## Logic and Set Theory ||||| |:--------------------|:--------------------------|:----------------------------|:----- |$\forall$ `\forall` |$\complement$ `\complement`|$\therefore$ `\therefore` |$\emptyset$ `\emptyset` |$\exists$ `\exists` |$\subset$ `\subset` |$\because$ `\because` |$\empty$ `\empty` |$\exist$ `\exist` |$\supset$ `\supset` |$\mapsto$ `\mapsto` |$\varnothing$ `\varnothing` |$\nexists$ `\nexists`|$\mid$ `\mid` |$\to$ `\to` |$\implies$ `\implies` |$\in$ `\in` |$\land$ `\land` |$\gets$ `\gets` |$\impliedby$ `\impliedby` |$\isin$ `\isin` |$\lor$ `\lor` |$\leftrightarrow$ `\leftrightarrow`|$\iff$ `\iff` |$\notin$ `\notin` |$\ni$ `\ni` |$\notni$ `\notni` |$\neg$ `\neg` or `\lnot` Direct Input: $∀ ∴ ∁ ∵ ∃ ∣ ∈ ∉ ∋ ⊂ ⊃ ∧ ∨ ↦ → ← ↔ ¬$ ℂ ℍ ℕ ℙ ℚ ℝ ## Macros ||| |:-------------------------------------|:------ |$\def\foo{x^2} \foo + \foo$ | `\def\foo{x^2} \foo + \foo` |$\gdef\bar#1{#1^2} \bar{y} + \bar{y}$ | `\gdef\bar#1{#1^2} \bar{y} + \bar{y}` | | `\edef\macroname#1#2…{definition to be expanded}` | | `\xdef\macroname#1#2…{definition to be expanded}` | | `\let\foo=\bar` | | `\futurelet\foo\bar x` | | `\global\def\macroname#1#2…{definition}` | | `\newcommand\macroname[numargs]{definition}` | | `\renewcommand\macroname[numargs]{definition}` | | `\providecommand\macroname[numargs]{definition}` Macros can also be defined in the KaTeX [rendering options](options.md). Macros accept up to nine arguments: #1, #2, etc.

Macros defined by `\gdef`, `\xdef`, `\global\def`, `\global\edef`, `\global\let`, and `\global\futurelet` will persist between math expressions. (Exception: macro persistence may be disabled. There are legitimate security reasons for that.) KaTeX has no `\par`, so all macros are long by default and `\long` will be ignored. Available functions include: `\char` `\mathchoice` `\TextOrMath` `\@ifstar` `\@ifnextchar` `\@firstoftwo` `\@secondoftwo` `\relax` `\expandafter` `\noexpand` @ is a valid character for commands, as if `\makeatletter` were in effect. ## Operators ### Big Operators ||||| |------------------|-------------------------|--------------------------|--------------| | $\sum$ `\sum` | $\prod$ `\prod` | $\bigotimes$ `\bigotimes`| $\bigvee$ `\bigvee` | $\int$ `\int` | $\coprod$ `\coprod` | $\bigoplus$ `\bigoplus` | $\bigwedge$ `\bigwedge` | $\iint$ `\iint` | $\intop$ `\intop` | $\bigodot$ `\bigodot` | $\bigcap$ `\bigcap` | $\iiint$ `\iiint`| $\smallint$ `\smallint` | $\biguplus$ `\biguplus` | $\bigcup$ `\bigcup` | $\oint$ `\oint` | $\oiint$ `\oiint` | $\oiiint$ `\oiiint` | $\bigsqcup$ `\bigsqcup` Direct Input: $∫ ∬ ∭ ∮ ∏ ∐ ∑ ⋀ ⋁ ⋂ ⋃ ⨀ ⨁ ⨂ ⨄ ⨆$ ∯ ∰ ### Binary Operators ||||| |-------------|-------------------|-------------------|--------------------| | $+$ `+`| $\cdot$ `\cdot` | $\gtrdot$ `\gtrdot`| $x \pmod a$ `x \pmod a`| | $-$ `-`| $\cdotp$ `\cdotp` | $\intercal$ `\intercal` | $x \pod a$ `x \pod a` | | $/$ `/`| $\centerdot$ `\centerdot`| $\land$ `\land` | $\rhd$ `\rhd` | | $*$ `*`| $\circ$ `\circ` | $\leftthreetimes$ `\leftthreetimes` | $\rightthreetimes$ `\rightthreetimes` | | $\amalg$ `\amalg` | $\circledast$ `\circledast` | $\ldotp$ `\ldotp` | $\rtimes$ `\rtimes` | | $\And$ `\And`| $\circledcirc$ `\circledcirc` | $\lor$ `\lor`| $\setminus$ `\setminus` | | $\ast$ `\ast`| $\circleddash$ `\circleddash` | $\lessdot$ `\lessdot` | $\smallsetminus$ `\smallsetminus`| | $\barwedge$ `\barwedge` | $\Cup$ `\Cup`| $\lhd$ `\lhd`| $\sqcap$ `\sqcap` | | $\bigcirc$ `\bigcirc` | $\cup$ `\cup`| $\ltimes$ `\ltimes`| $\sqcup$ `\sqcup` | | $\bmod$ `\bmod` | $\curlyvee$ `\curlyvee` | $x \mod a$ `x\mod a`| $\times$ `\times` | | $\boxdot$ `\boxdot`| $\curlywedge$ `\curlywedge` | $\mp$ `\mp` | $\unlhd$ `\unlhd` | | $\boxminus$ `\boxminus` | $\div$ `\div`| $\odot$ `\odot` | $\unrhd$ `\unrhd` | | $\boxplus$ `\boxplus` | $\divideontimes$ `\divideontimes` | $\ominus$ `\ominus`| $\uplus$ `\uplus` | | $\boxtimes$ `\boxtimes` | $\dotplus$ `\dotplus` | $\oplus$ `\oplus` | $\vee$ `\vee` | | $\bullet$ `\bullet`| $\doublebarwedge$ `\doublebarwedge` | $\otimes$ `\otimes`| $\veebar$ `\veebar` | | $\Cap$ `\Cap`| $\doublecap$ `\doublecap`| $\oslash$ `\oslash`| $\wedge$ `\wedge` | | $\cap$ `\cap`| $\doublecup$ `\doublecup`| $\pm$ `\pm` or `\plusmn` | $\wr$ `\wr` | Direct Input: $+ - / * ⋅ ± × ÷ ∓ ∔ ∧ ∨ ∩ ∪ ≀ ⊎ ⊓ ⊔ ⊕ ⊖ ⊗ ⊘ ⊙ ⊚ ⊛ ⊝ ◯$ ### Fractions and Binomials |||| |:--------------------------|:----------------------------|:----- |$\frac{a}{b}$ `\frac{a}{b}`|$\tfrac{a}{b}$ `\tfrac{a}{b}`|$\genfrac ( ] {2pt}{1}a{a+1}$ `\genfrac ( ] {2pt}{1}a{a+1}` |${a \over b}$ `{a \over b}`|$\dfrac{a}{b}$ `\dfrac{a}{b}`|${a \above{2pt} b+1}$ `{a \above{2pt} b+1}` |$a/b$ `a/b` | |$\cfrac{a}{1 + \cfrac{1}{b}}$ `\cfrac{a}{1 + \cfrac{1}{b}}` |||| |:------------------------------|:------------------------------|:-------- |$\binom{n}{k}$ `\binom{n}{k}` |$\dbinom{n}{k}$ `\dbinom{n}{k}`|${n\brace k}$ `{n\brace k}` |${n \choose k}$ `{n \choose k}`|$\tbinom{n}{k}$ `\tbinom{n}{k}`|${n\brack k}$ `{n\brack k}` ### Math Operators ||||| |:--------------------|:--------------------|:----------------|:--------------| | $\arcsin$ `\arcsin` | $\cosec$ `\cosec` | $\deg$ `\deg` | $\sec$ `\sec` | | $\arccos$ `\arccos` | $\cosh$ `\cosh` | $\dim$ `\dim` | $\sin$ `\sin` | | $\arctan$ `\arctan` | $\cot$ `\cot` | $\exp$ `\exp` | $\sinh$ `\sinh` | | $\arctg$ `\arctg` | $\cotg$ `\cotg` | $\hom$ `\hom` | $\sh$ `\sh` | | $\arcctg$ `\arcctg` | $\coth$ `\coth` | $\ker$ `\ker` | $\tan$ `\tan` | | $\arg$ `\arg` | $\csc$ `\csc` | $\lg$ `\lg` | $\tanh$ `\tanh` | | $\ch$ `\ch` | $\ctg$ `\ctg` | $\ln$ `\ln` | $\tg$ `\tg` | | $\cos$ `\cos` | $\cth$ `\cth` | $\log$ `\log` | $\th$ `\th` | | $\operatorname{f}$ `\operatorname{f}` | ||| | $\argmax$ `\argmax` | $\injlim$ `\injlim` | $\min$ `\min` | $\varinjlim$ `\varinjlim` | | $\argmin$ `\argmin` | $\lim$ `\lim` | $\plim$ `\plim` | $\varliminf$ `\varliminf` | | $\det$ `\det` | $\liminf$ `\liminf` | $\Pr$ `\Pr` | $\varlimsup$ `\varlimsup` | | $\gcd$ `\gcd` | $\limsup$ `\limsup` | $\projlim$ `\projlim` | $\varprojlim$ `\varprojlim` | | $\inf$ `\inf` | $\max$ `\max` | $\sup$ `\sup` |$\operatorname*{f}$ `\operatorname*{f}`| Functions in the bottom five rows of this table can take `\limits`. ### \sqrt $\sqrt{x}$ `\sqrt{x}` $\sqrt[3]{x}$ `\sqrt[3]{x}` ## Relations $\stackrel{!}{=}$ `\stackrel{!}{=}` ||||| |:--------|:------------------------|:----------------------------|:------------------| | $=$ `=` | $\doteqdot$ `\doteqdot` | $\lessapprox$ `\lessapprox` | $\smile$ `\smile` | | $<$ `<` | $\eqcirc$ `\eqcirc` | $\lesseqgtr$ `\lesseqgtr` | $\sqsubset$ `\sqsubset` | | $>$ `>` | $\eqcolon$ `\eqcolon` or
    `\minuscolon` | $\lesseqqgtr$ `\lesseqqgtr` | $\sqsubseteq$ `\sqsubseteq` | | $:$ `:` | $\Eqcolon$ `\Eqcolon` or
    `\minuscoloncolon` | $\lessgtr$ `\lessgtr` | $\sqsupset$ `\sqsupset` | | $\approx$ `\approx` | $\eqqcolon$ `\eqqcolon` or
    `\equalscolon` | $\lesssim$ `\lesssim` | $\sqsupseteq$ `\sqsupseteq` | | $\approxcolon$ `\approxcolon` | $\Eqqcolon$ `\Eqqcolon` or
    `\equalscoloncolon` | $\ll$ `\ll` | $\Subset$ `\Subset` | | $\approxcoloncolon$ `\approxcoloncolon` | $\eqsim$ `\eqsim` | $\lll$ `\lll` | $\subset$ `\subset` or `\sub` | | $\approxeq$ `\approxeq` | $\eqslantgtr$ `\eqslantgtr` | $\llless$ `\llless` | $\subseteq$ `\subseteq` or `\sube` | | $\asymp$ `\asymp` | $\eqslantless$ `\eqslantless` | $\lt$ `\lt` | $\subseteqq$ `\subseteqq` | | $\backepsilon$ `\backepsilon` | $\equiv$ `\equiv` | $\mid$ `\mid` | $\succ$ `\succ` | | $\backsim$ `\backsim` | $\fallingdotseq$ `\fallingdotseq` | $\models$ `\models` | $\succapprox$ `\succapprox` | | $\backsimeq$ `\backsimeq` | $\frown$ `\frown` | $\multimap$ `\multimap` | $\succcurlyeq$ `\succcurlyeq` | | $\between$ `\between` | $\ge$ `\ge` | $\origof$ `\origof` | $\succeq$ `\succeq` | | $\bowtie$ `\bowtie` | $\geq$ `\geq` | $\owns$ `\owns` | $\succsim$ `\succsim` | | $\bumpeq$ `\bumpeq` | $\geqq$ `\geqq` | $\parallel$ `\parallel` | $\Supset$ `\Supset` | | $\Bumpeq$ `\Bumpeq` | $\geqslant$ `\geqslant` | $\perp$ `\perp` | $\supset$ `\supset` | | $\circeq$ `\circeq` | $\gg$ `\gg` | $\pitchfork$ `\pitchfork` | $\supseteq$ `\supseteq` or `\supe` | | $\colonapprox$ `\colonapprox` | $\ggg$ `\ggg` | $\prec$ `\prec` | $\supseteqq$ `\supseteqq` | | $\Colonapprox$ `\Colonapprox` or
    `\coloncolonapprox` | $\gggtr$ `\gggtr` | $\precapprox$ `\precapprox` | $\thickapprox$ `\thickapprox` | | $\coloneq$ `\coloneq` or
    `\colonminus` | $\gt$ `\gt` | $\preccurlyeq$ `\preccurlyeq` | $\thicksim$ `\thicksim` | | $\Coloneq$ `\Coloneq` or
    `\coloncolonminus` | $\gtrapprox$ `\gtrapprox` | $\preceq$ `\preceq` | $\trianglelefteq$ `\trianglelefteq` | | $\coloneqq$ `\coloneqq` or
   `\colonequals` | $\gtreqless$ `\gtreqless` | $\precsim$ `\precsim` | $\triangleq$ `\triangleq` | | $\Coloneqq$ `\Coloneqq` or
    `\coloncolonequals` | $\gtreqqless$ `\gtreqqless` | $\propto$ `\propto` | $\trianglerighteq$ `\trianglerighteq` | | $\colonsim$ `\colonsim` | $\gtrless$ `\gtrless` | $\risingdotseq$ `\risingdotseq` | $\varpropto$ `\varpropto` | | $\Colonsim$ `\Colonsim` or
    `\coloncolonsim` | $\gtrsim$ `\gtrsim` | $\shortmid$ `\shortmid` | $\vartriangle$ `\vartriangle` | | $\cong$ `\cong` | $\imageof$ `\imageof` | $\shortparallel$ `\shortparallel` | $\vartriangleleft$ `\vartriangleleft` | | $\curlyeqprec$ `\curlyeqprec` | $\in$ `\in` or `\isin` | $\sim$ `\sim` | $\vartriangleright$ `\vartriangleright` | | $\curlyeqsucc$ `\curlyeqsucc` | $\Join$ `\Join` | $\simcolon$ `\simcolon` | $\vcentcolon$ `\vcentcolon` or
   `\ratio` | | $\dashv$ `\dashv` | $\le$ `\le` | $\simcoloncolon$ `\simcoloncolon` | $\vdash$ `\vdash` | | $\dblcolon$ `\dblcolon` or
   `\coloncolon` | $\leq$ `\leq` | $\simeq$ `\simeq` | $\vDash$ `\vDash` | | $\doteq$ `\doteq` | $\leqq$ `\leqq` | $\smallfrown$ `\smallfrown` | $\Vdash$ `\Vdash` | | $\Doteq$ `\Doteq` | $\leqslant$ `\leqslant` | $\smallsmile$ `\smallsmile` | $\Vvdash$ `\Vvdash` | Direct Input: $= < > : ∈ ∋ ∝ ∼ ∽ ≂ ≃ ≅ ≈ ≊ ≍ ≎ ≏ ≐ ≑ ≒ ≓ ≖ ≗ ≜ ≡ ≤ ≥ ≦ ≧ ≫ ≬ ≳ ≷ ≺ ≻ ≼ ≽ ≾ ≿ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ⊩ ⊪ ⊸ ⋈ ⋍ ⋐ ⋑ ⋔ ⋙ ⋛ ⋞ ⋟ ⌢ ⌣ ⩾ ⪆ ⪌ ⪕ ⪖ ⪯ ⪰ ⪷ ⪸ ⫅ ⫆ ≲ ⩽ ⪅ ≶ ⋚ ⪋ ⟂ ⊨ ⊶ ⊷$ `≔ ≕ ⩴` ### Negated Relations $\not =$ `\not =` ||||| |--------------|-------------------|---------------------|------------------| | $\gnapprox$ `\gnapprox` | $\ngeqslant$ `\ngeqslant`| $\nsubseteq$ `\nsubseteq` | $\precneqq$ `\precneqq`| | $\gneq$ `\gneq`| $\ngtr$ `\ngtr` | $\nsubseteqq$ `\nsubseteqq` | $\precnsim$ `\precnsim`| | $\gneqq$ `\gneqq` | $\nleq$ `\nleq` | $\nsucc$ `\nsucc`| $\subsetneq$ `\subsetneq` | | $\gnsim$ `\gnsim` | $\nleqq$ `\nleqq` | $\nsucceq$ `\nsucceq` | $\subsetneqq$ `\subsetneqq` | | $\gvertneqq$ `\gvertneqq` | $\nleqslant$ `\nleqslant`| $\nsupseteq$ `\nsupseteq` | $\succnapprox$ `\succnapprox`| | $\lnapprox$ `\lnapprox` | $\nless$ `\nless` | $\nsupseteqq$ `\nsupseteqq` | $\succneqq$ `\succneqq`| | $\lneq$ `\lneq`| $\nmid$ `\nmid` | $\ntriangleleft$ `\ntriangleleft` | $\succnsim$ `\succnsim`| | $\lneqq$ `\lneqq` | $\notin$ `\notin` | $\ntrianglelefteq$ `\ntrianglelefteq` | $\supsetneq$ `\supsetneq` | | $\lnsim$ `\lnsim` | $\notni$ `\notni` | $\ntriangleright$ `\ntriangleright`| $\supsetneqq$ `\supsetneqq` | | $\lvertneqq$ `\lvertneqq` | $\nparallel$ `\nparallel`| $\ntrianglerighteq$ `\ntrianglerighteq` | $\varsubsetneq$ `\varsubsetneq` | | $\ncong$ `\ncong` | $\nprec$ `\nprec` | $\nvdash$ `\nvdash` | $\varsubsetneqq$ `\varsubsetneqq` | | $\ne$ `\ne` | $\npreceq$ `\npreceq` | $\nvDash$ `\nvDash` | $\varsupsetneq$ `\varsupsetneq` | | $\neq$ `\neq` | $\nshortmid$ `\nshortmid`| $\nVDash$ `\nVDash` | $\varsupsetneqq$ `\varsupsetneqq` | | $\ngeq$ `\ngeq`| $\nshortparallel$ `\nshortparallel` | $\nVdash$ `\nVdash` | | $\ngeqq$ `\ngeqq` | $\nsim$ `\nsim` | $\precnapprox$ `\precnapprox`| Direct Input: $∉ ∌ ∤ ∦ ≁ ≆ ≠ ≨ ≩ ≮ ≯ ≰ ≱ ⊀ ⊁ ⊈ ⊉ ⊊ ⊋ ⊬ ⊭ ⊮ ⊯ ⋠ ⋡ ⋦ ⋧ ⋨ ⋩ ⋬ ⋭ ⪇ ⪈ ⪉ ⪊ ⪵ ⪶ ⪹ ⪺ ⫋ ⫌$ ### Arrows |||| |:----------|:----------|:----------| |$\circlearrowleft$ `\circlearrowleft`|$\leftharpoonup$ `\leftharpoonup`|$\rArr$ `\rArr` |$\circlearrowright$ `\circlearrowright`|$\leftleftarrows$ `\leftleftarrows`|$\rarr$ `\rarr` |$\curvearrowleft$ `\curvearrowleft`|$\leftrightarrow$ `\leftrightarrow`|$\restriction$ `\restriction` |$\curvearrowright$ `\curvearrowright`|$\Leftrightarrow$ `\Leftrightarrow`|$\rightarrow$ `\rightarrow` |$\Darr$ `\Darr`|$\leftrightarrows$ `\leftrightarrows`|$\Rightarrow$ `\Rightarrow` |$\dArr$ `\dArr`|$\leftrightharpoons$ `\leftrightharpoons`|$\rightarrowtail$ `\rightarrowtail` |$\darr$ `\darr`|$\leftrightsquigarrow$ `\leftrightsquigarrow`|$\rightharpoondown$ `\rightharpoondown` |$\dashleftarrow$ `\dashleftarrow`|$\Lleftarrow$ `\Lleftarrow`|$\rightharpoonup$ `\rightharpoonup` |$\dashrightarrow$ `\dashrightarrow`|$\longleftarrow$ `\longleftarrow`|$\rightleftarrows$ `\rightleftarrows` |$\downarrow$ `\downarrow`|$\Longleftarrow$ `\Longleftarrow`|$\rightleftharpoons$ `\rightleftharpoons` |$\Downarrow$ `\Downarrow`|$\longleftrightarrow$ `\longleftrightarrow`|$\rightrightarrows$ `\rightrightarrows` |$\downdownarrows$ `\downdownarrows`|$\Longleftrightarrow$ `\Longleftrightarrow`|$\rightsquigarrow$ `\rightsquigarrow` |$\downharpoonleft$ `\downharpoonleft`|$\longmapsto$ `\longmapsto`|$\Rrightarrow$ `\Rrightarrow` |$\downharpoonright$ `\downharpoonright`|$\longrightarrow$ `\longrightarrow`|$\Rsh$ `\Rsh` |$\gets$ `\gets`|$\Longrightarrow$ `\Longrightarrow`|$\searrow$ `\searrow` |$\Harr$ `\Harr`|$\looparrowleft$ `\looparrowleft`|$\swarrow$ `\swarrow` |$\hArr$ `\hArr`|$\looparrowright$ `\looparrowright`|$\to$ `\to` |$\harr$ `\harr`|$\Lrarr$ `\Lrarr`|$\twoheadleftarrow$ `\twoheadleftarrow` |$\hookleftarrow$ `\hookleftarrow`|$\lrArr$ `\lrArr`|$\twoheadrightarrow$ `\twoheadrightarrow` |$\hookrightarrow$ `\hookrightarrow`|$\lrarr$ `\lrarr`|$\Uarr$ `\Uarr` |$\iff$ `\iff`|$\Lsh$ `\Lsh`|$\uArr$ `\uArr` |$\impliedby$ `\impliedby`|$\mapsto$ `\mapsto`|$\uarr$ `\uarr` |$\implies$ `\implies`|$\nearrow$ `\nearrow`|$\uparrow$ `\uparrow` |$\Larr$ `\Larr`|$\nleftarrow$ `\nleftarrow`|$\Uparrow$ `\Uparrow` |$\lArr$ `\lArr`|$\nLeftarrow$ `\nLeftarrow`|$\updownarrow$ `\updownarrow` |$\larr$ `\larr`|$\nleftrightarrow$ `\nleftrightarrow`|$\Updownarrow$ `\Updownarrow` |$\leadsto$ `\leadsto`|$\nLeftrightarrow$ `\nLeftrightarrow`|$\upharpoonleft$ `\upharpoonleft` |$\leftarrow$ `\leftarrow`|$\nrightarrow$ `\nrightarrow`|$\upharpoonright$ `\upharpoonright` |$\Leftarrow$ `\Leftarrow`|$\nRightarrow$ `\nRightarrow`|$\upuparrows$ `\upuparrows` |$\leftarrowtail$ `\leftarrowtail`|$\nwarrow$ `\nwarrow` |$\leftharpoondown$ `\leftharpoondown`|$\Rarr$ `\Rarr` Direct Input: $← ↑ → ↓ ↔ ↕ ↖ ↗ ↘ ↙ ↚ ↛ ↞ ↠ ↢ ↣ ↦ ↩ ↪ ↫ ↬ ↭ ↮ ↰ ↱↶ ↷ ↺ ↻ ↼ ↽ ↾ ↾ ↿ ⇀ ⇁ ⇂ ⇃ ⇄ ⇆ ⇇ ⇈ ⇉ ⇊ ⇋ ⇌⇍ ⇎ ⇏ ⇐ ⇑ ⇒ ⇓ ⇔ ⇕ ⇚ ⇛ ⇝ ⇠ ⇢ ⟵ ⟶ ⟷ ⟸ ⟹ ⟺ ⟼$ ↽ **Extensible Arrows** ||| |:----------------------------------------------------|:----- |$\xleftarrow{abc}$ `\xleftarrow{abc}` |$\xrightarrow[under]{over}$ `\xrightarrow[under]{over}` |$\xLeftarrow{abc}$ `\xLeftarrow{abc}` |$\xRightarrow{abc}$ `\xRightarrow{abc}` |$\xleftrightarrow{abc}$ `\xleftrightarrow{abc}` |$\xLeftrightarrow{abc}$ `\xLeftrightarrow{abc}` |$\xhookleftarrow{abc}$ `\xhookleftarrow{abc}` |$\xhookrightarrow{abc}$ `\xhookrightarrow{abc}` |$\xtwoheadleftarrow{abc}$ `\xtwoheadleftarrow{abc}` |$\xtwoheadrightarrow{abc}$ `\xtwoheadrightarrow{abc}` |$\xleftharpoonup{abc}$ `\xleftharpoonup{abc}` |$\xrightharpoonup{abc}$ `\xrightharpoonup{abc}` |$\xleftharpoondown{abc}$ `\xleftharpoondown{abc}` |$\xrightharpoondown{abc}$ `\xrightharpoondown{abc}` |$\xleftrightharpoons{abc}$ `\xleftrightharpoons{abc}`|$\xrightleftharpoons{abc}$ `\xrightleftharpoons{abc}` |$\xtofrom{abc}$ `\xtofrom{abc}` |$\xmapsto{abc}$ `\xmapsto{abc}` |$\xlongequal{abc}$ `\xlongequal{abc}` Extensible arrows all can take an optional argument in the same manner
as `\xrightarrow[under]{over}`. ## Special Notation **Bra-ket Notation** |||| |:----------|:----------|:----------| |$\bra{\phi}$ `\bra{\phi}` |$\ket{\psi}$ `\ket{\psi}` |$\braket{\phi\vert\psi}$ `\braket{\phi\vert\psi}` | |$\Bra{\phi}$ `\Bra{\phi}` |$\Ket{\psi}$ `\Ket{\psi}` || ## Style, Color, Size, and Font **Class Assignment** `\mathbin` `\mathclose` `\mathinner` `\mathop`
`\mathopen` `\mathord` `\mathpunct` `\mathrel` **Color** $\color{blue} F=ma$ `\color{blue} F=ma` Note that `\color` acts like a switch. Other color functions expect the content to be a function argument: $\textcolor{blue}{F=ma}$ `\textcolor{blue}{F=ma}`
$\textcolor{#228B22}{F=ma}$ `\textcolor{#228B22}{F=ma}`
$\colorbox{aqua}{$F=ma$}$ `\colorbox{aqua}{$F=ma$}`
$\fcolorbox{red}{aqua}{$F=ma$}$ `\fcolorbox{red}{aqua}{$F=ma$}` Note that, as in LaTeX, `\colorbox` & `\fcolorbox` renders its third argument as text, so you may want to switch back to math mode with `$` as in the examples above. For color definition, KaTeX color functions will accept the standard HTML [predefined color names](https://developer.mozilla.org/en-US/docs/Web/CSS/color_value#Color_keywords). They will also accept an RGB argument in CSS hexadecimal style. The "#" is optional before a six-digit specification. **Font** |||| |:------------------------------|:------------------------------|:----- |$\mathrm{Ab0}$ `\mathrm{Ab0}` |$\mathbf{Ab0}$ `\mathbf{Ab0}` |$\mathit{Ab0}$ `\mathit{Ab0}` |$\mathnormal{Ab0}$ `\mathnormal{Ab0}`|$\textbf{Ab0}$ `\textbf{Ab0}` |$\textit{Ab0}$ `\textit{Ab0}` |$\textrm{Ab0}$ `\textrm{Ab0}` |$\bf Ab0$ `\bf Ab0` |$\it Ab0$ `\it Ab0` |$\rm Ab0$ `\rm Ab0` |$\bold{Ab0}$ `\bold{Ab0}` |$\textup{Ab0}$ `\textup{Ab0}` |$\textnormal{Ab0}$ `\textnormal{Ab0}`|$\boldsymbol{Ab0}$ `\boldsymbol{Ab}`|$\Bbb{AB}$ `\Bbb{AB}` |$\text{Ab0}$ `\text{Ab0}` |$\bm{Ab0}$ `\bm{Ab0}` |$\mathbb{AB}$ `\mathbb{AB}` |$\mathsf{Ab0}$ `\mathsf{Ab0}` |$\textmd{Ab0}$ `\textmd{Ab0}` |$\frak{Ab0}$ `\frak{Ab0}` |$\textsf{Ab0}$ `\textsf{Ab0}` |$\mathtt{Ab0}$ `\mathtt{Ab0}` |$\mathfrak{Ab0}$ `\mathfrak{Ab0}` |$\sf Ab0$ `\sf Ab0` |$\texttt{Ab0}$ `\texttt{Ab0}` |$\mathcal{AB0}$ `\mathcal{AB0}` | |$\tt Ab0$ `\tt Ab0` |$\cal AB0$ `\cal AB0` | | |$\mathscr{AB}$ `\mathscr{AB}` One can stack font family, font weight, and font shape by using the `\textXX` versions of the font functions. So `\textsf{\textbf{H}}` will produce $\textsf{\textbf{H}}$. The other versions do not stack, e.g., `\mathsf{\mathbf{H}}` will produce $\mathsf{\mathbf{H}}$. In cases where KaTeX fonts do not have a bold glyph, `\pmb` can simulate one. For example, `\pmb{\mu}` renders as : $\pmb{\mu}$ **Size** ||| |:----------------------|:----- |$\Huge AB$ `\Huge AB` |$\normalsize AB$ `\normalsize AB` |$\huge AB$ `\huge AB` |$\small AB$ `\small AB` |$\LARGE AB$ `\LARGE AB`|$\footnotesize AB$ `\footnotesize AB` |$\Large AB$ `\Large AB`|$\scriptsize AB$ `\scriptsize AB` |$\large AB$ `\large AB`|$\tiny AB$ `\tiny AB` **Style** || |:-------------------------------------------------------| |$\displaystyle\sum_{i=1}^n$ `\displaystyle\sum_{i=1}^n` |$\textstyle\sum_{i=1}^n$ `\textstyle\sum_{i=1}^n` |$\scriptstyle x$ `\scriptstyle x`         (The size of a first sub/superscript) |$\scriptscriptstyle x$ `\scriptscriptstyle x` (The size of subsequent sub/superscripts) |$\lim\limits_x$ `\lim\limits_x` |$\lim\nolimits_x$ `\lim\nolimits_x` |$\verb!x^2!$ `\verb!x^2!` `\text{…}` will accept nested `$…$` fragments and render them in math mode. ## Symbols and Punctuation |||| |:----------|:----------|:----------| |`% comment`|$\dots$ `\dots`|$\KaTeX$ `\KaTeX` |$\%$ `\%`|$\cdots$ `\cdots`|$\LaTeX$ `\LaTeX` |$\#$ `\#`|$\ddots$ `\ddots`|$\TeX$ `\TeX` |$\&$ `\&`|$\ldots$ `\ldots`|$\nabla$ `\nabla` |$\_$ `\_`|$\vdots$ `\vdots`|$\infty$ `\infty` |$\text{\textunderscore}$ `\text{\textunderscore}`|$\dotsb$ `\dotsb`|$\infin$ `\infin` |$\text{--}$ `\text{--}`|$\dotsc$ `\dotsc`|$\checkmark$ `\checkmark` |$\text{\textendash}$ `\text{\textendash}`|$\dotsi$ `\dotsi`|$\dag$ `\dag` |$\text{---}$ `\text{---}`|$\dotsm$ `\dotsm`|$\dagger$ `\dagger` |$\text{\textemdash}$ `\text{\textemdash}`|$\dotso$ `\dotso`|$\text{\textdagger}$ `\text{\textdagger}` |$\text{\textasciitilde}$ `\text{\textasciitilde}`|$\sdot$ `\sdot`|$\ddag$ `\ddag` |$\text{\textasciicircum}$ `\text{\textasciicircum}`|$\mathellipsis$ `\mathellipsis`|$\ddagger$ `\ddagger` |$`$ `|$\text{\textellipsis}$ `\text{\textellipsis}`|$\text{\textdaggerdbl}$ `\text{\textdaggerdbl}` |$\text{\textquoteleft}$ `text{\textquoteleft}`|$\Box$ `\Box`|$\Dagger$ `\Dagger` |$\lq$ `\lq`|$\square$ `\square`|$\angle$ `\angle` |$\text{\textquoteright}$ `\text{\textquoteright}`|$\blacksquare$ `\blacksquare`|$\measuredangle$ `\measuredangle` |$\rq$ `\rq`|$\triangle$ `\triangle`|$\sphericalangle$ `\sphericalangle` |$\text{\textquotedblleft}$ `\text{\textquotedblleft}`|$\triangledown$ `\triangledown`|$\top$ `\top` |$"$ `"`|$\triangleleft$ `\triangleleft`|$\bot$ `\bot` |$\text{\textquotedblright}$ `\text{\textquotedblright}`|$\triangleright$ `\triangleright`|$\$$ `\$` |$\colon$ `\colon`|$\bigtriangledown$ `\bigtriangledown`|$\text{\textdollar}$ `\text{\textdollar}` |$\backprime$ `\backprime`|$\bigtriangleup$ `\bigtriangleup`|$\pounds$ `\pounds` |$\prime$ `\prime`|$\blacktriangle$ `\blacktriangle`|$\mathsterling$ `\mathsterling` |$\text{\textless}$ `\text{\textless}`|$\blacktriangledown$ `\blacktriangledown`|$\text{\textsterling}$ `\text{\textsterling}` |$\text{\textgreater}$ `\text{\textgreater}`|$\blacktriangleleft$ `\blacktriangleleft`|$\yen$ `\yen` |$\text{\textbar}$ `\text{\textbar}`|$\blacktriangleright$ `\blacktriangleright`|$\surd$ `\surd` |$\text{\textbardbl}$ `\text{\textbardbl}`|$\diamond$ `\diamond`|$\degree$ `\degree` |$\text{\textbraceleft}$ `\text{\textbraceleft}`|$\Diamond$ `\Diamond`|$\text{\textdegree}$ `\text{\textdegree}` |$\text{\textbraceright}$ `\text{\textbraceright}`|$\lozenge$ `\lozenge`|$\mho$ `\mho` |$\text{\textbackslash}$ `\text{\textbackslash}`|$\blacklozenge$ `\blacklozenge`|$\diagdown$ `\diagdown` |$\text{\P}$ `\text{\P}`|$\star$ `\star`|$\diagup$ `\diagup` |$\text{\S}$ `\text{\S}`|$\bigstar$ `\bigstar`|$\flat$ `\flat` |$\text{\sect}$ `\text{\sect}`|$\clubsuit$ `\clubsuit`|$\natural$ `\natural` |$\copyright$ `\copyright`|$\clubs$ `\clubs`|$\sharp$ `\sharp` |$\circledR$ `\circledR`|$\diamondsuit$ `\diamondsuit`|$\heartsuit$ `\heartsuit` |$\text{\textregistered}$ `\text{\textregistered}`|$\diamonds$ `\diamonds`|$\hearts$ `\hearts` |$\circledS$ `\circledS`|$\spadesuit$ `\spadesuit`|$\spades$ `\spades` |$\text{\textcircled a}$ `\text{\textcircled a}`|$\maltese$ `\maltese`|$\minuso$ `\minuso`| Direct Input: $£ ¥ ∇ ∞ · ∠ ∡ ∢ ♠ ♡ ♢ ♣ ♭ ♮ ♯ ✓ … ⋮ ⋯ ⋱ !$ ‼ ⦵ ## Units In KaTeX, units are proportioned as they are in TeX.
KaTeX units are different than CSS units.