%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Contents: TeX and LaTeX and AMS symbols for Maths % $Id: lssym.tex,v 1.2 1996/01/25 14:01:06 oetiker Exp oetiker $ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{List of Mathematical Symbols} \label{symbols} In the following tables you find all the symbols normally accessible from \emph{math mode}. % % Conditional Text in case the AMS Fonts are installed % \ifx\noAMS\relax To use the symbols listed in Tables~\ref{AMSD}--\ref{AMSNBR}\footnote{These tables were derived from \texttt{symbols.tex} by David~Carlisle and subsequently changed extensively as suggested by Josef~Tkadlec}, the package \pai{amssymb} must be loaded in the preamble of the document and the AMS math fonts must be installed on the system. If the AMS package and fonts are not installed, on your system, have a look at\\ \texttt{CTAN:/tex-archive/macros/latex/packages/amslatex}\fi \begin{table}[!h] \caption{Math Mode Accents} \label{mathacc} \begin{symbols}{*4{cl}} \W{\hat}{a} & \W{\check}{a} & \W{\tilde}{a} & \W{\acute}{a} \\ \W{\grave}{a} & \W{\dot}{a} & \W{\ddot}{a} & \W{\breve}{a} \\ \W{\bar}{a} &\W{\vec}{a} &\W{\widehat}{A}&\W{\widetilde}{A}\\ \end{symbols} \end{table} \begin{table}[!h] \caption{Lowercase Greek Letters} \begin{symbols}{*4{cl}} \X{\alpha} & \X{\theta} & \X{o} & \X{\upsilon} \\ \X{\beta} & \X{\vartheta} & \X{\pi} & \X{\phi} \\ \X{\gamma} & \X{\iota} & \X{\varpi} & \X{\varphi} \\ \X{\delta} & \X{\kappa} & \X{\rho} & \X{\chi} \\ \X{\epsilon} & \X{\lambda} & \X{\varrho} & \X{\psi} \\ \X{\varepsilon}& \X{\mu} & \X{\sigma} & \X{\omega} \\ \X{\zeta} & \X{\nu} & \X{\varsigma} & & \\ \X{\eta} & \X{\xi} & \X{\tau} \end{symbols} \end{table} \begin{table}[!h] \caption{Uppercase Greek Letters} \begin{symbols}{*4{cl}} \X{\Gamma} & \X{\Lambda} & \X{\Sigma} & \X{\Psi} \\ \X{\Delta} & \X{\Xi} & \X{\Upsilon} & \X{\Omega} \\ \X{\Theta} & \X{\Pi} & \X{\Phi} \end{symbols} \end{table} \clearpage \begin{table}[!tbp] \caption{Binary Relations} \bigskip You can produce corresponding negations by adding a \verb|\not| command as prefix to the following symbols. \begin{symbols}{*3{cl}} \X{<} & \X{>} & \X{=} \\ \X{\leq}or \verb|\le| & \X{\geq}or \verb|\ge| & \X{\equiv} \\ \X{\ll} & \X{\gg} & \X{\doteq} \\ \X{\prec} & \X{\succ} & \X{\sim} \\ \X{\preceq} & \X{\succeq} & \X{\simeq} \\ \X{\subset} & \X{\supset} & \X{\approx} \\ \X{\subseteq} & \X{\supseteq} & \X{\cong} \\ \X{\sqsubset}$^a$ & \X{\sqsupset}$^a$ & \X{\Join}$^a$ \\ \X{\sqsubseteq} & \X{\sqsupseteq} & \X{\bowtie} \\ \X{\in} & \X{\ni}, \verb|\owns| & \X{\propto} \\ \X{\vdash} & \X{\dashv} & \X{\models} \\ \X{\mid} & \X{\parallel} & \X{\perp} \\ \X{\smile} & \X{\frown} & \X{\asymp} \\ \X{:} & \X{\notin} & \X{\neq}or \verb|\ne| \end{symbols} \centerline{\footnotesize $^a$Use the \textsf{latexsym} package to access this symbol} \end{table} \begin{table}[!tbp] \caption{Binary Operators} \begin{symbols}{*3{cl}} \X{+} & \X{-} & & \\ \X{\pm} & \X{\mp} & \X{\triangleleft} \\ \X{\cdot} & \X{\div} & \X{\triangleright}\\ \X{\times} & \X{\setminus} & \X{\star} \\ \X{\cup} & \X{\cap} & \X{\ast} \\ \X{\sqcup} & \X{\sqcap} & \X{\circ} \\ \X{\vee}, \verb|\lor| & \X{\wedge}, \verb|\land| & \X{\bullet} \\ \X{\oplus} & \X{\ominus} & \X{\diamond} \\ \X{\odot} & \X{\oslash} & \X{\uplus} \\ \X{\otimes} & \X{\bigcirc} & \X{\amalg} \\ \X{\bigtriangleup} &\X{\bigtriangledown}& \X{\dagger} \\ \X{\lhd}$^a$ & \X{\rhd}$^a$ & \X{\ddagger} \\ \X{\unlhd}$^a$ & \X{\unrhd}$^a$ & \X{\wr} \end{symbols} \end{table} \begin{table}[!tbp] \caption{BIG Operators} \begin{symbols}{*4{cl}} \X{\sum} & \X{\bigcup} & \X{\bigvee} & \X{\bigoplus}\\ \X{\prod} & \X{\bigcap} & \X{\bigwedge} &\X{\bigotimes}\\ \X{\coprod} & \X{\bigsqcup} & & & \X{\bigodot} \\ \X{\int} & \X{\oint} & & & \X{\biguplus} \end{symbols} \end{table} \begin{table}[!tbp] \caption{Arrows} \begin{symbols}{*3{cl}} \X{\leftarrow}or \verb|\gets|& \X{\longleftarrow} & \X{\uparrow} \\ \X{\rightarrow}or \verb|\to|& \X{\longrightarrow} & \X{\downarrow} \\ \X{\leftrightarrow} & \X{\longleftrightarrow}& \X{\updownarrow} \\ \X{\Leftarrow} & \X{\Longleftarrow} & \X{\Uparrow} \\ \X{\Rightarrow} & \X{\Longrightarrow} & \X{\Downarrow} \\ \X{\Leftrightarrow} & \X{\Longleftrightarrow}& \X{\Updownarrow} \\ \X{\mapsto} & \X{\longmapsto} & \X{\nearrow} \\ \X{\hookleftarrow} & \X{\hookrightarrow} & \X{\searrow} \\ \X{\leftharpoonup} & \X{\rightharpoonup} & \X{\swarrow} \\ \X{\leftharpoondown} & \X{\rightharpoondown} & \X{\nwarrow} \\ \X{\rightleftharpoons} & \X{\iff}(bigger spaces)& \X{\leadsto}$^a$ \end{symbols} \centerline{\footnotesize $^a$Use the \textsf{latexsym} package to access this symbol} \end{table} \begin{table}[!tbp] \caption{Delimiters}\label{tab:delimiters} \begin{symbols}{*4{cl}} \X{(} & \X{)} & \X{\uparrow} & \X{\Uparrow} \\ \X{[}or \verb|\lbrack| & \X{]}or \verb|\rbrack| & \X{\downarrow} & \X{\Downarrow} \\ \X{\{}or \verb|\lbrace| & \X{\}}or \verb|\rbrace| & \X{\updownarrow} & \X{\Updownarrow}\\ \X{\langle} & \X{\rangle} & \X{|}or \verb|\vert| &\X{\|}or \verb|\Vert|\\ \X{\lfloor} & \X{\rfloor} & \X{\lceil} & \X{\rceil} \\ \X{/} & \X{\backslash} & &. (dual. empty) \end{symbols} \end{table} \begin{table}[!tbp] \caption{Large Delimiters} \begin{symbols}{*4{cl}} \Y{\lgroup} & \Y{\rgroup} & \Y{\lmoustache} & \Y{\rmoustache} \\ \Y{\arrowvert} & \Y{\Arrowvert} & \Y{\bracevert} \end{symbols} \end{table} \begin{table}[!tbp] \caption{Miscellaneous Symbols} \begin{symbols}{*4{cl}} \X{\dots} & \X{\cdots} & \X{\vdots} & \X{\ddots} \\ \X{\hbar} & \X{\imath} & \X{\jmath} & \X{\ell} \\ \X{\Re} & \X{\Im} & \X{\aleph} & \X{\wp} \\ \X{\forall} & \X{\exists} & \X{\mho}$^a$ & \X{\partial} \\ \X{'} & \X{\prime} & \X{\emptyset} & \X{\infty} \\ \X{\nabla} & \X{\triangle} & \X{\Box}$^a$ & \X{\Diamond}$^a$ \\ \X{\bot} & \X{\top} & \X{\angle} & \X{\surd} \\ \X{\diamondsuit} & \X{\heartsuit} & \X{\clubsuit} & \X{\spadesuit} \\ \X{\neg}or \verb|\lnot| & \X{\flat} & \X{\natural} & \X{\sharp} \end{symbols} \centerline{\footnotesize $^a$Use the \textsf{latexsym} package to access this symbol} \end{table} \begin{table}[!tbp] \caption{Non-Mathematical Symbols} \bigskip These symbols can also be used in text mode. \begin{symbols}{*3{cl}} \SC{\dag} & \SC{\S} & \SC{\copyright} \\ \SC{\ddag} & \SC{\P} & \SC{\pounds} \\ \end{symbols} \end{table} % % % If the AMS Stuff is not available, we drop out right here :-) % \noAMS \begin{table}[!tbp] \caption{AMS Delimiters}\label{AMSD} \bigskip \begin{symbols}{*4{cl}} \X{\ulcorner}&\X{\urcorner}&\X{\llcorner}&\X{\lrcorner} \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Greek and Hebrew} \begin{symbols}{*5{cl}} \X{\digamma} &\X{\varkappa} & \X{\beth}& \X{\daleth} &\X{\gimel} \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Binary Relations} \begin{symbols}{*3{cl}} \X{\lessdot} & \X{\gtrdot} & \X{\doteqdot}or \verb|\Doteq| \\ \X{\leqslant} & \X{\geqslant} & \X{\risingdotseq} \\ \X{\eqslantless} & \X{\eqslantgtr} & \X{\fallingdotseq} \\ \X{\leqq} & \X{\geqq} & \X{\eqcirc} \\ \X{\lll}or \verb|\llless| & \X{\ggg}or \verb|\gggtr| & \X{\circeq} \\ \X{\lesssim} & \X{\gtrsim} & \X{\triangleq} \\ \X{\lessapprox} & \X{\gtrapprox} & \X{\bumpeq} \\ \X{\lessgtr} & \X{\gtrless} & \X{\Bumpeq} \\ \X{\lesseqgtr} & \X{\gtreqless} & \X{\thicksim} \\ \X{\lesseqqgtr} & \X{\gtreqqless} & \X{\thickapprox} \\ \X{\preccurlyeq} & \X{\succcurlyeq} & \X{\approxeq} \\ \X{\curlyeqprec} & \X{\curlyeqsucc} & \X{\backsim} \\ \X{\precsim} & \X{\succsim} & \X{\backsimeq} \\ \X{\precapprox} & \X{\succapprox} & \X{\vDash} \\ \X{\subseteqq} & \X{\supseteqq} & \X{\Vdash} \\ \X{\Subset} & \X{\Supset} & \X{\Vvdash} \\ \X{\sqsubset} & \X{\sqsupset} & \X{\backepsilon} \\ \X{\therefore} & \X{\because} & \X{\varpropto} \\ \X{\shortmid} & \X{\shortparallel} & \X{\between} \\ \X{\smallsmile} & \X{\smallfrown} & \X{\pitchfork} \\ \X{\vartriangleleft} & \X{\vartriangleright} & \X{\blacktriangleleft}\\ \X{\trianglelefteq} & \X{\trianglerighteq} &\X{\blacktriangleright} \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Arrows} \begin{symbols}{*3{cl}} \X{\dashleftarrow} & \X{\dashrightarrow} & \X{\multimap} \\ \X{\leftleftarrows} & \X{\rightrightarrows} & \X{\upuparrows} \\ \X{\leftrightarrows} & \X{\rightleftarrows} & \X{\downdownarrows} \\ \X{\Lleftarrow} & \X{\Rrightarrow} & \X{\upharpoonleft} \\ \X{\twoheadleftarrow} & \X{\twoheadrightarrow} & \X{\upharpoonright} \\ \X{\leftarrowtail} & \X{\rightarrowtail} & \X{\downharpoonleft} \\ \X{\leftrightharpoons} & \X{\rightleftharpoons} & \X{\downharpoonright} \\ \X{\Lsh} & \X{\Rsh} & \X{\rightsquigarrow} \\ \X{\looparrowleft} & \X{\looparrowright} &\X{\leftrightsquigarrow}\\ \X{\curvearrowleft} & \X{\curvearrowright} & & \\ \X{\circlearrowleft} & \X{\circlearrowright} & & \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Negated Binary Relations and Arrows}\label{AMSNBR} \begin{symbols}{*3{cl}} \X{\nless} & \X{\ngtr} & \X{\varsubsetneqq} \\ \X{\lneq} & \X{\gneq} & \X{\varsupsetneqq} \\ \X{\nleq} & \X{\ngeq} & \X{\nsubseteqq} \\ \X{\nleqslant} & \X{\ngeqslant} & \X{\nsupseteqq} \\ \X{\lneqq} & \X{\gneqq} & \X{\nmid} \\ \X{\lvertneqq} & \X{\gvertneqq} & \X{\nparallel} \\ \X{\nleqq} & \X{\ngeqq} & \X{\nshortmid} \\ \X{\lnsim} & \X{\gnsim} & \X{\nshortparallel} \\ \X{\lnapprox} & \X{\gnapprox} & \X{\nsim} \\ \X{\nprec} & \X{\nsucc} & \X{\ncong} \\ \X{\npreceq} & \X{\nsucceq} & \X{\nvdash} \\ \X{\precneqq} & \X{\succneqq} & \X{\nvDash} \\ \X{\precnsim} & \X{\succnsim} & \X{\nVdash} \\ \X{\precnapprox} & \X{\succnapprox} & \X{\nVDash} \\ \X{\subsetneq} & \X{\supsetneq} & \X{\ntriangleleft} \\ \X{\varsubsetneq} & \X{\varsupsetneq} & \X{\ntriangleright} \\ \X{\nsubseteq} & \X{\nsupseteq} & \X{\ntrianglelefteq}\\ \X{\subsetneqq} & \X{\supsetneqq} &\X{\ntrianglerighteq}\\[0.5ex] \X{\nleftarrow} & \X{\nrightarrow} & \X{\nleftrightarrow}\\ \X{\nLeftarrow} & \X{\nRightarrow} & \X{\nLeftrightarrow} \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Binary Operators} \begin{symbols}{*3{cl}} \X{\dotplus} & \X{\centerdot} & \X{\intercal} \\ \X{\ltimes} & \X{\rtimes} & \X{\divideontimes} \\ \X{\Cup}or \verb|\doublecup|& \X{\Cap}or \verb|\doublecap|& \X{\smallsetminus} \\ \X{\veebar} & \X{\barwedge} & \X{\doublebarwedge}\\ \X{\boxplus} & \X{\boxminus} & \X{\circleddash} \\ \X{\boxtimes} & \X{\boxdot} & \X{\circledcirc} \\ \X{\leftthreetimes} & \X{\rightthreetimes}& \X{\circledast} \\ \X{\curlyvee} & \X{\curlywedge} \end{symbols} \end{table} \begin{table}[!tbp] \caption{AMS Miscellaneous} \begin{symbols}{*3{cl}} \X{\hbar} & \X{\hslash} & \X{\Bbbk} \\ \X{\square} & \X{\blacksquare} & \X{\circledS} \\ \X{\vartriangle} & \X{\blacktriangle} & \X{\complement} \\ \X{\triangledown} &\X{\blacktriangledown} & \X{\Game} \\ \X{\lozenge} & \X{\blacklozenge} & \X{\bigstar} \\ \X{\angle} & \X{\measuredangle} & \X{\sphericalangle} \\ \X{\diagup} & \X{\diagdown} & \X{\backprime} \\ \X{\nexists} & \X{\Finv} & \X{\varnothing} \\ \X{\eth} & \X{\mho} \end{symbols} \end{table} \begin{table}[!tbp] \caption{Math Alphabets} \begin{symbols}{@{}*3l@{}} Example& Command &Required package\\ \hline \rule{0pt}{1.05em}$\mathrm{ABCdef}$ & \verb|\mathrm{ABCdef}| & \\ $\mathit{ABCdef}$ & \verb|\mathit{ABCdef}| & \\ $\mathnormal{ABCdef}$ & \verb|\mathnormal{ABCdef}| & \\ $\mathcal{ABC}$ & \verb|\mathcal{ABC}| & \\ \ifx\EuScript\undefined\else $\EuScript{ABC}$ & \verb|\mathcal{ABC}| &\textsf{eucal} with option: \textsf{mathcal} \\ \quad or & \verb|\mathscr{ABC}| &\textsf{eucal} with option: \textsf{mathscr}\\ $\mathfrak{ABCdef}$ & \verb|\mathfrak{ABCdef}| &\textsf{eufrak} \\ \fi $\mathbb{ABC}$ & \verb|\mathbb{ABC}| &\textsf{amsfonts} or \textsf{amssymb} \\ \end{symbols} \end{table} \endinput %%% Local Variables: %%% mode: latex %%% TeX-master: "lshort2e" %%% End: