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Math Symbol Tables APPENDIX A I Math symbol tables A.I Hebrew letters Type: Print: Type: Print: \aleph ~ \beth :J \daleth l \gimel J All symbols but \aleph need the amssymb package. 346 Appendix A A.2 Greek characters Type: Print: Type: Print: Type: Print: \alpha a \beta f3 \gamma 'Y \digamma F \delta b \epsilon E \varepsilon E \zeta ( \eta 'f/ \theta () \vartheta {) \iota ~ \kappa ,.. \varkappa x \lambda ,\ \mu /-l \nu v \xi ~ \pi 7r \varpi tv \rho p \varrho (} \sigma (J \varsigma <; \tau T \upsilon v \phi ¢ \varphi 'P \chi X \psi 'ljJ \omega w \digamma and \ varkappa require the amssymb package. Type: Print: Type: Print: \Gamma r \varGamma r \Delta L\ \varDelta L.\ \Theta e \varTheta e \Lambda A \varLambda A \Xi ~ \varXi ~ \Pi II \varPi II \Sigma 2: \varSigma E \Upsilon T \varUpsilon Y \Phi <I> \varPhi t[> \Psi III \varPsi 1ft \Omega n \varOmega D All symbols whose name begins with var need the amsmath package. Math symbol tables 347 A.3 Y1EX binary relations Type: Print: Type: Print: \in E \ni \leq < \geq >'" \11 « \gg \prec \succ \preceq \succeq \sim \cong \simeq \approx \equiv \doteq \subset c \supset \subseteq c \supseteq \sqsubseteq c \sqsupseteq \smile \frown \perp 1- \models F \mid I \parallel II \vdash f- \dashv -1 \propto <X \asymp \bowtie [Xl \sqsubset \sqsupset \Join The latter three symbols need the latexsym package. 348 Appendix A A.4 AMS binary relations Type: Print: Type: Print: \leqs1ant :::::; \geqs1ant ): \eqs1ant1ess :< \eqs1antgtr :::> \lesssim < \gtrsim > '" '" < > \lessapprox ~ \gtrapprox \approxeq ~ \lessdot <:: \gtrdot Y \111 «< \ggg »> \lessgtr S \gtr1ess Z < >- \lesseqgtr > \gtreq1ess < > < \gtreqq1ess \lesseqqgtr > < ~ \doteqdot --;- \eqcirc = .2... '- \circeq - \fa11ingdotseq ---0 ~ A \risingdotseq ;- \triang1eq - \backsim '-" \thicksim '" \backsimeq '-"- \thickapprox ~ \preccur1yeq ~ \succcur1yeq ~ \cur1yeqprec =1:: \cur1yeqsucc ~ \precsim -< \succsim >- '" '" --< >- \precapprox ~ \succapprox ~ C :l \subseteqq - \supseteqq - \Subset IS \Supset 3! \vartriang1e1eft <l \vartriang1eright [> [> \triang1e1efteq <l- \triang1erighteq - \vDash 1= Wdash If- \Vvdash 1If- \sma11smile '--' \sma11frown r-. \shortmid I \shortpara11e1 II ~ \bumpeq ~ \Bumpeq ~ \between Q \pitchfork rh \varpropto ex \backepsilon ~ \b1acktriang1e1eft ... \b1acktriang1eright ~ \therefore . \because .. All symbols require the amssymb package. Math symbol tables 349 A.S AMS negated binary relations Type: Print: Type: Print: \ne =I- \notin rf- \nless 1- \ngtr f \nleq i \ngeq i \nleqslant 1, \ngeqslant 'I \nleqq ~ \ngeqq t \lneq :;; \gneq 2: \lneqq <7= \gneqq 7=> \lvertneqq ~ \gvertneqq >=1= \lnsim < ?- \gnsim ~ \lnapprox < r:j::, \gnapprox ~ \nprec -I< \nsucc ';f \npreceq ~ \nsucceq 'i \precneqq ~ \succneqq (:;; \precnsim -< ?- \succnsim ?->- \precnapprox -< >- ~ \succnapprox ~ \nsim "'" \ncong ~ \nshortmid { \nshortparallel 11 \nmid f \nparallel {t \nvdash J.L \nvDash ¥ \nVdash .w: \nVDash .l¥ \ntriangleleft 11 \ntriangleright ~ \ntrianglelefteq jl \ntrianglerighteq rt \nsubseteq ~ \nsupseteq 1J- \nsubseteqq ~ \nsupseteqq ;g \subsetneq ~ \supsetneq "2 \varsubsetneq ~ \varsupsetneq ;2 \subsetneqq C J 7= \supsetneqq 7= \varsubsetneqq ~ \varsupsetneqq ~ All symbols but \ne require the amssymb package. 350 Appendix A A.6 Binary operations Type: Print: Type: Print: \pm ± \mp =f \times x \cdot \circ 0 \bigcirc 0 \div \diamond <) \ast * \star * \cap n \cup U \sqcap n \sqcup U \wedge 1\ \vee V \triangleleft <J \triangleright I> \bigtriangleup /":, \bigtriangledown V \oplus EB \ominus e \otimes ® \oslash 0 \odot 8 \bullet • \dagger t \ddagger :j: \setminus \ \uplus I±I \wr I \amalg II \lhd <J \rhd (> (> \unlhd -<J \unrhd \dotplus + \centerdot \ltimes I>< \rtimes ~ \leftthreetimes A \rightthreetimes A \circleddash 8 \smallsetminus "- \barwedge /\ \doublebarwedge 1\ \curlywedge A \curlyvee y \veebar ":{ \intercal T \Cap Iii) \Cup l!!J \circledast ® \circledcirc @ \boxminus El \boxtimes ~ \boxdot c:J \boxplus B3 \divideontimes * I \And & This table is divided into four parts. The first part contains the binary operations in :£b.TEX. The second part requires the latexsym package. The third part contains the AMS additions; they require the amssymb package. The symbol \And requires the amsmath package. Math symbol tables 351 A.7 Arrows Type: Print: Type: Print: \leftarrow <- \rightarrow or \ to ---. \longleftarrow ~ \longrightarrow ---+ \Leftarrow ~ \Rightarrow :::} \Longleftarrow {== \Longrightarrow ==} \leftrightarrow f-+ \longleftrightarrow ~ \Leftrightarrow ¢:} \Longleftrightarrow ~ \uparrow i \downarrow 1 \Uparrow 11' \Downarrow JJ- \updownarrow 1 \Updownarrow ~ \nearrow / \searrow \swarrow ,/ \nwarrow "" \mapsto f-+ \longmapsto f-----+"" \hookleftarrow +--" \hookrightarrow ~ \leftharpoonup ~ \rightharpoonup ~ \leftharpoondown ~ \rightharpoondown ~ \rightleftharpoons ~ \leadsto "'* \leftleftarrows l= \rightrightarrows :4 \leftrightarrows =+ \rightleftarrows <= \Lleftarrow ~ \Rrightarrow ~ \twoheadleftarrow «--- \twoheadrightarrow -* \leftarrowtail r-< \rightarrowtail >---> \looparrowleft <--P \looparrowright '1-+ \upuparrows n \downdownarrows 11 \upharpoonleft 1 \upharpoonright r \downharpoonleft J \downharpoonright l \leftrightsquigarrow """" \rightsquigarrow """' \multimap -0 \nleftarrow +f- \nrightarrow -+> \nLeftarrow -#= \nRightarrow ~ \nleftrightarrow <++ \nLeftrightarrow {f;> This table is divided into three parts. The top part contains the symbols provided by Ib-TEX; the last command, \leadsto, requires the latexsym package. The middle table contains the AMS arrows; they all require the amssymb package. The bottom table lists the negated arrow symbols; they also require amssymb. 352 Appendix A A.8 Miscellaneous symbols Type: Print: Type: Print: \hbar Ii \ell C \imath z \jmath J \wp 8J \Re ~ \lm 'S \partial {) \infty 00 \prime I \emptyset 0 \backslash \ \forall 't/ \exists :3 \smallint J \triangle 6 \surd J \Vert II \top T \bot ..l \P ~ \8 § \dag t \ddag :j: \flat D \natural q \sharp ~ \angle L \clubsuit "- \diamondsuit <> \heartsuit 0 \spadesuit \neg -, • \Box 0 \Diamond <> \mho U \hslash Ii \complement C \backprime \ \vartriangle 6. \Bbbk Ik \varnothing 0 \diagup / \diagdown \blacktriangle A \blacktriangledown ""~ \triangledown \l \Game ~ \ square D \blacksquare \lozenge (; \blacklozenge • \measuredangle L \sphericalangle •<l: \circled8 ® \bigstar \Finv ..:J \eth *(3 \nexists ~ This table is divided into two parts. The top part contains the symbols provided by U\TEX; the last three commands require the latexsym package. The bottom table lists symbols from the AMS; they all require the amssymb package. Math symbol tables 353 A.9 Math spacing commands Short form: Full form: Size: Short form: Full form: \, \thinspace u \! \negthinspace \: \medspace u \negmedspace \; \thickspace u \negthickspace \quad LJ \qquad L--J The \medspace, \thickspace, \negmedspace, and \negthickspace commands require the amsmath package. A.iO Delimiters Name: Type: Print: Name: Type: Print: Left paren ( ( Right paren ) ) Left bracket [ [ Right bracket ] 1 Left brace \{ { Right brace \} } Reverse slash \backslash \ Forward slash / / Left angle \langle ( Right angle \rangle ) Vertical line 1 I Double vert. line \1 II Left floor \lfloor l Right floor \rfloor J Left ceiling \lceil I Right ceiling \rceil 1 Upper left corner \ulcorner r Upper right corner \urcorner I Lower left corner \llcorner L Lower right corner \lrcorner ...J The corners require the amsmath package. Name: Type: Print: Upward arrow \uparrow i Double upward arrow \Uparrow 1t' Downward arrow \downarrow ! Double downward arrow \Downarrow .lJ. Up-and-down arrow \updownarrow 1 Double up-and-down arrow \Updownarrow ~ 354 Appendix A A.ll Operators \arccos \arcsin \arctan \arg \cos \cosh \cot \coth \csc \dim \exp \hom \ker \lg \In \log \sec \sin \sinh \tan \tanh \varliminf \varlimsup \varinjlim \varprojlim The \var commands require the amsmath package. \det \gcd \inf \injlim \lim \liminf \limsup \max \min \projlim \Pr \sup The \injlim and \projlim commands require the amsmath package. Type: Inline Displayed Type: Inline Displayed n n \prod_{i=1Y{n} \coprod_{i=1}-{n} Un I1~=1 II i=1 II i=1 i=1 n n \bigcap_{i=1}-{n} \bigcup_{i=1}-{n} Un n~=1 n i=1 U i=1 i=1 n n \bigwedge_{i=1}-{n} \bigvee_{i=1}-{n} n 1\7=1 1\ V i=1 V i=1 i=l n n \bigsqcup_{i=1}-{n} U~=1 U \biguplus_{i=1}-{n} ltJ~=1 l±J i=1 i=1 n n \bigotimes_{i=1}-{n} Q9~1 ® \bigoplus_{i=1}-{n} EB~=1 EB i=1 i=1 n n \bigodot_{i=1}-{n} O~=1 0 \SUID_ {i=1Y{n} 2:~=1 L i=1 ;=1 Math symbol tables 355 A.12 Math accents \hat{a} a \Hat{a} a \widehat{a} a a\sphat a ~ \tilde{a} a \Tilde{a} a \widetilde{a} a a\sptilde a~ \acute{a} a \Acute{a} a \bar{a} a \Bar{a} a \breve{a} a \Breve{a} a a\spbreve aU \check{a} a \Check{a} a a\spcheck a V \dot{a} a \Dot{a} a a\spdot a' .. \ddot{a} ii \Ddot{a} a a\spddot a \dddot{a} a a\spdddot a ... \ddddot{a} a \grave{a} a \Grave{a} a \imath z \vec{a} a \Vec{a} a \jmath J The \dddot and \ddddot commands and all the capitalized commands require the amsmath package; the commands in the fourth column require the amsxtra package. A.13 Math font commands Type: Print: \mathbf{A} A \mathit{A} A \mathsf{A} A \mathrm{A} A \mathtt{A} A \mathnormal{A} A \mathbb{A} Pi,. \mathfrak{A} 2t \mathcal{A} A \boldsymbol{\alpha} Q The \mathbb, \mathfrak, and \mathcal commands require the amsfonts package. The \boldsymbol command requires the amsbsy package. APPENDIX B I Text symbol tables B.l Special text characters Type: Print: Type: Print: Type: Print: \# # \$ $ \% % - \& & \-n \- - , \-n \{ { \} } $1$ 1 @ @ $*$ * $\backslash$ \ Text symbol tables 357 B.2 Text accents
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