#LyX 1.2 created this file. For more info see http://www.lyx.org/ \lyxformat 220 \textclass article \language english \inputencoding auto \fontscheme default \graphics default \float_placement H \paperfontsize default \spacing single \papersize Default \paperpackage widemarginsa4 \use_geometry 0 \use_amsmath 1 \use_natbib 0 \use_numerical_citations 0 \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \quotes_times 2 \papercolumns 1 \papersides 1 \paperpagestyle default \layout Section Converting to and from mathed \layout Standard Math can be typed in the body of the document and converted to mathed-mode by highlighting it and typing \family sans M-c\SpecialChar ~ m \family default . The text can be bounded with delimiters or not. That is, highlighting any of the formulae below: \layout Standard \align center \begin_inset Tabular \begin_inset Text \layout Standard \backslash begin{math} \backslash frac{abc}{xyz} \backslash end{math} \end_inset \begin_inset Text \layout Standard \backslash ( \backslash frac{abc}{xyz} \backslash ) \end_inset \begin_inset Text \layout Standard $ \backslash frac{abc}{xyz} $ \end_inset \begin_inset Text \layout Standard \backslash begin{displaymath} \backslash frac{abc}{xyz} \backslash end{displaymath} \end_inset \begin_inset Text \layout Standard \backslash [ \backslash frac{abc}{xyz} \backslash ] \end_inset \end_inset \layout Standard will convert it to: \layout Standard \begin_inset Formula \[ \frac{abc}{xyz}\] \end_inset \layout Standard At present, no formal way exists to convert the contents of a math inset back into plain text. It can be done using a \begin_inset Quotes eld \end_inset fudge \begin_inset Quotes erd \end_inset however. Highlight the contents of a math inset (not the math inset itself, just the contents), but do \emph on not \emph default copy it into LyX's buffer. It is now stored in the X system buffer and can be pasted back into the document using the middle mouse button. \layout Section Displaying LaTeX symbols \layout Standard Historically, LyX has provided visual support for a relatively small subset of the math symbols available in LaTeX. That changes with version 1.2; we now have visual support for most of the symbols defined in basic LaTeX and \emph on all \emph default the extra ones defined by the AMS. For completeness, the tables of symbols in Lamport's and in Goosen's books are presented below. \layout Standard In order to display these extra symbols, however, the extra fonts that LyX requires must be made available to it. That can be done by creating a directory containing symbolic links to the fonts that LyX requires using the following script \layout LyX-Code #!/bin/sh \layout LyX-Code \layout LyX-Code LYXDIR=`pwd` \layout LyX-Code LYX_XFONTS=$LYXDIR/xfonts \layout LyX-Code \layout LyX-Code if [ ! -d $LYX_XFONTS ]; then \layout LyX-Code mkdir $LYX_XFONTS || exit \layout LyX-Code fi \layout LyX-Code \layout LyX-Code rm -f $LYX_XFONTS/fonts.dir $LYX_XFONTS/fonts.scale \layout LyX-Code \layout LyX-Code for file in `sed -e 's/^ \backslash (.* \backslash .pf[ab] \backslash ) .*$/ \backslash 1/' < fonts-xlfd`; do \layout LyX-Code filepath=`kpsewhich $file` \layout LyX-Code if [ $? -eq 0 ]; then \layout LyX-Code if [ ! -e $LYX_XFONTS/$file ]; then \layout LyX-Code ln -s $filepath $LYX_XFONTS/$file \layout LyX-Code fi \layout LyX-Code echo `grep -e $file fonts-xlfd` >> $LYX_XFONTS/fonts.scale \layout LyX-Code echo "$file found." \layout LyX-Code fi \layout LyX-Code done \layout LyX-Code \layout LyX-Code awk "/ \backslash .pf/ { nlines++ } \backslash \layout LyX-Code END { print nlines }" < $LYX_XFONTS/fonts.scale > $LYX_XFONTS/fonts.dir \layout LyX-Code \layout LyX-Code cat $LYX_XFONTS/fonts.scale >> $LYX_XFONTS/fonts.dir \layout LyX-Code cp $LYX_XFONTS/fonts.dir $LYX_XFONTS/fonts.scale \layout Standard where the file \family typewriter fonts-xlfd \family default contains \layout LyX-Code cmmi10.pfb -bluesky-cmr-medium-i-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code cmsy10.pfb -bluesky-cmsy-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code cmex10.pfb -bluesky-cmex-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code eufr10.pfb -bluesky-eufrak--medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code eufb10.pfb -bluesky-eufrak-bold-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code eusr10.pfb -bluesky-eus-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code eusb10.pfb -bluesky-eus-bold-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code msam10.pfb -bluesky-msam-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code msbm10.pfb -bluesky-msbm-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code marvosym.pfb -marvo-marvosym-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code wasy10.pfb -hoekwater-wasy-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code wasyb10.pfb -hoekwater-wasy-bold-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code logo10.pfb -hoekwater-logo-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code logobf10.pfb -hoekwater-logo-bold-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code plcrm.pfa -adobe-lcrm-medium-i-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code plcry.pfa -adobe-lcry-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout LyX-Code plcrv.pfa -adobe-lcrv-medium-r-normal--0-0-0-0-p-0-adobe-fontspecific \layout Standard Thereafter, you must tell X where to find this directory and the fonts therein. Type \newline \family typewriter xset +fp LYX_XFONTS; xset fp rehash \newline \family default at the console, start LyX, load up this document and enjoy! \layout Section Math tables from Goossen et al.'s \begin_inset Quotes eld \end_inset The LaTeX companion \begin_inset Quotes erd \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Math mode accents \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\hat{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash hat{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\acute{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash acute{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\bar{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bar{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\dot{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash dot{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\breve{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash breve{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\check{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash check{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\grave{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash grave{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\vec{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vec{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\ddot{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ddot{a} \end_inset \begin_inset Text \layout Standard \family typewriter \begin_inset Formula $\tilde{a}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash tilde{a} \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Greek letters \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\alpha $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash alpha \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\beta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash beta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gamma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gamma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\delta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash delta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\epsilon $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash epsilon \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varepsilon $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varepsilon \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\zeta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash zeta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\eta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash eta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\theta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash theta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vartheta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vartheta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\iota $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash iota \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\kappa $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash kappa \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lambda $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lambda \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\mu $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash mu \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nu $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nu \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\xi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash xi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $o$ \end_inset \end_inset \begin_inset Text \layout Standard o \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\pi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash pi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varpi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varpi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rho $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rho \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varrho $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varrho \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sigma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sigma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varsigma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varsigma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\tau $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash tau \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\upsilon $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash upsilon \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\phi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash phi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varphi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varphi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\chi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash chi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\psi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash psi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\omega $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash omega \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Gamma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Gamma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Delta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Delta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Theta $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Theta \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Lambda $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Lambda \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Xi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Xi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Pi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Pi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Sigma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Sigma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Upsilon $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Upsilon \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Phi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Phi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Psi $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Psi \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Omega $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Omega \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Binary operation symbols \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\pm $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash pm \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\cap $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash cap \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\diamond $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash diamond \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\oplus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash oplus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\mp $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash mp \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\cup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash cup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bigtriangleup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bigtriangleup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ominus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ominus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\times $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash times \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\uplus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash uplus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bigtriangledown $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bigtriangledown \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\otimes $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash otimes \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\div $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash div \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqcap $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqcap \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\triangleleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash triangleleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\oslash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash oslash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ast $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ast \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqcup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqcup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\triangleright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash triangleright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\odot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash odot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\star $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash star \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vee $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vee \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lhd $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lhd \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bigcirc $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bigcirc \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\circ $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash circ \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\wedge $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash wedge \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rhd $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rhd \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\dagger $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash dagger \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bullet $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bullet \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\setminus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash setminus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\unlhd $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash unlhd \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ddagger $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ddagger \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\cdot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash cdot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\wr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash wr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\unrhd $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash unrhd \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\amalg $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash amalg \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Relation symbols \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\leq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leq \backslash le \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\geq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash geq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\equiv $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash equiv \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\models $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash models \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\prec $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash prec \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succ $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succ \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\perp $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash perp \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\preceq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash preceq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\simeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash simeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\mid $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash mid \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ll $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ll \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gg $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gg \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\asymp $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash asymp \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\parallel $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash parallel \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\subset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash subset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\supset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash supset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\approx $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash approx \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bowtie $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bowtie \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\subseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash subseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\supseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash supseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\cong $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash cong \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Join $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Join \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsubset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsubset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsupset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsupset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\neq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash neq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\smile $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash smile \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsubseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsubseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsupseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsupseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\doteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash doteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\frown $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash frown \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\in $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash in \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ni $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ni \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\propto $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash propto \end_inset \begin_inset Text \layout Standard \begin_inset Formula $=$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter = \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vdash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vdash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\dashv $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash dashv \end_inset \begin_inset Text \layout Standard \begin_inset Formula $<$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter < \end_inset \begin_inset Text \layout Standard \begin_inset Formula $>$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter > \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Arrow symbols \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\leftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\longleftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash longleftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\uparrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash uparrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Leftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Leftarrow \end_inset \begin_inset Text \layout 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\begin_inset Text \layout Standard \begin_inset Formula $\Leftrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Leftrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Longleftrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Longleftrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Updownarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Updownarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\mapsto $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash mapsto \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\longmapsto $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash longmapsto \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nearrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nearrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\hookleftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash hookleftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\hookrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash hookrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\searrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash searrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\leftharpoonup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leftharpoonup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightharpoonup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash 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$\ldots $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ldots \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\cdots $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash cdots \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vdots $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vdots \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ddots $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ddots \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\aleph $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash aleph \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\prime $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash prime \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\forall $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash forall \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\infty $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash infty \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\hbar $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash hbar \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\emptyset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash emptyset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\exists $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash exists \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nabla $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nabla \end_inset 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typewriter \backslash sharp \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\wp $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash wp \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\clubsuit $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash clubsuit \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\diamondsuit $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash diamondsuit \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\heartsuit $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash heartsuit \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\spadesuit $ \end_inset \end_inset 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htbp wide false collapsed false \layout Caption Variable-sized symbols \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\sum $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sum \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\prod $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash prod \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\coprod $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash coprod \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\int $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash int \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\oint $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash oint \end_inset \begin_inset Text \layout Standard \begin_inset 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\end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption Large delimiters \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\rmoustache $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rmoustache \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lmoustache $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lmoustache \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rgroup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rgroup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lgroup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lgroup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\arrowvert $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash arrowvert \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Arrowvert $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Arrowvert \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bracevert $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bracevert \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption LaTeX math constructs \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\widetilde{abc}$ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash widetilde{abc} \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\widehat{abc}$ \end_inset \end_inset \begin_inset 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Float table placement htbp wide false collapsed false \layout Caption AMS Greek and Hebrew \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\digamma $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash digamma \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varkappa $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varkappa \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\beth $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash beth \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\daleth $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash daleth \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gimel $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gimel \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS delimiters \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\ulcorner $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ulcorner \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\urcorner $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash urcorner \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\llcorner $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash llcorner \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lrcorner $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lrcorner \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS arrows 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Standard \begin_inset Formula $\twoheadleftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash twoheadleftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\leftarrowtail $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leftarrowtail \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\looparrowleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash looparrowleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\leftrightharpoons $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leftrightharpoons \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\curvearrowleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash curvearrowleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\circlearrowleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash circlearrowleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Lsh $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Lsh \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\upuparrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash upuparrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\upharpoonleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash upharpoonleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\downharpoonleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash downharpoonleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\multimap $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash multimap \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\leftrightsquigarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leftrightsquigarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightrightarrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightrightarrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightleftarrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightleftarrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightrightarrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightrightarrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightleftarrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightleftarrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\twoheadrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash twoheadrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightarrowtail $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightarrowtail \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\looparrowright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash looparrowright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightleftharpoons $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightleftharpoons \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\curvearrowright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash curvearrowright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\circlearrowright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash circlearrowright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Rsh $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Rsh \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\downdownarrows $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash downdownarrows \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\upharpoonright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash upharpoonright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\downharpoonright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash downharpoonright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\rightsquigarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash rightsquigarrow \end_inset \begin_inset Text \layout Standard \end_inset \begin_inset Text \layout Standard \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS negated arrows \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\nleftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nleftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nLeftarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nLeftarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nRightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nRightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nleftrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nleftrightarrow \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nLeftrightarrow $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nLeftrightarrow \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS binary relations \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\leqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\leqslant $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash leqslant \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\eqslantless $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash eqslantless \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lesssim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lesssim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lessapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lessapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\approxeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash approxeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lessdot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lessdot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lll $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lll \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lessgtr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lessgtr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lesseqgtr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lesseqgtr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lesseqqgtr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lesseqqgtr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\doteqdot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash doteqdot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\risingdotseq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash risingdotseq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\fallingdotseq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash fallingdotseq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\backsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash backsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\backsimeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash backsimeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\subseteqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash subseteqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Subset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Subset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsubset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsubset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\preccurlyeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash preccurlyeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\curlyeqprec $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash curlyeqprec \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\precsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash precsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\precapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash precapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vartriangleleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vartriangleleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\trianglelefteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash trianglelefteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vDash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vDash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Vvdash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Vvdash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\smallsmile $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash smallsmile \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\smallfrown $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash smallfrown \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\bumpeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash bumpeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Bumpeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Bumpeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\geqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash geqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\geqslant $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash geqslant \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\eqslantgtr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash eqslantgtr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtrsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtrsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtrapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtrapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtrdot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtrdot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ggg $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ggg \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtrless $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtrless \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtreqless $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtreqless \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gtreqqless $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gtreqqless \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\eqcirc $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash eqcirc \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\circeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash circeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\triangleq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash triangleq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\thicksim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash thicksim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\thickapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash thickapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\supseteqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash supseteqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Supset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Supset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\sqsupset $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash sqsupset \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succcurlyeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succcurlyeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\curlyeqsucc $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash curlyeqsucc \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\vartriangleright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash vartriangleright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\trianglerighteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash trianglerighteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Vdash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Vdash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\shortmid $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash shortmid \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\shortparallel $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash shortparallel \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\between $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash between \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\pitchfork $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash pitchfork \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varpropto $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varpropto \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\blacktriangleleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash blacktriangleleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\therefore $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash therefore \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\backepsilon $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash backepsilon \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\blacktriangleright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash blacktriangleright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\because $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash because \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS negated binary relations \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\nless $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nless \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nleq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nleq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nleqslant $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nleqslant \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nleqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nleqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lvertneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lvertneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lnsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lnsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\lnapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash lnapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nprec $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nprec \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\npreceq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash npreceq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\precnsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash precnsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\precnapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash precnapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nshortmid $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nshortmid \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nmid $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nmid \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nvdash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nvdash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nvDash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nvDash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ntriangleleft $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ntriangleleft \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ntrianglelefteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ntrianglelefteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsubseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsubseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\subsetneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash subsetneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varsubsetneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varsubsetneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\subsetneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash subsetneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varsubsetneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varsubsetneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ngtr $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ngtr \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ngeq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ngeq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ngeqslant $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ngeqslant \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ngeqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ngeqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gvertneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gvertneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gnsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gnsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\gnapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash gnapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsucc $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsucc \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsucceq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsucceq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succnsim $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succnsim \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\succnapprox $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash succnapprox \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ncong $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ncong \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nshortparallel $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nshortparallel \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nparallel $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nparallel \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nvDash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nvDash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nVDash $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nVDash \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ntriangleright $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ntriangleright \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ntrianglerighteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash ntrianglerighteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsupseteq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsupseteq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\nsupseteqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash nsupseteqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\supsetneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash supsetneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varsupsetneq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varsupsetneq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\supsetneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash supsetneqq \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\varsupsetneqq $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash varsupsetneqq \end_inset \end_inset \end_inset \layout Standard \begin_inset Float table placement htbp wide false collapsed false \layout Caption AMS binary operators \layout Standard \begin_inset Tabular \begin_inset Text \layout Standard \begin_inset Formula $\dotplus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash dotplus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\smallsetminus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash smallsetminus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Cap $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Cap \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\Cup $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash Cup \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\barwedge $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash barwedge \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\veebar $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash veebar \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\doublebarwedge $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash doublebarwedge \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\boxminus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash boxminus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\boxtimes $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash boxtimes \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\boxdot $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash boxdot \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\boxplus $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash boxplus \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\divideontimes $ \end_inset \end_inset \begin_inset Text \layout Standard \family typewriter \backslash divideontimes \end_inset \begin_inset Text \layout Standard \begin_inset Formula $\ltimes $ \end_inset 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