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-%-*-tex-*-
-\ifundefined{writestatus} \input status \relax \fi %
-\chcode{matsym}
-
-
-\def\cqu{\cquote{{\leftskip=0ptplus1fill\def\\%
-{\endgraf}Yet what are all such gaieties to me\\Whose thoughts are full of
-indices and surds?\\$x^2+7x+53$\\ $\displaystyle={11\over3}$.\\ }}{
-Four~Riddles, Lewis~Carroll (1832-1898)}}
-
-
-\chapterhead{matsym}{MATHEMATICS:\cr SYMBOLS\cr FONTS}
-\tex\ supplies a vast array of mathematical symbols, both in fixed and
-extensible forms. For the most part, the symbols mentioned are available only
-in mathematics mode. Other symbols that are useful in
-regular text mode have been listed in Section \ref{specialtextsymbols}
-This chapter describes the symbols available. These
-symbols can be used in any font size that is on the system. Although it is
-possible to build your own symbols from simpler ones, it takes a little care
-to make sure that they are the correct size for all possible uses.
-
-\shead{mathfonts}{Ordinary Fonts in Mathematics}
-The mathematics symbol font contains characters that are very similar to
-to text italic font. The major difference is the spacing. {\it For instance} is
-in ordinary italic but $For\ instance$, is in math italic and was invoked with
-|$For\|\]|instance$|, where |\|\] forces the space.
-However, it is an easy matter to put
-roman or {\bf bold} letters in mathematics by just using
-|$x={\bf the\ spot}$| to obtain $x={\bf the\ spot}$. The real fun
-comes with something like the following:
-
-\def\xbf{{\vec{\bf x}}}
-$$ \xbf = 2^{\xbf^\xbf} $$
-which is given by
-\begintt
-\def\xbf{{\vec{\bf x}}}
-$$
-\xbf = 2^{\xbf^\xbf}
-$$
-\endtt
-Note that the bold face is scaled correctly up into the superscripts. The
-extra $\{\ldots\}$ are necessary so that the third |\xbf| will look like a
-single token to the second |\@|.
-
-\shead{mathtypes}{Mathematical Symbol Types}
-Some symbols, even though they may look the same are given different command
-sequences in \tex. The reason for this is that their use demands different
-spacing and line breaking when in mathematics mode.
-For this reason there are four mathematics symbols for a vertical
-bar $\mid$, namely |\mid|, |\left\vert|, |\right\vert|, and |\vert|. The
-first is a {\it relation} -- called {\it Rel} -- like the $=$; the second
-and third are opening and
-closing brackets like ( and ) --- \tex\ calls these {\it openings} and {\it
-closings}; and the last is an {\it ordinary} --- called {\it Ord} --- symbol
-like $\infty$. Two other types are {\it large operators} --- called {\it Op}
---- like $\sum$ and {\it binary operators} --- called {\it Bin} --- like $+$.
-Finally there is the {\it punctuation} --- called {\it Punct} --- like the
-period.
-
-\shead{greekletters}{Greek Letters}
-All the Greek letters are of type {\it Ord}. They are all assumed to be in
-mathematics mode.
-
-\bshortcomlist
-\@|\alpha {\rm A} A|&$\alpha$ A $A$ \cr
-\@|\beta {\rm B} B|&$\beta$ B $B$\cr
-\@|\gamma \Gamma {\mit\Gamma}|&$\gamma$ $\Gamma$ ${\mit\Gamma}$ \cr
-\@|\delta \Delta {\mit\Delta} |&$\delta$ $\Delta$ ${\mit\Delta}$ \cr
-\@|\epsilon {\rm E} E|&$\epsilon$ E $E$ \cr
-\@|\varepsilon|&$\varepsilon$\cr
-\@|\zeta {\rm Z} Z|&$\zeta$ Z $Z$ \cr
-\@|\eta {\rm H} H|&$\eta$ H $H$ \cr
-\@|\theta \Theta {\mit\Theta} |&$\theta$ $\Theta$ $\mit\Theta$ \cr
-\@|\vartheta|&$\vartheta$ \cr
-\@|\iota {\rm I} I|&$\iota$ I $I$ \cr
-\@|\kappa {\rm K} K |&$\kappa$ K $K$ \cr
-\@|\lambda \Lambda {\mit\Lambda} |&$\lambda$ $\Lambda$ $\mit\Lambda$ \cr
-\@|\mu {\rm M} M |&$\mu$ M $M$ \cr
-\@|\nu {\rm N} N|&$\nu$ N $N$ \cr
-\@|\xi \Xi {\mit\Xi} |&$\xi$ $\Xi$ $\mit\Xi$ \cr
- |o {\rm O} O|&$o$ O $O$ \cr
-\@|\pi \Pi {\mit\Pi}|&$\pi$ $\Pi$ $\mit\Pi$ \cr
-\@|\varpi|&$\varpi$\cr
-\@|\rho {\rm R} R|&$\rho$ R $R$\cr
-\@|\sigma \Sigma {\mit\Sigma}|&$\sigma$ $\Sigma$ $\mit\Sigma$ \cr
-\@|\tau {\rm T} T|&$\tau$ T $T$ \cr
-\@|\upsilon \Upsilon {\mit\Upsilon}|&$\upsilon$ $\Upsilon$ $\mit\Upsilon$ \cr
-\@|\phi \Phi {\mit\Phi}|&$\phi$ $\Phi$ $\mit\Phi$ \cr
-\@|\varphi|&$\varphi$ \cr
-\@|\chi {\rm X} X|&$\chi$ X $X$ \cr
-\@|\psi \Psi {\mit\Psi}|&$\psi$ $\Psi$ $\mit\Psi$\cr
-\@|\omega \Omega {\mit\Omega}|&$\omega$ $\Omega$ $\mit\Omega$\cr
-\eshortcomlist
-
-\shead{caligraphic}{Calligraphic Capitals}
-These look like ${\cal A} \ldots{\cal Z}$ and are obtained in math mode by
-the construction |{\cal <capital letter>}| while in math
-mode.
-
-\shead{opsrels}{Ords, Operators, and Relations}
-The following is a composite list of the symbols of
-type ordinary, relation and operator supplied by
-{\it plain}. The type is specified along with the symbol. The meaning of the
-type abbreviations has been given in Section \ref{mathtypes}.
-\medbreak
-\beginmulticolumnformat
-\hfuzz=20pt
-\parindent=0pt
-\def\bin{\leavevmode\hbox to 30pt{\it Bin\hss}}
-\def\ord{\leavevmode\hbox to 30pt{\it Ord\hss}}
-\def\rel{\leavevmode\hbox to 30pt{\it Rel\hss}}
-\def\op{\leavevmode\hbox to 30pt{\it Op\hss}}
-\intercolumnsep = {\hskip 3em}
-\numberofcolumns = 2
-\obeylines
-\bin\hbox to 20pt{$+$\quad\hss}\@|+|
-\bin\hbox to 20pt{$-$\quad\hss}\@|-|
-\rel\hbox to 20pt{$=$\quad\hss}\@|=|
-\rel\hbox to 20pt{$\not=$\quad\hss}\@|\not=| |\ne| |\neq|
-\rel\hbox to 20pt{$<$\quad\hss}\@|<|
-\rel\hbox to 20pt{$\not<$\quad\hss}\@|\not<|
-\rel\hbox to 20pt{$>$\quad\hss}\@|>|
-\rel\hbox to 20pt{$\not>$\quad\hss}\@|\not>|
-\ord\hbox to 20pt{$\aleph$\quad\hss}\@|\aleph|
-\ord\hbox to 20pt{$\amalg$\quad\hss}\@|\amalg|
-\ord\hbox to 20pt{$\angle$\quad\hss}\@|\angle|
-\rel\hbox to 20pt{$\approx$\quad\hss}\@|\approx|
-\rel\hbox to 20pt{$\not\approx$\quad\hss}\@|\not\approx|
-\bin\hbox to 20pt{$\ast$\quad\hss}\@|\ast| or *
-\rel\hbox to 20pt{$\asymp$\quad\hss}\@|\asymp|
-\ord\hbox to 20pt{$\backslash$\quad\hss}\@|\backslash|
-\op\hbox to 20pt{$\bigcap$\quad\hss}\@|\bigcap|
-\bin\hbox to 20pt{$\bigcirc$\quad\hss}\@|\bigcirc|
-\op\hbox to 20pt{$\bigcup$\quad\hss}\@|\bigcup|
-\op\hbox to 20pt{$\bigodot$\quad\hss}\@|\bigodot|
-\op\hbox to 20pt{$\bigoplus$\quad\hss}\@|\bigoplus|
-\op\hbox to 20pt{$\bigotimes$\quad\hss}\@|\bigotimes|
-\op\hbox to 20pt{$\bigsqcup$\quad\hss}\@|\bigsqcup|
-\bin\hbox to 20pt{$\bigtriangledown$\quad\hss}\@|\bigtriangledown|
-\bin\hbox to 20pt{$\bigtriangleup$\quad\hss}\@|\bigtriangleup|
-\op\hbox to 20pt{$\biguplus$\quad\hss}\@|\biguplus|
-\op\hbox to 20pt{$\bigvee$\quad\hss}\@|\bigvee|
-\op\hbox to 20pt{$\bigwedge$\quad\hss}\@|\bigwedge|
-\ord\hbox to 20pt{$\bot$\quad\hss}\@|\bot|
-\rel\hbox to 20pt{$\bowtie$\quad\hss}\@|\bowtie|
-\bin\hbox to 20pt{$\bullet$\quad\hss}\@|\bullet|
-\bin\hbox to 20pt{$\cap$\quad\hss}\@|\cap|
-\bin\hbox to 20pt{$\cdot$\quad\hss}\@|\cdot|
-\bin\hbox to 20pt{$\circ$\quad\hss}\@|\circ|
-\ord\hbox to 20pt{$\clubsuit$\quad\hss}\@|\clubsuit|
-\rel\hbox to 20pt{$\cong$\quad\hss}\@|\cong|
-\rel\hbox to 20pt{$\not\cong$\quad\hss}\@|\not\cong|
-\op\hbox to 20pt{$\coprod$\quad\hss}\@|\coprod|
-\bin\hbox to 20pt{$\cup$\quad\hss}\@|\cup|
-\bin\hbox to 20pt{$\dagger$\quad\hss}\@|\dagger|
-\rel\hbox to 20pt{$\dashv$\quad\hss}\@|\dashv|
-\bin\hbox to 20pt{$\ddagger$\quad\hss}\@|\ddagger|
-\ord\hbox to 20pt{$\diamondsuit$\quad\hss}\@|\diamondsuit|
-\balancecolumnsize = 470pt
-\bin\hbox to 20pt{$\diamond$\quad\hss}\@|\diamond|
-\bin\hbox to 20pt{$\div$\quad\hss}\@|\div|
-\rel\hbox to 20pt{$\doteq$\quad\hss}\@|\doteq|
-\rel\hbox to 20pt{$\Downarrow$\quad\hss}\@|\Downarrow|
-\rel\hbox to 20pt{$\downarrow$\quad\hss}\@|\downarrow|
-\ord\hbox to 20pt{$\ell$\quad\hss}\@|\ell|
-\ord\hbox to 20pt{$\emptyset$\quad\hss}\@|\emptyset|
-\rel\hbox to 20pt{$\equiv$\quad\hss}\@|\equiv|
-\rel\hbox to 20pt{$\not\equiv$\quad\hss}\@|\not\equiv|
-\ord\hbox to 20pt{$\exists$\quad\hss}\@|\exists|
-\ord\hbox to 20pt{$\flat$\quad\hss}\@|\flat|
-\ord\hbox to 20pt{$\forall$\quad\hss}\@|\forall|
-\ord\hbox to 20pt{$\frown$\quad\hss}\@|\frown|
-\rel\hbox to 20pt{$\geq$\quad\hss}\@|\ge| \@|\geq|
-\rel\hbox to 20pt{$\not\geq$\quad\hss}\@|\not\geq|
-\rel\hbox to 20pt{$\gg$\quad\hss}\@|\gg|
-\rel\hbox to 20pt{$\not\gg$\quad\hss}\@|\not\gg|
-\ord\hbox to 20pt{$\hbar$\quad\hss}\@|\hbar|
-\ord\hbox to 20pt{$\heartsuit$\quad\hss}\@|\heartsuit|
-\rel\hbox to 20pt{$\hookleftarrow$\quad\hss}\@|\hookleftarrow|
-\rel\hbox to 20pt{$\hookrightarrow$\quad\hss}\@|\hookrightarrow|
-\ord\hbox to 20pt{$\Im$\quad\hss}\@|\Im|
-\ord\hbox to 20pt{$\imath$\quad\hss}\@|\imath|
-\ord\hbox to 20pt{$\infty$\quad\hss}\@|\infty|
-\op\hbox to 20pt{$\int$\quad\hss}\@|\int|
-\rel\hbox to 20pt{$\in$\quad\hss}\@|\in|
-\rel\hbox to 20pt{$\not\in$\quad\hss}\@|\not\in|
-\ord\hbox to 20pt{$\jmath$\quad\hss}\@|\jmath|
-\rel\hbox to 20pt{$\Leftarrow$\quad\hss}\@|\Leftarrow|
-\rel\hbox to 20pt{$\leftarrow$\quad\hss}\@|\leftarrow|
-\rel\hbox to 20pt{$\leftharpoondown$\quad\hss}\@|\leftharpoondown|
-\rel\hbox to 20pt{$\leftharpoonup$\quad\hss}\@|\leftharpoonup|
-\rel\hbox to 20pt{$\Leftrightarrow$\quad\hss}\@|\Leftrightarrow|
-\rel\hbox to 20pt{$\leftrightarrow$\quad\hss}\@|\leftrightarrow|
-\rel\hbox to 20pt{$\leq$\quad\hss}\@|\le| \@|\leq|
-\rel\hbox to 20pt{$\not\leq$\quad\hss}\@|\not\leq|
-\rel\hbox to 20pt{$\ll$\quad\hss}\@|\ll|
-\rel\hbox to 20pt{$\not\ll$\quad\hss}\@|\not\ll|
-\rel\hbox to 20pt{$\Longleftarrow$\quad\hss}\@|\Longleftarrow|
-\rel\hbox to 20pt{$\longleftarrow$\quad\hss}\@|\longleftarrow|
-\rel\hbox to 20pt{$\Longleftrightarrow$\quad\hss}\@|\Longleftrightarrow|
-\rel\hbox to 20pt{$\longleftrightarrow$\quad\hss}\@|\longleftrightarrow|
-\rel\hbox to 20pt{$\longmapsto$\quad\hss}\@|\longmapsto|
-\rel\hbox to 20pt{$\Longrightarrow$\quad\hss}\@|\Longrightarrow|
-\rel\hbox to 20pt{$\longrightarrow$\quad\hss}\@|\longrightarrow|
-\rel\hbox to 20pt{$\mapsto$\quad\hss}\@|\mapsto|
-\rel\hbox to 20pt{$\mid$\quad\hss}\@|\mid|
-\rel\hbox to 20pt{$\models$\quad\hss}\@|\models|
-\bin\hbox to 20pt{$\mp$\quad\hss}\@|\mp|
-\ord\hbox to 20pt{$\nabla$\quad\hss}\@|\nabla|
-\ord\hbox to 20pt{$\natural$\quad\hss}\@|\natural|
-\rel\hbox to 20pt{$\nearrow$\quad\hss}\@|\nearrow|
-\rel\hbox to 20pt{$\nwarrow$\quad\hss}\@|\nwarrow|
-\ord\hbox to 20pt{$\neg$\quad\hss}\@|\neg| \@|\lnot|
-\rel\hbox to 20pt{$\ni$\quad\hss}\@|\ni| \@|\owns|
-\bin\hbox to 20pt{$\odot$\quad\hss}\@|\odot|
-\op\hbox to 20pt{$\oint$\quad\hss}\@|\oint|
-\bin\hbox to 20pt{$\ominus$\quad\hss}\@|\ominus|
-\bin\hbox to 20pt{$\oplus$\quad\hss}\@|\oplus|
-\bin\hbox to 20pt{$\oslash$\quad\hss}\@|\oslash|
-\bin\hbox to 20pt{$\otimes$\quad\hss}\@|\otimes|
-\rel\hbox to 20pt{$\parallel$\quad\hss}\@|\parallel|
-\ord\hbox to 20pt{$\partial$\quad\hss}\@|\partial|
-\bin\hbox to 20pt{$\perp$\quad\hss}\@|\perp|
-\bin\hbox to 20pt{$\pm$\quad\hss}\@|\pm|
-\rel\hbox to 20pt{$\preceq$\quad\hss}\@|\preceq|
-\rel\hbox to 20pt{$\not\preceq$\quad\hss}\@|\not\preceq|
-\rel\hbox to 20pt{$\prec$\quad\hss}\@|\prec|
-\rel\hbox to 20pt{$\not\prec$\quad\hss}\@|\not\prec|
-\ord\hbox to 20pt{$\prime$\quad\hss}\@|\prime|
-\op\hbox to 20pt{$\prod$\quad\hss}\@|\prod|
-\rel\hbox to 20pt{$\propto$\quad\hss}\@|\propto|
-\ord\hbox to 20pt{$\Re$\quad\hss}\@|\Re|
-\rel\hbox to 20pt{$\Rightarrow$\quad\hss}\@|\Rightarrow|
-\rel\hbox to 20pt{$\rightarrow$\quad\hss}\@|\rightarrow|
-\rel\hbox to 20pt{$\rightharpoondown$\quad\hss}\@|\rightharpoondown|
-\rel\hbox to 20pt{$\rightharpoonup$\quad\hss}\@|\rightharpoonup|
-\rel\hbox to 20pt{$\rightleftharpoons$\quad\hss}\@|\rightleftharpoons|
-\bin\hbox to 20pt{$\setminus$\quad\hss}\@|\setminus|
-\ord\hbox to 20pt{$\sharp$\quad\hss}\@|\sharp|
-\rel\hbox to 20pt{$\simeq$\quad\hss}\@|\simeq|
-\rel\hbox to 20pt{$\not\simeq$\quad\hss}\@|\not\simeq|
-\rel\hbox to 20pt{$\sim$\quad\hss}\@|\sim|
-\rel\hbox to 20pt{$\not\sim$\quad\hss}\@|\not\sim|
-\rel\hbox to 20pt{$\smile$\quad\hss}\@|\smile|
-\ord\hbox to 20pt{$\spadesuit$\quad\hss}\@|\spadesuit|
-\bin\hbox to 20pt{$\sqcap$\quad\hss}\@|\sqcap|
-\bin\hbox to 20pt{$\sqcup$\quad\hss}\@|\sqcup|
-\rel\hbox to 20pt{$\sqsubseteq$\quad\hss}\@|\sqsubseteq|
-\rel\hbox to 20pt{$\not\sqsubseteq$\quad\hss}\@|\not\sqsubseteq|
-\rel\hbox to 20pt{$\sqsupseteq$\quad\hss}\@|\sqsupseteq|
-\rel\hbox to 20pt{$\not\sqsupseteq$\quad\hss}\@|\not\sqsupseteq|
-\ord\hbox to 20pt{$\star$\quad\hss}\@|\star|
-\rel\hbox to 20pt{$\subseteq$\quad\hss}\@|\subseteq|
-\rel\hbox to 20pt{$\not\subseteq$\quad\hss}\@|\not\subseteq|
-\rel\hbox to 20pt{$\subset$\quad\hss}\@|\subset|
-\rel\hbox to 20pt{$\not\subset$\quad\hss}\@|\not\subset|
-\rel\hbox to 20pt{$\succeq$\quad\hss}\@|\succeq|
-\rel\hbox to 20pt{$\not\succeq$\quad\hss}\@|\not\succeq|
-\rel\hbox to 20pt{$\succ$\quad\hss}\@|\succ|
-\rel\hbox to 20pt{$\not\succ$\quad\hss}\@|\not\succ|
-\op\hbox to 20pt{$\sum$\quad\hss}\@|\sum|
-\rel\hbox to 20pt{$\supseteq$\quad\hss}\@|\supseteq|
-\rel\hbox to 20pt{$\not\supseteq$\quad\hss}\@|\not\supseteq|
-\rel\hbox to 20pt{$\supset$\quad\hss}\@|\supset|
-\rel\hbox to 20pt{$\not\supset$\quad\hss}\@|\not\supset|
-\ord\hbox to 20pt{$\surd$\quad\hss}\@|\surd|
-\rel\hbox to 20pt{$\searrow$\quad\hss}\@|\searrow|
-\rel\hbox to 20pt{$\swarrow$\quad\hss}\@|\swarrow|
-\bin\hbox to 20pt{$\times$\quad\hss}\@|\times|
-\bin\hbox to 20pt{$\top$\quad\hss}\@|\top|
-\bin\hbox to 20pt{$\triangleleft$\quad\hss}\@|\triangleleft|
-\bin\hbox to 20pt{$\triangleright$\quad\hss}\@|\triangleright|
-\ord\hbox to 20pt{$\triangle$\quad\hss}\@|\triangle|
-\bin\hbox to 20pt{$\uplus$\quad\hss}\@|\uplus|
-\rel\hbox to 20pt{$\Uparrow$\quad\hss}\@|\Uparrow|
-\rel\hbox to 20pt{$\uparrow$\quad\hss}\@|\uparrow|
-\rel\hbox to 20pt{$\Updownarrow$\quad\hss}\@|\Updownarrow|
-\rel\hbox to 20pt{$\updownarrow$\quad\hss}\@|\updownarrow|
-\ord\hbox to 20pt{$\Vert$\quad\hss}\@|\Vert| or |\|\vrt
-\ord\hbox to 20pt{$\vert$\quad\hss}\@|\vert| or \vrt
-\rel\hbox to 20pt{$\vdash$\quad\hss}\@|\vdash|
-\bin\hbox to 20pt{$\vee$\quad\hss}\@|\lor| \@|\vee|
-\bin\hbox to 20pt{$\wedge$\quad\hss}\@|\land| \@|\wedge|
-\ord\hbox to 20pt{$\wp$\quad\hss}\@|\wp|
-\bin\hbox to 20pt{$\wr$\quad\hss}\@|\wr|
-\endmulticolumnformat
-
-\shead{delims}{Brackets or Delimiters}
-\tex\ supplies a large variety of delimiters or brackets, some of different
-sizes and others that grow to be the correct size. Here is a list of the
-delimiters supplied by {\it plain}.
-
-\bshortcomlist
-\@|\big\Arrowvert|&center part of double up arrow -- $\big\Arrowvert$\cr
-\@|\big\arrowvert|&center part of up arrow -- $\big\arrowvert$\cr
-\@|\langle|&left angle bracket -- $\langle$\cr
-\@|\rangle|&right angle bracket -- $\rangle$\cr
-\@|\big\bracevert|&center part of large braces -- $\big\bracevert$ \cr
-|\{| or \@|\lbrace|&left brace -- $\{$\cr
-|\}| or \@|\rbrace|&right brace -- $\}$\cr
-|[| or \@|\lbrack|&left square bracket -- $[$\cr
-|]| or \@|\rbrack|&right square bracket -- $]$\cr
-\@|\lceil|&left ceiling -- $\lceil$\cr
-\@|\rceil|&right ceiling -- $\rceil$\cr
-\@|\lfloor|&left floor -- $\lfloor$\cr
-\@|\rfloor|&right floor -- $\rfloor$\cr
-\@|\big\lgroup|&large left paren without middle -- $\big\lgroup$\cr
-\@|\big\rgroup|&large right paren without middle -- $\big\rgroup$\cr
-\@|\big\lmoustache|& -- $\big\lmoustache$\cr
-\@|\big\rmoustache|& -- $\big\rmoustache$\cr
-|/|&slash -- $/$\cr
-\@|\backslash|&reverse slash -- $\backslash$\cr
-\vrt\ or |\vert|&vertical bar -- $\vert$\cr
-|\|\vrt\ or |\Vert|&double vertical bar -- $\Vert$\cr
-|\downarrow|&down arrow -- $\downarrow$\cr
-|\Downarrow|&double down arrow -- $\Downarrow$\cr
-|\uparrow|&up arrow -- $\uparrow$\cr
-|\Uparrow|&double up arrow -- $\Uparrow$\cr
-|\updownarrow|&up-and-down arrow -- $\updownarrow$\cr
-|\Updownarrow|&double up-and-down arrow -- $\Updownarrow$\cr
-|(|&left paren -- $($\cr
-|)|&right paren -- $)$\cr
-\eshortcomlist
-
-Two very powerful operators exist for the delimiters, namely |\left| and
-|\right|. They must be used in pairs as
-\par
-\hbox to \hsize{\hss\@|$\left<delimiter> ...\right<delimiter>$|,\hss}
-\noindent
-where the |<delimiter>| is one of the above. The result
-of these operators is a pair of braces that grow the correct size for the
-particular formula in which they are used. This saves you from the problem of
-measuring. A |\right.| implies there is nothing at the place of the right
-delimiter and |\left.| similarly on the left. This allows a delimiter on only
-one side of a formula but to still have the operators match in pairs.
-
-Finally there is a second set of four pairs of operators, \@|\bigl|, |\Bigl|,
-\@|\biggl|, \@|\Biggl| and the corresponding right hand ones \@|\bigr|, \@|\Bigr|,
-\@|\biggr|, and \@|\Biggr|. These produce big, but fixed size delimiters for instance we have
-\begintt
-$$
- \bigl\{\quad
-\Bigl[\quad
-\biggl\lfloor\quad
-\Biggl\Updownarrow\quad\Biggr\Updownarrow
-\quad\biggr\rfloor
-\quad\Bigr]
-\quad\bigr\}
-$$
-\endtt
-produces
-$$
- \bigl\{\quad
-\Bigl[\quad
-\biggl\lfloor\quad
-\Biggl\Updownarrow\quad\Biggr\Updownarrow
-\quad\biggr\rfloor
-\quad\Bigr]
-\quad\bigr\}
-$$
-
-\shead{sincos}{Common Mathematical Functions}
-Certain functions such as |sin|, |cos|, and |limsup| for example are shown in
-mathematics text in Roman font. In addition some like |lim| sometimes take
-limits that should be placed in the same way as the limits on the large
-operators ({\it Op}). For example
-\begintt
-$$
-\limsup_{t \leftrightarrow \infty}
-$$
-\endtt
-gives
-$$
-\limsup_{t \leftrightarrow \infty}
-$$
-There are 32 of these already defined in {\it plain}. They are
-\beginthreecolumn
-\@|\arg|
-\@|\arccos|
-\@|\arcsin|
-\@|\arctan|
-\@|\cot|
-\@|\coth|
-\@|\cosh|
-\@|\cos|
-\@|\csc|
-\@|\det|
-\@|\deg|
-\@|\dim|
-\@|\exp|
-\@|\gcd|
-\@|\hom|
-\@|\inf|
-\@|\ker|
-\@|\lg|
-\@|\liminf|
-\@|\limsup|
-\@|\lim|
-\@|\ln|
-\@|\log|
-\@|\max|
-\@|\min|
-\@|\Pr|
-\@|\sec|
-\@|\sin|
-\@|\sinh|
-\@|\sup|
-\@|\tanh|
-\@|\tan|
-\endthreecolumn
-
-\shead{buildown}{Build Your Own Symbols}
-There are several advanced facilities in \tex\ for building your own symbols.
-However, there is one rather simple form using
-\@|\buildrel <superscript> \over <relation>|. For example
-|\buildrel \triangle \over =| gives $\buildrel \triangle \over =$.
-
-\ejectpage
-\done