Math Symbol Tables

APPENDIX B Math symbol tables B.1 Hebrew and Greek letters Hebrew letters Type \aleph Typeset ℵ \beth i \daleth k \gimel ‫ג‬ 502 Appendix B Greek letters Lowercase Type Typeset Type Typeset Type Typeset \alpha α \iota ι \sigma σ \beta β \kappa κ \tau τ \gamma γ \lambda λ \upsilon υ \delta δ \mu µ \phi φ \epsilon  \nu ν \chi χ \zeta ζ \xi ξ \psi ψ \eta η \pi π \omega ω \theta θ \rho ρ \varepsilon ε \varpi $ \varsigma ς \vartheta ϑ \varrho % \varphi ϕ \digamma z \varkappa κ Uppercase Type Typeset Type Typeset Type Typeset \Gamma Γ \Xi Ξ \Phi Φ \Delta ∆ \Pi Π \Psi Ψ \Theta Θ \Sigma Σ \Omega Ω \Lambda Λ \Upsilon Υ \varGamma Γ \varXi Ξ \varPhi Φ \varDelta ∆ \varPi Π \varPsi Ψ \varTheta Θ \varSigma Σ \varOmega Ω \varLambda Λ \varUpsilon Υ B.2 Binary relations B.2 503 Binary relations Type < = \in \leq or \le \ll \prec \preceq \sim \simeq \equiv \subset \subseteq \sqsubseteq \smile \perp \mid \vdash \propto \bowtie \sqsubset \Join Typeset < = ∈ ≤  ≺  ∼ ' ≡ ⊂ ⊆ v ^ ⊥ | ` ∝ ./ < 1 Type Typeset > : \ni or \owns \geq or \ge \gg \succ \succeq \approx \cong \doteq \supset \supseteq \sqsupseteq \frown \models \parallel \dashv \asymp > : 3 ≥    ≈ ∼ = . = ⊃ ⊇ w _ |= k a  \sqsupset = Note the \colon command used in f : x → x2 , typed as f \colon x \to x^2 504 Appendix B More binary relations Type Typeset Type Typeset \leqq 5 \geqq = \leqslant 6 \geqslant > \eqslantless 0 \eqslantgtr 1 \lesssim . \gtrsim & \lessapprox / \gtrapprox ' \approxeq u \lessdot l \gtrdot m \lll ≪ \ggg ≫ \lessgtr ≶ \gtrless ≷ \lesseqgtr Q \gtreqless R \lesseqqgtr S \gtreqqless T \doteqdot + \eqcirc P \circeq $ \triangleq , \risingdotseq : \fallingdotseq ; \backsim v \thicksim ∼ \backsimeq w \thickapprox ≈ \preccurlyeq 4 \succcurlyeq < \curlyeqprec 2 \curlyeqsucc 3 \precsim - \succsim % \precapprox w \succapprox v \subseteqq j \supseteqq k \Subset b \Supset c \vartriangleleft C \vartriangleright B \trianglelefteq E \trianglerighteq D \Vdash \vDash  \Vvdash  \smallsmile ` \smallfrown a \shortmid p \shortparallel q \bumpeq l \Bumpeq m \between G \pitchfork t \varpropto ∝ \backepsilon  \blacktriangleleft J \blacktriangleright I \therefore ∴ \because ∵ B.2 Binary relations 505 Negated binary relations Type \neq or \ne \nless \nleq Typeset \notin ≮ \ngtr ≯  \ngeq  ∈ / \ngeqslant  \lneq \lneqq Typeset 6= \nleqslant \nleqq Type \ngeqq  \gneq  \lvertneqq \gneqq \gvertneqq
\lnsim  \gnsim  \lnapprox  \gnapprox  \nprec ⊀ \nsucc  \npreceq  \nsucceq  \precneqq  \succneqq  \precnsim  \succnsim  \precnapprox  \succnapprox  \nsim  \ncong  \nshortmid . \nshortparallel / \nmid - \nparallel ∦ \nvdash 0 \nvDash 2 \nVdash 1 \nVDash 3 \ntriangleleft 6 \ntriangleright 7 \ntrianglelefteq 5 \ntrianglerighteq 4 \nsubseteq * \nsupseteq + \nsubseteqq " \nsupseteqq # \subsetneq ( \supsetneq ) \varsupsetneq ! \varsubsetneq \subsetneqq $ \supsetneqq % \varsubsetneqq & \varsupsetneqq ' 506 B.3 Appendix B Binary operations Type + \pm \times \circ \div \cap \sqcap \wedge or \land \triangleleft \bigtriangleup \oplus \otimes \odot \dagger \setminus \wr \ast \diamond \lhd \unlhd \dotplus \ltimes \leftthreetimes \circleddash \barwedge \curlywedge \veebar \doublecap or \Cap \circledast \boxminus \boxdot \divideontimes \And Typeset + ± × ◦ ÷ ∩ u ∧ / 4 ⊕ ⊗ † \ o ∗ 
 u n h  Z f Y e ~ > & Type \mp \cdot \bigcirc \bmod \cup \sqcup \vee or \lor \triangleright \bigtriangledown \ominus \oslash \bullet \ddagger \smallsetminus \amalg \star \rhd \unrhd \centerdot \rtimes \rightthreetimes \uplus \doublebarwedge \curlyvee \intercal \doublecup or \Cup \circledcirc \boxtimes \boxplus \vartriangle Typeset − ∓ · mod ∪ t ∨ . 5 • ‡ r q ?    o i ] [ g | d } 
M B.4 Arrows B.4 507 Arrows Type \leftarrow \longleftarrow \Leftarrow \Longleftarrow \leftrightarrow \Leftrightarrow \uparrow \Uparrow \updownarrow \nearrow \swarrow \iff \mapsto \hookleftarrow \leftharpoonup \leftharpoondown \leadsto \leftleftarrows \leftrightarrows \Lleftarrow \twoheadleftarrow \leftarrowtail \looparrowleft \upuparrows \upharpoonleft \downharpoonleft \leftrightsquigarrow \multimap \nleftarrow \nLeftarrow \nleftrightarrow \dashleftarrow \curvearrowleft \circlearrowleft \leftrightharpoons \Lsh Typeset ← ←− ⇐ ⇐= ↔ ⇔ ↑ ⇑ l % . ⇐⇒ 7→ ←( ) ; ⇔  W   "    ! ( 8 : = L99 x  Type Typeset \rightarrow or \to \longrightarrow \Rightarrow \Longrightarrow \longleftrightarrow \Longleftrightarrow \downarrow \Downarrow \Updownarrow \searrow \nwarrow \mapstochar \longmapsto \hookrightarrow \rightharpoonup \rightharpoondown → −→ ⇒ =⇒ ←→ ⇐⇒ ↓ ⇓ m & 7 7−→ ,→ * + \rightrightarrows \rightleftarrows \Rrightarrow \twoheadrightarrow \rightarrowtail \looparrowright \downdownarrows \upharpoonright \downharpoonright \rightsquigarrow ⇒  V   #    \nrightarrow \nRightarrow \nLeftrightarrow \dashrightarrow \curvearrowright \circlearrowright \rightleftharpoons \Rsh 9 ; < 99K y   508 B.5 Appendix B Miscellaneous symbols Type Typeset \hbar \imath \wp \Im \infty \emptyset \forall \smallint \top \P \dag \flat \sharp \clubsuit \heartsuit \surd \pounds \Box \mho ~ ı ℘ = ∞ ∅ ∀ ∫ > ¶ † [ ] ♣ ♥ √ \hslash \backprime \Bbbk \diagup \blacktriangle \triangledown \square \lozenge \measuredangle \circledS \Finv } 8 k  N O  ♦ ] s ` £ 2 0 Type Typeset \ell \jmath \partial \Re \prime \varnothing \exists \triangle \bot \S \ddag \natural \angle \diamondsuit \spadesuit \nabla \neg or \lnot \Diamond `  ∂ < 0 ∅ ∃ 4 ⊥ § ‡ \ ∠ ♦ ♠ ∇ ¬ 3 \complement \nexists { @ \diagdown \blacktriangledown \eth \blacksquare \blacklozenge \sphericalangle \bigstar \Game  H ð   ^ F a B.6 Delimiters B.6 509 Delimiters Name Type left parenthesis right parenthesis left bracket right bracket left brace right brace backslash forward slash left angle bracket right angle bracket vertical line double vertical line left floor right floor left ceiling right ceiling upward double upward downward double downward up-and-down double up-and-down upper-left corner upper-right corner lower-left corner lower-right corner ( ) [ or \lbrack ] or \rbrack \{ or \lbrace \} or \rbrace \backslash / \langle \rangle | or \vert \| or \Vert \lfloor \rfloor \lceil \rceil \uparrow \Uparrow \downarrow \Downarrow \updownarrow \Updownarrow \ulcorner \urcorner \llcorner \lrcorner Typeset ( ) [ ] { } \ / h i | k b c d e ↑ ⇑ ↓ ⇓ l m p q x y 510 B.7 Appendix B Operators “Pure” operators, with no limits Type Typeset Type Typeset Type Typeset Type Typeset \arccos \arcsin \arctan \arg \cos \cosh arccos arcsin arctan arg cos cosh \cot \coth \csc \deg \dim \exp cot coth csc deg dim exp \hom \ker \lg \ln \log \sec hom ker lg ln log sec \sin \sinh \tan \tanh sin sinh tan tanh Operators with limits Type Typeset Type Typeset \det \gcd \inf \lim \liminf \injlim det gcd inf lim lim inf inj lim \limsup \max \min \Pr \sup \projlim lim sup max min Pr sup proj lim \varliminf lim \varlimsup lim \varinjlim lim −→ \varprojlim lim ←− B.7 Operators 511 B.7.1 Large operators Type Inline Rb \int_{a}^{b} a a \idotsint_{a}^{b} \prod_{i=1}^{n} \coprod_{i=1}^{n} \bigcap_{i=1}^{n} \bigcup_{i=1}^{n} \bigwedge_{i=1}^{n} \bigvee_{i=1}^{n} \bigsqcup_{i=1}^{n} \biguplus_{i=1}^{n} \bigotimes_{i=1}^{n} \bigoplus_{i=1}^{n} \bigodot_{i=1}^{n} \sum_{i=1}^{n} a a ZZZ a RRRR b a R ··· Qn Rb a i=1 `n i=1 Tn i=1 Sn i=1 Vn i=1 Wn i=1 Fn i=1 Un i=1 Nn i=1 Ln i=1 Jn i=1 Pn b a RRR b \iiint_{a}^{b} b ZZ RR b \iint_{a}^{b} \iiiiint_{a}^{b} a I Hb \oint_{a}^{b} Displayed Z b i=1 b a ZZZZ Z ··· b a Z n Y i=1 n a i=1 n \ i=1 n [ i=1 n ^ i=1 n _ i=1 n G i=1 n ] i=1 n O i=1 n M i=1 n K i=1 n X i=1 a b 512 B.8 Appendix B Math accents and fonts Math accents amsxtra Type \acute{a} \bar{a} \breve{a} \check{a} \dot{a} \ddot{a} \dddot{a} \ddddot{a} \grave{a} \hat{a} \widehat{a} \mathring{a} \tilde{a} \widetilde{a} \vec{a} Typeset á ā ă ǎ ȧ ä ... a .... a à â b a å ã e a ~a Type \spbreve \spcheck \spdot \spddot \spdddot \sphat \sptilde Typeset ˘ ∨ . .. ... b ∼ Math fonts Type LATEX \mathbf{A} \mathcal{A} \mathit{A} \mathnormal{A} \mathrm{A} \mathsf{A} \mathtt{A} \boldsymbol{\alpha} \mathbb{A} \mathfrak{A} \mathscr{a} Typeset A A A A A A A α A A A \mathscr requires the eucal package with the mathscr option B.9 Math spacing commands B.9 513 Math spacing commands Name Width Short Long 1 mu (math unit) \mspace{1mu} thinspace \, \thinspace medspace \: \medspace thickspace \; \thickspace interword space \ 1 em \quad 2 em \qquad Negative space 1 mu thinspace \mspace{-1mu} \! \negthinspace medspace \negmedspace thickspace \negthickspace APPENDIX C Text symbol tables C.1 Some European characters Name Type Typeset Type Typeset a-ring \aa å \AA Å aesc \ae æ \AE Æ ethel \oe œ \OE Œ eszett \ss ß \SS SS inverted question mark ?‘ ¿ inverted exclamation mark !‘ ¡ slashed L \l l \L L slashed O \o ø \O Ø 516 C.2 Appendix C Text accents Name Type acute \’{o} breve Typeset Name Type ó macron \={o} ō \u{o} ŏ overdot \.{g} ġ caron/haček \v{o} ǒ ring \r{u} ů cedilla \c{c} ç tie \t{oo} o o circumflex \^{o} ô tilde \~{n} ñ dieresis/umlaut \"{u} ü underdot \d{m} double acute \H{o} ő underbar \b{o} grave \‘{o} ò m . o ¯ dotless i \i ı dotless j \j  \’{\i} ı́ \v{\j} ̌ C.3 Text font commands C.3.1 Text font family commands Command with Argument Command Declaration Typeset Switches to the font family \textnormal{...} {\normalfont ...} document \emph{...} {\em ...} emphasis \textrm{...} {\rmfamily ...} roman \textsf{...} {\sffamily ...} sans serif \texttt{...} {\ttfamily ...} typewriter style \textup{...} {\upshape ...} upright shape \textit{...} {\itshape ...} italic shape \textsl{...} {\slshape ...} slanted shape \textsc{...} {\scshape ...} small capitals \textbf{...} {\bfseries ...} bold \textmd{...} {\mdseries ...} normal weight and width C.3 Text font commands 517 C.3.2 Text font size changes Command LATEX sample text AMS sample text \Tiny [not available] sample text \tiny sample text sample text \SMALL or \scriptsize sample text sample text \Small or \footnotesize sample text sample text \small sample text sample text \normalsize sample text sample text \large sample text sample text \Large sample text sample text \LARGE sample text sample text \huge sample text sample text \Huge sample text sample text 518 C.4 Appendix C Additional text symbols Name Type Typeset ampersand \& & asterisk bullet \textasteriskcentered backslash \textbackslash ∗ bar (caesura) \textbar brace left \{ brace right \} bullet \textbullet circled a \textcircled{a} circumflex \textasciicircum ˆ copyright \copyright c dagger \dag double dagger (diesis) \ddag † dollar \$ $ double quotation left \textquotedblleft or ‘‘ “ double quotation right \textquotedblright or ’’ ” em dash \textemdash or --- — en dash \textendash or -- – exclamation down \textexclamdown or !‘ ¡ greater than \textgreater > less than \textless < lowline \_ midpoint \textperiodcentered octothorp \# # percent \% % pilcrow (paragraph) \P question down \textquestiondown or ?‘ ¶ registered trademark \textregistered R section \S § \ | { } • a ‡ · ¿ C.5 Additional text symbols with T1 encoding 519 Additional text symbols, continued Name Type Typeset single quote left \textquoteleft or ‘ ‘ single quote right \textquoteright or ’ ’ sterling \pounds £ superscript \textsuperscript{a} a tilde \textasciitilde ˜ trademark \texttrademark visible space \textvisiblespace TM For the \textsubscript command, see Section 12.3. C.5 Additional text symbols with T1 encoding An accent Name Type Ogonek \k{e} Typeset ę European characters Name Type Typeset Type Typeset Eth Dyet Eng Thorn \dh \dj \ng \th ð đ ŋ þ \DH \DJ \NG \TH Ð Ð Ŋ Þ Quotation marks Name Type Single Guillemet Double Guillemet Single Quotation Double Quotation \guilsinglleft \guillemotleft \quotesinglbase \quotedblbase Typeset ‹ « ‚ „ Type \guilsinglright \guillemotright \textquoteright \textquotedbl Typeset › » ’ " 520 Appendix C C.6 Text spacing commands Name Width Short command Long command Positive Space Normal varies Intersentence varies \@. Interword varies \ Italic Corr. varies \/ Tie varies ~ Thinspace \, \thinspace Medspace \: \medspace Thickspace \; \thickspace 1 em \quad 2 em \qquad Negative Space Thinspace \! \negthinspace Medspace \negmedspace Thickspace \negthickspace