%\input paperhead
{
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%   SpecChars.tex  -- Print the special characters available in math
%                     mode.
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%   This version swiped from TeX82, version 0.97, with PLAIN.TEX loaded.
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%  Major munging applied 1/84 to jive with Appendix F of the TeXbook
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\def\ctr#1{\hss#1\hss}
\def\\{\char `\\}
\def\v{\vrule height 20pt depth 10pt width 0pt}
\tabskip 1em
\parskip 6pt plus 2pt
\abovedisplayskip 0pt
\belowdisplayskip 0pt
\def\dcolumn#1{$\vcenter
               {
                \halign{\v$\ctr{##}$&$\displaystyle\ctr{##}$&{\tt ##}\cr#1}
               }$
             }
\def\column#1{$\vcenter
               {
                \halign{$\ctr{##}$&{\tt ##}\cr#1}
               }$
             }
\def\sect#1{\penalty-1000
            \vskip 12pt plus 6pt
            {\sl #1}
            \vskip 4pt
            \penalty9999\ignorespaces}
\Appendix{A}{Special characters available in \TeX's ``math mode''}

There are many special-purpose characters available from \TeX, but most of
them don't appear on most keyboards.  Therefore, the following control
sequences have been pre-defined in plain.tex for your convenience.
Note, however, that most of these special sequences are {\sl only\/}
available in math mode.  Consult Appendix~F of {\sl The \TeX book\/}
for complete details.

\sect{(a) Lower-case Greek letters:}
\hbox to \hsize{
    \hfill
    \column{
        \alpha&\\alpha\cr
        \beta&\\beta\cr
        \gamma&\\gamma\cr
        \delta&\\delta\cr
        \epsilon&\\epsilon\cr
        \zeta&\\zeta\cr
        \eta&\\eta\cr
        \theta&\\theta\cr
        \iota&\\iota\cr
    }
    \column{
        \kappa&\\kappa\cr
        \lambda&\\lambda\cr
        \mu&\\mu\cr
        \nu&\\nu\cr
        \xi&\\xi\cr
        \pi&\\pi\cr
        \rho&\\rho\cr
        \sigma&\\sigma\cr
        \tau&\\tau\cr
    }
    \column{
        \upsilon&\\upsilon\cr
        \phi&\\phi\cr
        \chi&\\chi\cr
        \psi&\\psi\cr
        \omega&\\omega\cr
        \varepsilon&\\varepsilon\cr
        \varpi&\\varpi\cr
        \vartheta&\\vartheta\cr
        \varphi&\\varphi\cr
    }
    \hfill
}

\filbreak
\sect{(b) Upper-case Greek letters:}
\hbox to \hsize{
    \hfill
    \column{
        \Gamma&\\Gamma\cr
        \Delta&\\Delta\cr
        \Theta&\\Theta\cr
        \Lambda&\\Lambda\cr
        \Xi&\\Xi\cr
        \Pi&\\Pi\cr
    }
    \column{
        \Sigma&\\Sigma\cr
        \Upsilon&\\Upsilon\cr
        \Phi&\\Phi\cr
        \Psi&\\Psi\cr
        \Omega&\\Omega\cr
    }
%    \column{
%        \Gammait&\\Gammait\cr
%        \Deltait&\\Deltait\cr
%        \Thetait&\\Thetait\cr
%        \Lambdait&\\Lambdait\cr
%        \Xiit&\\Xiit\cr
%        \Piit&\\Piit\cr
%    }
%    \column{
%        \Sigmait&\\Sigmait\cr
%        \Upsilonit&\\Upsilonit\cr
%        \Phiit&\\Phiit\cr
%        \Psiit&\\Psiit\cr
%        \Omegait&\\Omegait\cr
%    }
    \hfill
}

\filbreak
\sect{(c) Script letters (Characters from the {\tt \\cal} font):}
{\def\{{\char`\{}\def\}{\char`\}}
\hbox to \hsize{
    \hfill
    \column{
        {\cal A}&\{\\cal A\}\cr
        {\cal B}&\{\\cal B\}\cr
        {\cal C}&\{\\cal C\}\cr
        {\cal D}&\{\\cal D\}\cr
        {\cal E}&\{\\cal E\}\cr
        {\cal F}&\{\\cal F\}\cr
        {\cal G}&\{\\cal G\}\cr
        {\cal H}&\{\\cal H\}\cr
        {\cal I}&\{\\cal I\}\cr
    }
    \column{
        {\cal J}&\{\\cal J\}\cr
        {\cal K}&\{\\cal K\}\cr
        {\cal L}&\{\\cal L\}\cr
        {\cal M}&\{\\cal M\}\cr
        {\cal N}&\{\\cal N\}\cr
        {\cal O}&\{\\cal O\}\cr
        {\cal P}&\{\\cal P\}\cr
        {\cal Q}&\{\\cal Q\}\cr
        {\cal R}&\{\\cal R\}\cr
    }
    \column{
        {\cal S}&\{\\cal S\}\cr
        {\cal T}&\{\\cal T\}\cr
        {\cal U}&\{\\cal U\}\cr
        {\cal V}&\{\\cal V\}\cr
        {\cal W}&\{\\cal W\}\cr
        {\cal X}&\{\\cal X\}\cr
        {\cal Y}&\{\\cal Y\}\cr
        {\cal Z}&\{\\cal Z\}\cr
    }
    \hfill
}}
There are also ``oldstyle numerals'' available via
{\tt \$\\oldstyle 0123456789\$}: $\oldstyle 0123456789$.
\filbreak
\sect{(d) Binary operators:}
\hbox to \hsize{
    \hfill
    \column{
        \mp&\\mp\cr
        \pm&\\pm\cr
        \setminus&\\setminus\cr
        \cdot&\\cdot\cr
        \times&\\times\cr
        \ast&\\ast\cr
	\star&\\star\cr
        \diamond&\\diamond\cr
        \circ&\\circ\cr
        \bullet&\\bullet\cr
        \div&\\div\cr
    }
    \column{
        \cap&\\cap\cr
        \cup&\\cup\cr
        \uplus&\\uplus\cr
        \sqcap&\\sqcap\cr
        \sqcup&\\sqcup\cr
        \triangleleft&\\triangleleft\cr
        \triangleright&\\triangleright\cr
        \wr&\\wr\cr
        \bigcirc&\\bigcirc\cr
        \bigtriangleup&\\bigtriangleup\cr
        \bigtriangledown&\\bigtriangdown\cr
    }
    \column{
        \lor&\\lor (or \\vee)\cr
        \land&\\land (or \\wedge)\cr
        \oplus&\\oplus\cr
        \ominus&\\ominus\cr
        \otimes&\\otimes\cr
        \oslash&\\oslash\cr
        \odot&\\odot\cr
        \dagger&\\dagger\cr
        \ddagger&\\ddagger\cr
        \amalg&\\amalg\cr
    }
    \hfill
}

\filbreak
\sect{(e) Binary relations:}
\hbox to \hsize{
    \hfill
    \column{
	\leq&\\leq\cr
	\prec&\\prec\cr
	\preceq&\\preceq\cr
	\ll&\\ll\cr
	\subset&\\subset\cr
	\subseteq&\\subseteq\cr
	\sqsubseteq&\\sqsubseteq\cr
	\in&\\in\cr
	\vdash&\\vdash\cr
	\smile&\\smile\cr
	\frown&\\frown\cr
    }
    \hfill
    \column{
	\geq&\\geq\cr
	\succ&\\succ\cr
	\succeq&\\succeq\cr
	\gg&\\gg\cr
	\supset&\\supset\cr
	\supseteq&\\subseteq\cr
	\sqsupseteq&\\sqsubseteq\cr
	\ni&\\ni\cr
	\dashv&\\dashv\cr
	\mid&\\mid\cr
	\parallel&\\parallel\cr
    }
    \hfill
    \column{
        \equiv&\\equiv\cr
        \sim&\\sim\cr
        \simeq&\\simeq\cr
        \asymp&\\asymp\cr
        \approx&\\approx\cr
        \cong&\\cong\cr
        \bowtie&\\bowtie\cr
        \propto&\\propto\cr
        \models&\\models\cr
        \doteq&\\doteq\cr
        \perp&\\perp\cr
    }
    \hfill
}
\noindent
You can also use the control sequence {\tt \\not} to negate or ``cross out''
most of the relations above.  For example, the symbol
``$\mathrel{\not\subseteq}$''
is really two symbols, obtained by typing ``{\tt \\not\\subseteq}''.
(The slashing character in the symbol font has a width of zero, so it will overlap
the following character.)  But watch out: you should actually type
``{\tt \\mathrel\char`\{\\not\\subseteq\char`\}}'', in order to prevent
\TeX\ from breaking a line after {\tt \\not}.
\filbreak
\sect{(f) Arrows : }
\vskip 6pt plus 2pt
\hbox to \hsize{
    \hfill
    \column{
        \uparrow&\\uparrow\cr
        \Uparrow&\\Uparrow\cr
        \downarrow&\\downarrow\cr
        \Downarrow&\\Downarrow\cr
        \updownarrow&\\updownarrow\cr
        \Updownarrow&\\Updownarrow\cr
        \nearrow&\\nearrow\cr
        \searrow&\\searrow\cr
        \swarrow&\\swarrow\cr
        \nwarrow&\\nwarrow\cr
    }
    \column{
        \longleftarrow&\\longleftarrow\cr
        \Longleftarrow&\\Longleftarrow\cr
        \longrightarrow&\\longrightarrow\cr
        \Longrightarrow&\\Longrightarrow\cr
        \longleftrightarrow&\\longleftrightarrow\cr
        \Longleftrightarrow&\\Longleftrightarrow\cr
        \longmapsto&\\longmapsto\cr
        \hookrightarrow&\\hookrightarrow\cr
        \rightharpoonup&\\rightharpoonup\cr
        \rightharpoondown&\\rightharpoondown\cr
    }
    \column{
        \leftarrow&\\leftarrow\cr
        \Leftarrow&\\Leftarrow\cr
        \rightarrow&\\rightarrow\cr
        \Rightarrow&\\Rightarrow\cr
        \leftrightarrow&\\leftrightarrow\cr
        \Leftrightarrow&\\Leftrightarrow\cr
        \mapsto&\\mapsto\cr
        \hookleftarrow&\\hookleftarrow\cr
        \leftharpoonup&\\leftharpoonup\cr
        \leftharpoondown&\\leftharpoondown\cr
        \rightleftharpoons&\\rightleftharpoons\cr
    }
    \hfill
}

\filbreak
\sect{(g) ``Large'' operators (text and display styles):}
\hbox to \hsize{
    \hfill
    \dcolumn{
        \bigwedge&\bigwedge&\\bigwedge\cr
        \bigvee&\bigvee&\\bigvee\cr
        \int&\int&\\int\cr
        \oint&\oint&\\oint\cr
    }
    \dcolumn{
        \sum&\sum&\\sum\cr
        \prod&\prod&\\prod\cr
        \coprod&\coprod&\\coprod\cr
        \bigoplus&\bigoplus&\\bigoplus\cr
        \bigotimes&\bigotimes&\\bigotimes\cr
        \bigodot&\bigodot&\\bigodot\cr
    }
    \dcolumn{
        \bigcap&\bigcap&\\bigcap\cr
        \bigcup&\bigcup&\\bigcup\cr
        \biguplus&\biguplus&\\biguplus\cr
        \bigsqcup&\bigsqcup&\\bigsqcup\cr
    }
    \hfill
}

\filbreak
\sect{(h) Brackets:}
$$\vbox{
    \halign{$\ctr{#}$&{\tt #}\quad&$\ctr{#}$&{\tt #}\cr
        \lfloor&\\lfloor&\rfloor&\\rfloor\cr
        \lceil&\\lceil&\rceil&\\rceil\cr
        \lbrack&\\lbrack&\rbrack&\\rbrack\cr
        \{&\\\char`\{\ (or \\lbrace)&\}&\\\char`\}\ (or \\rbrace)\cr
        \langle&\\langle&\rangle&\\rangle\cr
    }
}$$

\filbreak
\sect{(i) Miscellaneous math symbols:}
\hbox to \hsize{
    \hfill
    \column{
        \imath&\\imath\cr
        \jmath&\\jmath\cr
	\ell&\\ell\cr
        \Re&\\Re\cr
        \Im&\\Im\cr
        \aleph&\\aleph\cr
        \wp&\\wp\cr
        \infty&\\infty\cr
    }
    \column{
        \emptyset&\\emptyset\cr
        \exists&\\exists\cr
        \forall&\\forall\cr
	\triangle&\\triangle\cr
        \angle&\\angle\cr
        \lnot&\\lnot (or \\neg)\cr
        \nabla&\\nabla\cr
    }
    \column{
        \partial&\\partial\cr
        \prime&\\prime\cr
        \smallint&\\smallint\cr
        \top&\\top\cr
        \bot&\\bot\cr
        \surd&\\surd\cr
	\hbar&\\hbar\cr
    }
    \hfill
}

\filbreak
\sect{(j) Miscellaneous nonmath symbols (math mode required):}
\hbox to \hsize{
    \hfill
    \column{
        \spadesuit&\\spadesuit\cr
        \heartsuit&\\heartsuit\cr
        \diamondsuit&\\diamondsuit\cr
        \clubsuit&\\clubsuit\cr
    }
    \column{
	\sharp&\\sharp\cr
	\flat&\\flat\cr
	\natural&\\natural\cr
    }
    \hfill
}
\filbreak
\sect{(k) Miscellaneous nonmath symbols (math mode {\bf not} required):}
\hbox to \hsize{
    \hfill
    \column{
        \$&\\\char `\$\cr
        \%&\\\char `\%\cr
        \copyright&\\copyright\cr
    }
    \column{
        \#&\\\char `\#\cr
        \S&\\S\cr
        \P&\\P\cr
    }
    \column{
        \&&\\\char `\&\cr
        \ddag&\\ddag\cr
        \dag&\\dag\cr
    }
    \hfill
}
}
