\mathbb{S}$, and~$\mathbb{Z}$ as $\MSYMmathbb{C}$, $\MSYMmathbb{N}$, $\MSYMmathbb{R}$, $\MSYMmathbb{S}$, and~$\MSYMmathbb{Z}$. As some people prefer the older glyphs---much to the \AMS's surprise---and because those glyphs fail to build under modern versions of \metafont, \person{Berthold}{Horn} uploaded \postscript fonts for the older blackboard-bold glyphs to \CTAN, to the \texttt{fonts/msym10} directory. As of this writing, however, there are no \latexE packages for utilizing the now-obsolete glyphs. \end{tablenote} \fi \end{center} \idxbothend{mathematical}{symbols}