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% Contents: TeX and LaTeX and AMS symbols for Maths
% $Id: lssym.tex 9927 2011-05-20 15:19:46Z ambs $
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\section{Lista de Símbolos Matemáticos}  \label{symbols}
 
As tabelas seguintes demonstram todos os símbolos normalmente
acessíveis no \emph{modo matemático}.

%
% Conditional Text in case the AMS Fonts are installed
%
Note que algumas tabelas apresentam símbolos apenas acessíveis depois
de importar o pacote \pai{amssymb} no preâmbulo do seu
documento\footnote{Estas tabelas são derivadas do \texttt{symbols.tex}
  por David~Carlisle e mudados extensivamente como sugerido por
  Josef~Tkadlex.}. Se o pacote \AmS{} e os respectivos tipos de letra
não estiverem instaladas no seu sistema, dê uma vista de olhos a
\CTANref|CTAN:macros/latex/required/amslatex|. Uma lista ainda mais
completa de símbolos pode ser encontrada em
\CTANref|CTAN:info/symbols/comprehensive|.
 
\begin{table}[!h]
\caption{Acentos Matemáticos.}  \label{mathacc}
\begin{symbols}{*3{cl}}
\W{\hat}{a}      & \W{\check}{a} & \W{\tilde}{a}     \\
\W{\grave}{a}    & \W{\dot}{a}   & \W{\ddot}{a}      \\
\W{\bar}{a}      & \W{\vec}{a}   & \W{\widehat}{A}   \\  
\W{\acute}{a}    & \W{\breve}{a} & \W{\widetilde}{A} \\
\W{\mathring}{a}
\end{symbols}
\end{table}
 
\begin{table}[!h]
\caption{Letras Gregas.}\label{greekletters}
\bigskip
Não existem versões maiúsculas para algumas letras, como \ci{Alpha} ou \ci{Beta}, 
porque são representadas por letras romana normais: A, B\ldots
\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}       &               \\
 \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}

\begin{table}[!tbp]
\caption{Relações Binárias.}\label{binaryrel}
\bigskip
Pode negar cada um dos seguintes símbolos adicionando o comando \ci{not} como
prefixo do símbolo em causa.
\begin{symbols}{*3{cl}}
 \X{<}           & \X{>}           & \X{=}          \\
 \X{\leq}ou \verb|\le|   & \X{\geq}ou \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}ou \verb|\ne|
\end{symbols}
\centerline{\footnotesize $^a$Use o pacote \textsf{latexsym} para aceder a estes símbolos}
\end{table}

\begin{table}[!tbp]
\caption{Operadores Binários.}
\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{Operadores GRANDES.}
\begin{symbols}{*4{cl}}
 \X{\sum}      & \X{\bigcup}   & \X{\bigvee}  \\
 \X{\prod}     & \X{\bigcap}   & \X{\bigwedge} \\
 \X{\coprod}   & \X{\bigsqcup} & \X{\biguplus} \\
 \X{\int}      & \X{\oint}     & \X{\bigodot} \\
 \X{\bigoplus} & \X{\bigotimes} & \\
\end{symbols}
 
\end{table}


\begin{table}[!tbp]
\caption{Setas.}\label{tab:arrows}
 \begin{symbols}{*2{cl}}
  \X{\leftarrow}ou \verb|\gets|& \X{\longleftarrow} \\
  \X{\rightarrow}ou \verb|\to|& \X{\longrightarrow} \\
  \X{\leftrightarrow}    & \X{\longleftrightarrow} \\
  \X{\Leftarrow}         & \X{\Longleftarrow}     \\
  \X{\Rightarrow}        & \X{\Longrightarrow}    \\
  \X{\Leftrightarrow}    & \X{\Longleftrightarrow}\\
  \X{\mapsto}            & \X{\longmapsto}        \\
  \X{\hookleftarrow}     & \X{\hookrightarrow}    \\
  \X{\leftharpoonup}     & \X{\rightharpoonup}    \\
  \X{\leftharpoondown}   & \X{\rightharpoondown}  \\
  \X{\rightleftharpoons} & \X{\iff}(espaços maiores) \\
  \X{\uparrow}   & \X{\downarrow} \\
  \X{\updownarrow} & \X{\Uparrow} \\
  \X{\Downarrow} &  \X{\Updownarrow} \\
  \X{\nearrow} &  \X{\searrow} \\
  \X{\swarrow} & \X{\nwarrow} \\
  \X{\leadsto}$^a$
\end{symbols}
\centerline{\footnotesize $^a$Use o pacote \textsf{latexsym} para aceder a estes símbolos}
\end{table}

 
 \begin{table}[!tbp]
\caption{Setas como Acentos.}  \label{arrowacc}
\begin{symbols}{*2{cl}}
\W{\overrightarrow}{AB}     & \W{\underrightarrow}{AB}     \\
\W{\overleftarrow}{AB}      & \W{\underleftarrow}{AB}      \\
\W{\overleftrightarrow}{AB} & \W{\underleftrightarrow}{AB} \\
\end{symbols}
\end{table}


\begin{table}[!tbp]
\caption{Delimitadores.}\label{tab:delimiters}
\begin{symbols}{*3{cl}}
  \X{(}            & \X{)}            & \X{\uparrow} \\
  \X{[}ou \verb|\lbrack|   & \X{]}ou \verb|\rbrack|  & \X{\downarrow}   \\
  \X{\{}ou \verb|\lbrace|  & \X{\}}ou \verb|\rbrace|  & \X{\updownarrow} \\
  \X{\langle}      & \X{\rangle}      &  \X{\Uparrow} \\
  \X{|}ou \verb|\vert| & \X{\|}ou \verb|\Vert| & \X{\Downarrow} \\
  \X{/}            & \X{\backslash}   &   \X{\Updownarrow}  \\ 
  \X{\lfloor}      & \X{\rfloor}      &  \\
  \X{\rceil}       &  \X{\lceil}  &&\\
\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Grandes Delimitadores.}
 \begin{symbols}{*3{cl}}
  \Y{\lgroup}      & \Y{\rgroup}      & \Y{\lmoustache}  \\
  \Y{\arrowvert}   & \Y{\Arrowvert}   & \Y{\bracevert} \\
  \Y{\rmoustache} \\
\end{symbols}
\end{table}


\begin{table}[!tbp]
\caption{Símbolos Sortidos.}
\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}ou \verb|\lnot| & \X{\flat}       & \X{\natural}    & \X{\sharp}
\end{symbols}
\centerline{\footnotesize $^a$Use o pacote \textsf{latexsym} para aceder a este símbolo}
\end{table}

\begin{table}[!tbp]
\caption{Símbolos não Matemáticos.}
\bigskip
Estes símbolos também podem ser usados em modo texto.
\begin{symbols}{*4{cl}}
\SC{\dag} & \SC{\S} & \SC{\copyright} & \SC{\textregistered} \\
\SC{\ddag} & \SC{\P} & \SC{\pounds}   & \SC{\%}              \\
\end{symbols}
\end{table}

\clearpage

%
%
% If the AMS Stuff is not available, we drop out right here :-)
%

\begin{table}[!tbp]
\caption{Delimitadores \AmS{}.}\label{AMSD}
\bigskip
\begin{symbols}{*4{cl}}
\X{\ulcorner}&\X{\urcorner}&\X{\llcorner}&\X{\lrcorner}\\
\X{\lvert}&\X{\rvert}&\X{\lVert}&\X{\rVert}

\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Letras \AmS{} gregas e hebraicas.}
\begin{symbols}{*5{cl}}
\X{\digamma}     &\X{\varkappa} & \X{\beth} &\X{\gimel} & \X{\daleth}    
\end{symbols}
\end{table}

\begin{table}[tbp]
  \caption{Alfabetos Matemáticos.} \label{mathalpha}
\bigskip Veja a tabela~\ref{mathfonts} (pág.~\pageref{mathfonts}) para outros tipos
de letras em modo matemático.
\begin{symbols}{@{}*3l@{}}
Exemplo & Comando & Pacote necessário \\
\hline
\rule{0pt}{1.05em}$\mathrm{ABCDE abcde 1234}$
        & \verb|\mathrm{ABCDE abcde 1234}|
        &       \\
$\mathit{ABCDE abcde 1234}$
        & \verb|\mathit{ABCDE abcde 1234}|
        &       \\
$\mathnormal{ABCDE abcde 1234}$
        & \verb|\mathnormal{ABCDE abcde 1234}|
        &  \\
$\mathcal{ABCDE abcde 1234}$
        & \verb|\mathcal{ABCDE abcde 1234}|
        &  \\
$\mathscr{ABCDE abcde 1234}$
        &\verb|\mathscr{ABCDE abcde 1234}|
        &\pai{mathrsfs}\\
$\mathfrak{ABCDE abcde 1234}$
        & \verb|\mathfrak{ABCDE abcde 1234}|
        &\pai{amsfonts}  ou \textsf{amssymb}  \\
$\mathbb{ABCDE abcde 1234}$
        & \verb|\mathbb{ABCDE abcde 1234}|
        &\pai{amsfonts}  ou \textsf{amssymb} \\
\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Operadores Binários \AmS{}.}
\begin{symbols}{*3{cl}}
 \X{\dotplus}        & \X{\centerdot}      &       \\
 \X{\ltimes}         & \X{\rtimes}         & \X{\divideontimes}   \\
 \X{\doublecup}      & \X{\doublecap}	   & \X{\smallsetminus}   \\
 \X{\veebar}         & \X{\barwedge}       & \X{\doublebarwedge}  \\
 \X{\boxplus}        & \X{\boxminus}       & \X{\circleddash}     \\
 \X{\boxtimes}       & \X{\boxdot}         & \X{\circledcirc}     \\
 \X{\intercal}       & \X{\circledast}     & \X{\rightthreetimes} \\
 \X{\curlyvee}       & \X{\curlywedge}     & \X{\leftthreetimes}
\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Relações Binárias \AmS{}.}
\begin{symbols}{*3{cl}}
 \X{\lessdot}           & \X{\gtrdot}            & \X{\doteqdot}         \\
 \X{\leqslant}          & \X{\geqslant}          & \X{\risingdotseq}     \\
 \X{\eqslantless}       & \X{\eqslantgtr}        & \X{\fallingdotseq}    \\
 \X{\leqq}              & \X{\geqq}              & \X{\eqcirc}           \\
 \X{\lll}               & \X{\ggg}               & \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{\shortparallel}     & \X{\Supset}            & \X{\Vvdash}           \\
 \X{\blacktriangleleft} & \X{\sqsupset}          & \X{\backepsilon}      \\
 \X{\vartriangleright}  & \X{\because}           & \X{\varpropto}        \\
 \X{\blacktriangleright}& \X{\Subset}            & \X{\between}          \\
 \X{\trianglerighteq}   & \X{\smallfrown}        & \X{\pitchfork}        \\
 \X{\vartriangleleft}   & \X{\shortmid} 	 & \X{\smallsmile}    	 \\
 \X{\trianglelefteq}    & \X{\therefore} 	 & \X{\sqsubset}  
\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Setas \AmS{}.}
\begin{symbols}{*2{cl}}
  \X{\dashleftarrow}      & \X{\dashrightarrow}     \\
  \X{\leftleftarrows}     & \X{\rightrightarrows}   \\
  \X{\leftrightarrows}    & \X{\rightleftarrows}    \\
  \X{\Lleftarrow}         & \X{\Rrightarrow}        \\
  \X{\twoheadleftarrow}   & \X{\twoheadrightarrow}  \\
  \X{\leftarrowtail}      & \X{\rightarrowtail}     \\
  \X{\leftrightharpoons}  & \X{\rightleftharpoons}  \\
  \X{\Lsh}                & \X{\Rsh}                \\
  \X{\looparrowleft}      & \X{\looparrowright}     \\
  \X{\curvearrowleft}     & \X{\curvearrowright}    \\
  \X{\circlearrowleft}    & \X{\circlearrowright}   \\
  \X{\multimap}  &  \X{\upuparrows}  \\
  \X{\downdownarrows} & \X{\upharpoonleft} \\
  \X{\upharpoonright} & \X{\downharpoonright} \\
  \X{\rightsquigarrow} & \X{\leftrightsquigarrow} \\
\end{symbols}
\end{table}

\begin{table}[!tbp]
\caption{Relações Binárias e Setas Negadas \AmS{}.}\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{} Sortidos.}\label{AMSmisc}
\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{\diagup}           & \X{\diagdown}         & \X{\backprime}       \\
 \X{\nexists}          & \X{\Finv}             & \X{\varnothing}      \\
 \X{\eth}              & \X{\sphericalangle}   & \X{\mho}        
\end{symbols}
\end{table}



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