The Wiki supports LaTeX markup: $pi=\frac\left\{3\right\}\left\{4\right\} \sqrt\left\{3\right\}+24 \int_0^\left\{1/4\right\}\left\{\sqrt\left\{x-x^2\right\}dx\right\}$ Mathematical Formula (LaTeX) can be inserted into text like this: {{{ $Insert formula here$ }}} For example: {{{ $\alpha^2+\beta^2=1$ }}} ...displays $\alpha^2+\beta^2=1$ == Displaying a Formula == The Wiki uses a subset of TeX markup, including some extensions from LaTeX and AMSLaTeX, for mathematical formulae. It generates either PNG images or simple HTML markup, depending on the complexity of the expression. While it can generate MathML, it is not currently used due to limited browser support. As browsers become more advanced and support for MathML becomes more wide-spread, this could be the preferred method of output as images have very real disadvantages. === Syntax === Math markup goes inside $...$. ===Pros of HTML=== # In-line HTML formulae always align properly with the rest of the HTML text. # The formula's background, font size and face match the rest of HTML contents and the appearance respects CSS and browser settings. # Pages using HTML will load faster. === Pros of TeX === # TeX is semantically superior to HTML. In TeX, "x" means "mathematical variable $x$", whereas in HTML "x" could mean anything. Information has been irrevocably lost. # TeX has been specifically designed for typesetting formulae, so input is easier and more natural, and output is more aesthetically pleasing. # One consequence of point 1 is that TeX can be transformed into HTML, but not vice-versa. This means that on the server side we can always transform a formula, based on its complexity and location within the text, user preferences, type of browser, etc. Therefore, where possible, all the benefits of HTML can be retained, together with the benefits of TeX. It's true that the current situation is not ideal, but that's not a good reason to drop information/contents. It's more a reason to help improve the situation. # Another consequence of point 1 is that TeX can be converted to !MathML for browsers which support it, thus keeping its semantics and allowing it to be rendered vectorially. # When writing in TeX, editors need not worry about whether this or that version of this or that browser supports this or that HTML entity. The burden of these decisions is put on the server. This doesn't hold for HTML formulae, which can easily end up being rendered wrongly or differently from the editor's intentions on a different browser. # TeX is the preferred text formatting language of most professional mathematicians, scientists, and engineers. It is easier to persuade them to contribute if they can write in TeX. === Example Formulas === The following are a few examples of formulas: {{{ $\sqrt\left\{1-e^2\right\}$ }}} $\sqrt\left\{1-e^2\right\}$ {{{ $\overbrace\left\{ 1+2+\cdots+100 \right\}^\left\{5050\right\}$ }}} $\overbrace\left\{ 1+2+\cdots+100 \right\}^\left\{5050\right\}$ {{{ $ax^2 + bx + c = 0$ }}} $ax^2 + bx + c = 0$ {{{ $\int_\left\{-N\right\}^\left\{N\right\} e^x\, dx$ }}} $\int_\left\{-N\right\}^\left\{N\right\} e^x\, dx$ == Functions, symbols, special characters == === Accents/Diacritics === || \acute{a} \grave{a} \hat{a} \tilde{a} \breve{a} || $\acute\left\{a\right\} \grave\left\{a\right\} \hat\left\{a\right\} \tilde\left\{a\right\} \breve\left\{a\right\}$ || || \check{a} \bar{a} \ddot{a} \dot{a} ||$\ \check\left\{a\right\} \bar\left\{a\right\} \ddot\left\{a\right\} \dot\left\{a\right\}$ || === Standard functions === || \sin a \cos b \tan c|| $\ \sin a \cos b \tan c$ || || \sec d \csc e \cot f|| $\sec d \csc e \cot f\,\!$ || || \arcsin h \arccos i \arctan j|| $\arcsin h \arccos i \arctan j\,\!$ || || \sinh k \cosh l \tanh m \coth n|| $\ \sinh k \cosh l \tanh m \coth n$ || || \operatorname{sh}\,o\,\operatorname{ch}\,p\,\operatorname{th}\,q|| $\ \operatorname\left\{sh\right\}\,o\,\operatorname\left\{ch\right\}\,p\,\operatorname\left\{th\right\}\,q$ || || \operatorname{arsinh}\,r\,\operatorname{arcosh}\,s\,\operatorname{artanh}\,t|| $\operatorname\left\{arsinh\right\}\,r\,\operatorname\left\{arcosh\right\}\,s\,\operatorname\left\{artanh\right\}\,t\,\!$ || || \lim u \limsup v \liminf w \min x \max y || $\ \lim u \limsup v \liminf w \min x \max y$ || || \inf z \sup a \exp b \ln c \lg d \log e \log_{10} f \ker g ||$\ \inf z \sup a \exp b \ln c \lg d \log e \log_\left\{10\right\} f \ker g$ || || \deg h \gcd i \Pr j \det k \hom l \arg m \dim n || $\deg h \gcd i \Pr j \det k \hom l \arg m \dim n\,\!$ || === Modular arithmetic === || s_k \equiv 0 \pmod{m} || $s_k \equiv 0 \pmod\left\{m\right\}\,\!$ || || a\,\bmod\,b || $a\,\bmod\,b\,\!$ || === Derivatives === || \nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac{dy}{dx}\, \frac{\partial^2 y}{\partial x_1\,\partial x_2} || $\nabla \, \partial x \, dx \, \dot x \, \ddot y\, dy/dx\, \frac\left\{dy\right\}\left\{dx\right\}\, \frac\left\{\partial^2 y\right\}\left\{\partial x_1\,\partial x_2\right\}$ || === Sets === || \forall \exists \empty \emptyset \varnothing || $\forall \exists \empty \emptyset \varnothing\,\!$ || || \in \ni \not \in \notin \subset \subseteq \supset \supseteq || $\in \ni \not \in \notin \subset \subseteq \supset \supseteq\,\!$ || || \cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus || $\cap \bigcap \cup \bigcup \biguplus \setminus \smallsetminus\,\!$ || || \sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup || $\sqsubset \sqsubseteq \sqsupset \sqsupseteq \sqcap \sqcup \bigsqcup\,\!$ || === Operators === || + \oplus \bigoplus \pm \mp -  || $+ \oplus \bigoplus \pm \mp - \,\!$ || || \times \otimes \bigotimes \cdot \circ \bullet \bigodot || $\times \otimes \bigotimes \cdot \circ \bullet \bigodot\,\!$ || || \star * / \div \frac{1}{2} || $\star * / \div \frac\left\{1\right\}\left\{2\right\}\,\!$ || === Logic === || \land (or \and) \wedge \bigwedge \bar{q} \to p || $\land \wedge \bigwedge \bar\left\{q\right\} \to p\,\!$ || || \lor \vee \bigvee \lnot \neg q \And || $\lor \vee \bigvee \lnot \neg q \And\,\!$ || === Root === || \sqrt{2} \sqrt[n]{x} || $\sqrt\left\{2\right\} \sqrt\left[n\right]\left\{x\right\}\,\!$ || === Relations === || \sim \approx \simeq \cong \dot= \overset{\underset{\mathrm{def}}{}}{=} || $\sim \approx \simeq \cong \dot= \overset\left\{\underset\left\{\mathrm\left\{def\right\}\right\}\left\{\right\}\right\}\left\{=\right\}\,\!$ || || \le < \ll \gg \ge > \equiv \not\equiv \ne \mbox{or} \neq \propto || $\le < \ll \gg \ge > \equiv \not\equiv \ne \mbox\left\{or\right\} \neq \propto\,\!$ || === Geometric === || \Diamond \Box \triangle \angle \perp \mid \nmid \| 45^\circ || $\Diamond \, \Box \, \triangle \, \angle \perp \, \mid \; \nmid \, \| 45^\circ\,\!$ || === Arrows === || \leftarrow (or \gets) \rightarrow (or \to) \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow || $\leftarrow \rightarrow \nleftarrow \not\to \leftrightarrow \nleftrightarrow \longleftarrow \longrightarrow \longleftrightarrow \,\!$ || || \Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow (or \iff) || $\Leftarrow \Rightarrow \nLeftarrow \nRightarrow \Leftrightarrow \nLeftrightarrow \Longleftarrow \Longrightarrow \Longleftrightarrow \,\!$ || || \uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow || $\ \uparrow \downarrow \updownarrow \Uparrow \Downarrow \Updownarrow \nearrow \searrow \swarrow \nwarrow$ || || \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons || $\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons \,\!$ || || \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright || $\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \Rrightarrow \rightarrowtail \looparrowright \,\!$ || || \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft || $\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \Lleftarrow \leftarrowtail \looparrowleft \,\!$ || || \mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow  || $\mapsto \longmapsto \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \,\!$ || === Special === || \And \eth \S \P \% \dagger \ddagger \ldots \cdots || $\And \eth \S \P \% \dagger \ddagger \ldots \cdots\,\!$ || || \smile \frown \wr \triangleleft \triangleright \infty \bot \top || $\smile \frown \wr \triangleleft \triangleright \infty \bot \top\,\!$ || || \vdash \vDash \Vdash \models \lVert \rVert \imath \hbar || $\vdash \vDash \Vdash \models \lVert \rVert \imath \hbar\,\!$ || || \ell \mho \Finv \Re \Im \wp \complement || $\ell \mho \Finv \Re \Im \wp \complement\,\!$ || || \diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp || $\diamondsuit \heartsuit \clubsuit \spadesuit \Game \flat \natural \sharp\,\!$ || === Unsorted (new stuff) === || \vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown || $\vartriangle \triangledown \lozenge \circledS \measuredangle \nexists \Bbbk \backprime \blacktriangle \blacktriangledown$ || || \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge || $\ \blacksquare \blacklozenge \bigstar \sphericalangle \diagup \diagdown \dotplus \Cap \Cup \barwedge$ || || \veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes || $\veebar \doublebarwedge \boxminus \boxtimes \boxdot \boxplus \divideontimes \ltimes \rtimes \leftthreetimes$ || || \rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant || $\rightthreetimes \curlywedge \curlyvee \circleddash \circledast \circledcirc \centerdot \intercal \leqq \leqslant$ || || \eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq || $\eqslantless \lessapprox \approxeq \lessdot \lll \lessgtr \lesseqgtr \lesseqqgtr \doteqdot \risingdotseq$ || || \fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft || $\fallingdotseq \backsim \backsimeq \subseteqq \Subset \preccurlyeq \curlyeqprec \precsim \precapprox \vartriangleleft$ || || \Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot || $\Vvdash \bumpeq \Bumpeq \geqq \geqslant \eqslantgtr \gtrsim \gtrapprox \eqsim \gtrdot$ || || \ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq || $\ggg \gtrless \gtreqless \gtreqqless \eqcirc \circeq \triangleq \thicksim \thickapprox \supseteqq$ || || \Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork || $\Supset \succcurlyeq \curlyeqsucc \succsim \succapprox \vartriangleright \shortmid \shortparallel \between \pitchfork$ || || \varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq || $\varpropto \blacktriangleleft \therefore \backepsilon \blacktriangleright \because \nleqslant \nleqq \lneq \lneqq$ || || \lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid || $\lvertneqq \lnsim \lnapprox \nprec \npreceq \precneqq \precnsim \precnapprox \nsim \nshortmid$ || || \nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr || $\nvdash \nVdash \ntriangleleft \ntrianglelefteq \nsubseteq \nsubseteqq \varsubsetneq \subsetneqq \varsubsetneqq \ngtr$ || || \subsetneq || $\subsetneq$ || || \ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq || $\ngeqslant \ngeqq \gneq \gneqq \gvertneqq \gnsim \gnapprox \nsucc \nsucceq \succneqq$ || || \succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq || $\succnsim \succnapprox \ncong \nshortparallel \nparallel \nvDash \nVDash \ntriangleright \ntrianglerighteq \nsupseteq$ || || \nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq || $\nsupseteqq \varsupsetneq \supsetneqq \varsupsetneqq$ || || \jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus || $\jmath \surd \ast \uplus \diamond \bigtriangleup \bigtriangledown \ominus\,\!$ || || \oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq || $\oslash \odot \bigcirc \amalg \prec \succ \preceq \succeq\,\!$ || || \dashv \asymp \doteq \parallel || $\dashv \asymp \doteq \parallel\,\!$ || || \ulcorner \urcorner \llcorner \lrcorner || $\ulcorner \urcorner \llcorner \lrcorner$ || == Larger Expressions == === Parenthesizing big expressions, brackets, bars === || '''Feature''' || '''Syntax''' || '''How it looks rendered''' || || Bad || ( \frac{1}{2} ) || $\left( \frac\left\{1\right\}\left\{2\right\} \right)$ || || Good || \left ( \frac{1}{2} \right ) || $\left \left( \frac\left\{1\right\}\left\{2\right\} \right \right)$ || You can use various delimiters with \left and \right: || '''Feature''' || '''Syntax''' || '''How it looks rendered''' || || Parentheses || \left ( \frac{a}{b} \right ) || $\left \left( \frac\left\{a\right\}\left\{b\right\} \right \right)$ || || Brackets || \left [ \frac{a}{b} \right ] \quad \left \lbrack \frac{a}{b} \right \rbrack || $\left \left[ \frac\left\{a\right\}\left\{b\right\} \right \right] \quad \left \lbrack \frac\left\{a\right\}\left\{b\right\} \right \rbrack$ || || Braces || \left \{ \frac{a}{b} \right \} \quad \left \lbrace \frac{a}{b} \right \rbrace || $\left \\left\{ \frac\left\{a\right\}\left\{b\right\} \right \\right\} \quad \left \lbrace \frac\left\{a\right\}\left\{b\right\} \right \rbrace$ || || Angle brackets || \left \langle \frac{a}{b} \right \rangle || $\left \langle \frac\left\{a\right\}\left\{b\right\} \right \rangle$ || || Bars and double bars || \left | \frac{a}{b} \right \vert \left \Vert \frac{c}{d} \right \| || $\left | \frac\left\{a\right\}\left\{b\right\} \right \vert \left \Vert \frac\left\{c\right\}\left\{d\right\} \right \|$ || || Floor and ceiling functions: || \left \lfloor \frac{a}{b} \right \rfloor \left \lceil \frac{c}{d} \right \rceil || $\left \lfloor \frac\left\{a\right\}\left\{b\right\} \right \rfloor \left \lceil \frac\left\{c\right\}\left\{d\right\} \right \rceil$ || || Slashes and backslashes || \left / \frac{a}{b} \right \backslash || $\left / \frac\left\{a\right\}\left\{b\right\} \right \backslash$ || || Up, down and up-down arrows || \left \uparrow \frac{a}{b} \right \downarrow \quad \left \Uparrow \frac{a}{b} \right \Downarrow \quad \left \updownarrow \frac{a}{b} \right \Updownarrow || $\left \uparrow \frac\left\{a\right\}\left\{b\right\} \right \downarrow \quad \left \Uparrow \frac\left\{a\right\}\left\{b\right\} \right \Downarrow \quad \left \updownarrow \frac\left\{a\right\}\left\{b\right\} \right \Updownarrow$ || || Delimiters can be mixed,[[BR]]as long as \left and \right match || \left [ 0,1 \right ) [[BR]] \left \langle \psi \right | || $\left \left[ 0,1 \right \right)$ [[BR]] $\left \langle \psi \right |$ || || Use \left. and \right. if you don't[[BR]]want a delimiter to appear: || \left . \frac{A}{B} \right \} \to X || $\left . \frac\left\{A\right\}\left\{B\right\} \right \\right\} \to X$ || || Size of the delimiters || \big( \Big( \bigg( \Bigg( \dots \Bigg] \bigg] \Big] \big]/ || $\big\left( \Big\left( \bigg\left( \Bigg\left( \dots \Bigg\right] \bigg\right] \Big\right] \big\right]$ || || . || \big\{ \Big\{ \bigg\{ \Bigg\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle || $\big\\left\{ \Big\\left\{ \bigg\\left\{ \Bigg\\left\{ \dots \Bigg\rangle \bigg\rangle \Big\rangle \big\rangle$ || || . || \big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big| || $\big\| \Big\| \bigg\| \Bigg\| \dots \Bigg| \bigg| \Big| \big|$ || || . || \big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil || $\big\lfloor \Big\lfloor \bigg\lfloor \Bigg\lfloor \dots \Bigg\rceil \bigg\rceil \Big\rceil \big\rceil$ || || . || \big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow || $\big\uparrow \Big\uparrow \bigg\uparrow \Bigg\uparrow \dots \Bigg\Downarrow \bigg\Downarrow \Big\Downarrow \big\Downarrow$ || || . || \big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow || $\big\updownarrow \Big\updownarrow \bigg\updownarrow \Bigg\updownarrow \dots \Bigg\Updownarrow \bigg\Updownarrow \Big\Updownarrow \big\Updownarrow$ || || . || \big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash || $\big / \Big / \bigg / \Bigg / \dots \Bigg\backslash \bigg\backslash \Big\backslash \big\backslash$ || == Alphabets and typefaces == Texvc cannot render arbitrary Unicode characters. Those it can handle can be entered by the expressions below. For others, such as Cyrillic, they can be entered as Unicode or HTML entities in running text, but cannot be used in displayed formulas. ||_\2. '''Greek alphabet''' || || \Alpha \Beta \Gamma \Delta \Epsilon \Zeta || $\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \,\!$ || || \Eta \Theta \Iota \Kappa \Lambda \Mu || $\Eta \Theta \Iota \Kappa \Lambda \Mu \,\!$ || || \Nu \Xi \Pi \Rho \Sigma \Tau || $\Nu \Xi \Pi \Rho \Sigma \Tau\,\!$ || || \Upsilon \Phi \Chi \Psi \Omega || $\Upsilon \Phi \Chi \Psi \Omega \,\!$ || || \alpha \beta \gamma \delta \epsilon \zeta || $\alpha \beta \gamma \delta \epsilon \zeta \,\!$ || || \eta \theta \iota \kappa \lambda \mu || $\eta \theta \iota \kappa \lambda \mu \,\!$ || || \nu \xi \pi \rho \sigma \tau || $\nu \xi \pi \rho \sigma \tau \,\!$ || || \upsilon \phi \chi \psi \omega || $\upsilon \phi \chi \psi \omega \,\!$ || || \varepsilon \digamma \vartheta \varkappa || $\varepsilon \digamma \vartheta \varkappa \,\!$ || || \varpi \varrho \varsigma \varphi || $\varpi \varrho \varsigma \varphi\,\!$ || ||_\2. '''Blackboard Bold/Scripts''' || || \mathbb{A} \mathbb{B} \mathbb{C} \mathbb{D} \mathbb{E} \mathbb{F} \mathbb{G} || $\mathbb\left\{A\right\} \mathbb\left\{B\right\} \mathbb\left\{C\right\} \mathbb\left\{D\right\} \mathbb\left\{E\right\} \mathbb\left\{F\right\} \mathbb\left\{G\right\} \,\!$ || || \mathbb{H} \mathbb{I} \mathbb{J} \mathbb{K} \mathbb{L} \mathbb{M} || $\mathbb\left\{H\right\} \mathbb\left\{I\right\} \mathbb\left\{J\right\} \mathbb\left\{K\right\} \mathbb\left\{L\right\} \mathbb\left\{M\right\} \,\!$ || || \mathbb{N} \mathbb{O} \mathbb{P} \mathbb{Q} \mathbb{R} \mathbb{S} \mathbb{T} || $\mathbb\left\{N\right\} \mathbb\left\{O\right\} \mathbb\left\{P\right\} \mathbb\left\{Q\right\} \mathbb\left\{R\right\} \mathbb\left\{S\right\} \mathbb\left\{T\right\} \,\!$ || || \mathbb{U} \mathbb{V} \mathbb{W} \mathbb{X} \mathbb{Y} \mathbb{Z} || $\mathbb\left\{U\right\} \mathbb\left\{V\right\} \mathbb\left\{W\right\} \mathbb\left\{X\right\} \mathbb\left\{Y\right\} \mathbb\left\{Z\right\}\,\!$ || ||_\2. '''boldface (vectors)''' || || \mathbf{A} \mathbf{B} \mathbf{C} \mathbf{D} \mathbf{E} \mathbf{F} \mathbf{G} || $\mathbf\left\{A\right\} \mathbf\left\{B\right\} \mathbf\left\{C\right\} \mathbf\left\{D\right\} \mathbf\left\{E\right\} \mathbf\left\{F\right\} \mathbf\left\{G\right\} \,\!$ || || \mathbf{H} \mathbf{I} \mathbf{J} \mathbf{K} \mathbf{L} \mathbf{M} || $\mathbf\left\{H\right\} \mathbf\left\{I\right\} \mathbf\left\{J\right\} \mathbf\left\{K\right\} \mathbf\left\{L\right\} \mathbf\left\{M\right\} \,\!$ || || \mathbf{N} \mathbf{O} \mathbf{P} \mathbf{Q} \mathbf{R} \mathbf{S} \mathbf{T} || $\mathbf\left\{N\right\} \mathbf\left\{O\right\} \mathbf\left\{P\right\} \mathbf\left\{Q\right\} \mathbf\left\{R\right\} \mathbf\left\{S\right\} \mathbf\left\{T\right\} \,\!$ || || \mathbf{U} \mathbf{V} \mathbf{W} \mathbf{X} \mathbf{Y} \mathbf{Z} || $\mathbf\left\{U\right\} \mathbf\left\{V\right\} \mathbf\left\{W\right\} \mathbf\left\{X\right\} \mathbf\left\{Y\right\} \mathbf\left\{Z\right\} \,\!$ || || \mathbf{a} \mathbf{b} \mathbf{c} \mathbf{d} \mathbf{e} \mathbf{f} \mathbf{g} || $\mathbf\left\{a\right\} \mathbf\left\{b\right\} \mathbf\left\{c\right\} \mathbf\left\{d\right\} \mathbf\left\{e\right\} \mathbf\left\{f\right\} \mathbf\left\{g\right\} \,\!$ || || \mathbf{h} \mathbf{i} \mathbf{j} \mathbf{k} \mathbf{l} \mathbf{m} || $\mathbf\left\{h\right\} \mathbf\left\{i\right\} \mathbf\left\{j\right\} \mathbf\left\{k\right\} \mathbf\left\{l\right\} \mathbf\left\{m\right\} \,\!$ || || \mathbf{n} \mathbf{o} \mathbf{p} \mathbf{q} \mathbf{r} \mathbf{s} \mathbf{t} || $\mathbf\left\{n\right\} \mathbf\left\{o\right\} \mathbf\left\{p\right\} \mathbf\left\{q\right\} \mathbf\left\{r\right\} \mathbf\left\{s\right\} \mathbf\left\{t\right\} \,\!$ || || \mathbf{u} \mathbf{v} \mathbf{w} \mathbf{x} \mathbf{y} \mathbf{z} || $\mathbf\left\{u\right\} \mathbf\left\{v\right\} \mathbf\left\{w\right\} \mathbf\left\{x\right\} \mathbf\left\{y\right\} \mathbf\left\{z\right\} \,\!$ || || \mathbf{0} \mathbf{1} \mathbf{2} \mathbf{3} \mathbf{4} || $\mathbf\left\{0\right\} \mathbf\left\{1\right\} \mathbf\left\{2\right\} \mathbf\left\{3\right\} \mathbf\left\{4\right\} \,\!$ || || \mathbf{5} \mathbf{6} \mathbf{7} \mathbf{8} \mathbf{9} || $\mathbf\left\{5\right\} \mathbf\left\{6\right\} \mathbf\left\{7\right\} \mathbf\left\{8\right\} \mathbf\left\{9\right\}\,\!$ || ||_\2. '''Boldface (greek)''' || || \boldsymbol{\Alpha} \boldsymbol{\Beta} \boldsymbol{\Gamma} \boldsymbol{\Delta} \boldsymbol{\Epsilon} \boldsymbol{\Zeta} || $\boldsymbol\left\{\Alpha\right\} \boldsymbol\left\{\Beta\right\} \boldsymbol\left\{\Gamma\right\} \boldsymbol\left\{\Delta\right\} \boldsymbol\left\{\Epsilon\right\} \boldsymbol\left\{\Zeta\right\} \,\!$ || || \boldsymbol{\Eta} \boldsymbol{\Theta} \boldsymbol{\Iota} \boldsymbol{\Kappa} \boldsymbol{\Lambda} \boldsymbol{\Mu} || $\boldsymbol\left\{\Eta\right\} \boldsymbol\left\{\Theta\right\} \boldsymbol\left\{\Iota\right\} \boldsymbol\left\{\Kappa\right\} \boldsymbol\left\{\Lambda\right\} \boldsymbol\left\{\Mu\right\}\,\!$ || || \boldsymbol{\Nu} \boldsymbol{\Xi} \boldsymbol{\Pi} \boldsymbol{\Rho} \boldsymbol{\Sigma} \boldsymbol{\Tau} || $\boldsymbol\left\{\Nu\right\} \boldsymbol\left\{\Xi\right\} \boldsymbol\left\{\Pi\right\} \boldsymbol\left\{\Rho\right\} \boldsymbol\left\{\Sigma\right\} \boldsymbol\left\{\Tau\right\}\,\!$ || || \boldsymbol{\Upsilon} \boldsymbol{\Phi} \boldsymbol{\Chi} \boldsymbol{\Psi} \boldsymbol{\Omega} || $\boldsymbol\left\{\Upsilon\right\} \boldsymbol\left\{\Phi\right\} \boldsymbol\left\{\Chi\right\} \boldsymbol\left\{\Psi\right\} \boldsymbol\left\{\Omega\right\}\,\!$ || || \boldsymbol{\alpha} \boldsymbol{\beta} \boldsymbol{\gamma} \boldsymbol{\delta} \boldsymbol{\epsilon} \boldsymbol{\zeta} || $\boldsymbol\left\{\alpha\right\} \boldsymbol\left\{\beta\right\} \boldsymbol\left\{\gamma\right\} \boldsymbol\left\{\delta\right\} \boldsymbol\left\{\epsilon\right\} \boldsymbol\left\{\zeta\right\}\,\!$ || || \boldsymbol{\eta} \boldsymbol{\theta} \boldsymbol{\iota} \boldsymbol{\kappa} \boldsymbol{\lambda} \boldsymbol{\mu} || $\boldsymbol\left\{\eta\right\} \boldsymbol\left\{\theta\right\} \boldsymbol\left\{\iota\right\} \boldsymbol\left\{\kappa\right\} \boldsymbol\left\{\lambda\right\} \boldsymbol\left\{\mu\right\}\,\!$ || || \boldsymbol{\nu} \boldsymbol{\xi} \boldsymbol{\pi} \boldsymbol{\rho} \boldsymbol{\sigma} \boldsymbol{\tau} || $\boldsymbol\left\{\nu\right\} \boldsymbol\left\{\xi\right\} \boldsymbol\left\{\pi\right\} \boldsymbol\left\{\rho\right\} \boldsymbol\left\{\sigma\right\} \boldsymbol\left\{\tau\right\}\,\!$ || || \boldsymbol{\upsilon} \boldsymbol{\phi} \boldsymbol{\chi} \boldsymbol{\psi} \boldsymbol{\omega} || $\boldsymbol\left\{\upsilon\right\} \boldsymbol\left\{\phi\right\} \boldsymbol\left\{\chi\right\} \boldsymbol\left\{\psi\right\} \boldsymbol\left\{\omega\right\}\,\!$ || || \boldsymbol{\varepsilon} \boldsymbol{\digamma} \boldsymbol{\vartheta} \boldsymbol{\varkappa} || $\boldsymbol\left\{\varepsilon\right\} \boldsymbol\left\{\digamma\right\} \boldsymbol\left\{\vartheta\right\} \boldsymbol\left\{\varkappa\right\} \,\!$ || || \boldsymbol{\varpi} \boldsymbol{\varrho} \boldsymbol{\varsigma} \boldsymbol{\varphi} || $\boldsymbol\left\{\varpi\right\} \boldsymbol\left\{\varrho\right\} \boldsymbol\left\{\varsigma\right\} \boldsymbol\left\{\varphi\right\}\,\!$ || ||_\2. '''Italics''' || || \mathit{A} \mathit{B} \mathit{C} \mathit{D} \mathit{E} \mathit{F} \mathit{G} || $\mathit\left\{A\right\} \mathit\left\{B\right\} \mathit\left\{C\right\} \mathit\left\{D\right\} \mathit\left\{E\right\} \mathit\left\{F\right\} \mathit\left\{G\right\} \,\!$ || || \mathit{H} \mathit{I} \mathit{J} \mathit{K} \mathit{L} \mathit{M} || $\mathit\left\{H\right\} \mathit\left\{I\right\} \mathit\left\{J\right\} \mathit\left\{K\right\} \mathit\left\{L\right\} \mathit\left\{M\right\} \,\!$ || || \mathit{N} \mathit{O} \mathit{P} \mathit{Q} \mathit{R} \mathit{S} \mathit{T} || $\mathit\left\{N\right\} \mathit\left\{O\right\} \mathit\left\{P\right\} \mathit\left\{Q\right\} \mathit\left\{R\right\} \mathit\left\{S\right\} \mathit\left\{T\right\} \,\!$ || || \mathit{U} \mathit{V} \mathit{W} \mathit{X} \mathit{Y} \mathit{Z} || $\mathit\left\{U\right\} \mathit\left\{V\right\} \mathit\left\{W\right\} \mathit\left\{X\right\} \mathit\left\{Y\right\} \mathit\left\{Z\right\} \,\!$ || || \mathit{a} \mathit{b} \mathit{c} \mathit{d} \mathit{e} \mathit{f} \mathit{g} || $\mathit\left\{a\right\} \mathit\left\{b\right\} \mathit\left\{c\right\} \mathit\left\{d\right\} \mathit\left\{e\right\} \mathit\left\{f\right\} \mathit\left\{g\right\} \,\!$ || || \mathit{h} \mathit{i} \mathit{j} \mathit{k} \mathit{l} \mathit{m} || $\mathit\left\{h\right\} \mathit\left\{i\right\} \mathit\left\{j\right\} \mathit\left\{k\right\} \mathit\left\{l\right\} \mathit\left\{m\right\} \,\!$ || || \mathit{n} \mathit{o} \mathit{p} \mathit{q} \mathit{r} \mathit{s} \mathit{t} || $\mathit\left\{n\right\} \mathit\left\{o\right\} \mathit\left\{p\right\} \mathit\left\{q\right\} \mathit\left\{r\right\} \mathit\left\{s\right\} \mathit\left\{t\right\} \,\!$ || || \mathit{u} \mathit{v} \mathit{w} \mathit{x} \mathit{y} \mathit{z} || $\mathit\left\{u\right\} \mathit\left\{v\right\} \mathit\left\{w\right\} \mathit\left\{x\right\} \mathit\left\{y\right\} \mathit\left\{z\right\} \,\!$ || || \mathit{0} \mathit{1} \mathit{2} \mathit{3} \mathit{4} || $\mathit\left\{0\right\} \mathit\left\{1\right\} \mathit\left\{2\right\} \mathit\left\{3\right\} \mathit\left\{4\right\} \,\!$ || || \mathit{5} \mathit{6} \mathit{7} \mathit{8} \mathit{9} || $\mathit\left\{5\right\} \mathit\left\{6\right\} \mathit\left\{7\right\} \mathit\left\{8\right\} \mathit\left\{9\right\}\,\!$ || ||_\2. '''Roman typeface''' || || \mathrm{A} \mathrm{B} \mathrm{C} \mathrm{D} \mathrm{E} \mathrm{F} \mathrm{G} || $\mathrm\left\{A\right\} \mathrm\left\{B\right\} \mathrm\left\{C\right\} \mathrm\left\{D\right\} \mathrm\left\{E\right\} \mathrm\left\{F\right\} \mathrm\left\{G\right\} \,\!$ || || \mathrm{H} \mathrm{I} \mathrm{J} \mathrm{K} \mathrm{L} \mathrm{M} || $\mathrm\left\{H\right\} \mathrm\left\{I\right\} \mathrm\left\{J\right\} \mathrm\left\{K\right\} \mathrm\left\{L\right\} \mathrm\left\{M\right\} \,\!$ || || \mathrm{N} \mathrm{O} \mathrm{P} \mathrm{Q} \mathrm{R} \mathrm{S} \mathrm{T} || $\mathrm\left\{N\right\} \mathrm\left\{O\right\} \mathrm\left\{P\right\} \mathrm\left\{Q\right\} \mathrm\left\{R\right\} \mathrm\left\{S\right\} \mathrm\left\{T\right\} \,\!$ || || \mathrm{U} \mathrm{V} \mathrm{W} \mathrm{X} \mathrm{Y} \mathrm{Z} || $\mathrm\left\{U\right\} \mathrm\left\{V\right\} \mathrm\left\{W\right\} \mathrm\left\{X\right\} \mathrm\left\{Y\right\} \mathrm\left\{Z\right\} \,\!$ || || \mathrm{a} \mathrm{b} \mathrm{c} \mathrm{d} \mathrm{e} \mathrm{f} \mathrm{g} || $\mathrm\left\{a\right\} \mathrm\left\{b\right\} \mathrm\left\{c\right\} \mathrm\left\{d\right\} \mathrm\left\{e\right\} \mathrm\left\{f\right\} \mathrm\left\{g\right\}\,\!$ || || \mathrm{h} \mathrm{i} \mathrm{j} \mathrm{k} \mathrm{l} \mathrm{m} || $\mathrm\left\{h\right\} \mathrm\left\{i\right\} \mathrm\left\{j\right\} \mathrm\left\{k\right\} \mathrm\left\{l\right\} \mathrm\left\{m\right\} \,\!$ || || \mathrm{n} \mathrm{o} \mathrm{p} \mathrm{q} \mathrm{r} \mathrm{s} \mathrm{t} || $\mathrm\left\{n\right\} \mathrm\left\{o\right\} \mathrm\left\{p\right\} \mathrm\left\{q\right\} \mathrm\left\{r\right\} \mathrm\left\{s\right\} \mathrm\left\{t\right\} \,\!$ || || \mathrm{u} \mathrm{v} \mathrm{w} \mathrm{x} \mathrm{y} \mathrm{z} || $\mathrm\left\{u\right\} \mathrm\left\{v\right\} \mathrm\left\{w\right\} \mathrm\left\{x\right\} \mathrm\left\{y\right\} \mathrm\left\{z\right\} \,\!$ || || \mathrm{0} \mathrm{1} \mathrm{2} \mathrm{3} \mathrm{4} || $\mathrm\left\{0\right\} \mathrm\left\{1\right\} \mathrm\left\{2\right\} \mathrm\left\{3\right\} \mathrm\left\{4\right\} \,\!$ || || \mathrm{5} \mathrm{6} \mathrm{7} \mathrm{8} \mathrm{9} || $\mathrm\left\{5\right\} \mathrm\left\{6\right\} \mathrm\left\{7\right\} \mathrm\left\{8\right\} \mathrm\left\{9\right\}\,\!$ || ||_\2. '''Fraktur typeface''' || || \mathfrak{A} \mathfrak{B} \mathfrak{C} \mathfrak{D} \mathfrak{E} \mathfrak{F} \mathfrak{G} || $\mathfrak\left\{A\right\} \mathfrak\left\{B\right\} \mathfrak\left\{C\right\} \mathfrak\left\{D\right\} \mathfrak\left\{E\right\} \mathfrak\left\{F\right\} \mathfrak\left\{G\right\} \,\!$ || || \mathfrak{H} \mathfrak{I} \mathfrak{J} \mathfrak{K} \mathfrak{L} \mathfrak{M} || $\mathfrak\left\{H\right\} \mathfrak\left\{I\right\} \mathfrak\left\{J\right\} \mathfrak\left\{K\right\} \mathfrak\left\{L\right\} \mathfrak\left\{M\right\} \,\!$ || || \mathfrak{N} \mathfrak{O} \mathfrak{P} \mathfrak{Q} \mathfrak{R} \mathfrak{S} \mathfrak{T} || $\mathfrak\left\{N\right\} \mathfrak\left\{O\right\} \mathfrak\left\{P\right\} \mathfrak\left\{Q\right\} \mathfrak\left\{R\right\} \mathfrak\left\{S\right\} \mathfrak\left\{T\right\} \,\!$ || || \mathfrak{U} \mathfrak{V} \mathfrak{W} \mathfrak{X} \mathfrak{Y} \mathfrak{Z} || $\mathfrak\left\{U\right\} \mathfrak\left\{V\right\} \mathfrak\left\{W\right\} \mathfrak\left\{X\right\} \mathfrak\left\{Y\right\} \mathfrak\left\{Z\right\} \,\!$ || || \mathfrak{a} \mathfrak{b} \mathfrak{c} \mathfrak{d} \mathfrak{e} \mathfrak{f} \mathfrak{g} || $\mathfrak\left\{a\right\} \mathfrak\left\{b\right\} \mathfrak\left\{c\right\} \mathfrak\left\{d\right\} \mathfrak\left\{e\right\} \mathfrak\left\{f\right\} \mathfrak\left\{g\right\} \,\!$ || || \mathfrak{h} \mathfrak{i} \mathfrak{j} \mathfrak{k} \mathfrak{l} \mathfrak{m} || $\mathfrak\left\{h\right\} \mathfrak\left\{i\right\} \mathfrak\left\{j\right\} \mathfrak\left\{k\right\} \mathfrak\left\{l\right\} \mathfrak\left\{m\right\} \,\!$ || || \mathfrak{n} \mathfrak{o} \mathfrak{p} \mathfrak{q} \mathfrak{r} \mathfrak{s} \mathfrak{t} || $\mathfrak\left\{n\right\} \mathfrak\left\{o\right\} \mathfrak\left\{p\right\} \mathfrak\left\{q\right\} \mathfrak\left\{r\right\} \mathfrak\left\{s\right\} \mathfrak\left\{t\right\} \,\!$ || || \mathfrak{u} \mathfrak{v} \mathfrak{w} \mathfrak{x} \mathfrak{y} \mathfrak{z} || $\mathfrak\left\{u\right\} \mathfrak\left\{v\right\} \mathfrak\left\{w\right\} \mathfrak\left\{x\right\} \mathfrak\left\{y\right\} \mathfrak\left\{z\right\} \,\!$ || || \mathfrak{0} \mathfrak{1} \mathfrak{2} \mathfrak{3} \mathfrak{4} || $\mathfrak\left\{0\right\} \mathfrak\left\{1\right\} \mathfrak\left\{2\right\} \mathfrak\left\{3\right\} \mathfrak\left\{4\right\} \,\!$ || || \mathfrak{5} \mathfrak{6} \mathfrak{7} \mathfrak{8} \mathfrak{9} || $\mathfrak\left\{5\right\} \mathfrak\left\{6\right\} \mathfrak\left\{7\right\} \mathfrak\left\{8\right\} \mathfrak\left\{9\right\}\,\!$ || ||_\2. '''Calligraphy/Script''' || || \mathcal{A} \mathcal{B} \mathcal{C} \mathcal{D} \mathcal{E} \mathcal{F} \mathcal{G} || $\mathcal\left\{A\right\} \mathcal\left\{B\right\} \mathcal\left\{C\right\} \mathcal\left\{D\right\} \mathcal\left\{E\right\} \mathcal\left\{F\right\} \mathcal\left\{G\right\} \,\!$ || || \mathcal{H} \mathcal{I} \mathcal{J} \mathcal{K} \mathcal{L} \mathcal{M} || $\mathcal\left\{H\right\} \mathcal\left\{I\right\} \mathcal\left\{J\right\} \mathcal\left\{K\right\} \mathcal\left\{L\right\} \mathcal\left\{M\right\} \,\!$ || || \mathcal{N} \mathcal{O} \mathcal{P} \mathcal{Q} \mathcal{R} \mathcal{S} \mathcal{T} || $\mathcal\left\{N\right\} \mathcal\left\{O\right\} \mathcal\left\{P\right\} \mathcal\left\{Q\right\} \mathcal\left\{R\right\} \mathcal\left\{S\right\} \mathcal\left\{T\right\} \,\!$ || || \mathcal{U} \mathcal{V} \mathcal{W} \mathcal{X} \mathcal{Y} \mathcal{Z} || $\mathcal\left\{U\right\} \mathcal\left\{V\right\} \mathcal\left\{W\right\} \mathcal\left\{X\right\} \mathcal\left\{Y\right\} \mathcal\left\{Z\right\}\,\!$ || ||_\2. '''Hebrew''' || || \aleph \beth \gimel \daleth || $\aleph \beth \gimel \daleth\,\!$ || == Formatting issues == === Spacing === Note that TeX handles most spacing automatically, but you may sometimes want manual control. || '''Feature''' || '''Syntax''' || '''How it looks rendered''' || || double quad space || a \qquad b || $a \qquad b$ || || quad space || a \quad b || $a \quad b$ || || text space || a\ b || $a\ b$ || || text space without PNG conversion || a \mbox{ } b || $a \mbox\left\{ \right\} b$ || || large space || a\;b || $a\;b$ || || medium space || a\>b || (not supported) || || small space || a\,b || $a\,b$ || || no space || ab || $ab\,$ || || small negative space || a\!b || $a\!b$ ||