It has been suggested that this article be merged into Glossary of mathematical symbols. (Discuss) Proposed since August 2023.

The following list of mathematical symbols by subject features a selection of the most common symbols used in modern mathematical notation within formulas, grouped by mathematical topic. As it is impossible to know if a complete list existing today of all symbols used in history is a representation of all ever used in history, as this would necessitate knowing if extant records are of all usages, only those symbols which occur often in mathematics or mathematics education are included. Many of the characters are standardized, for example in DIN 1302 General mathematical symbols or DIN EN ISO 80000-2 Quantities and units – Part 2: Mathematical signs for science and technology.

The following list is largely limited to non-alphanumeric characters. It is divided by areas of mathematics and grouped within sub-regions. Some symbols have a different meaning depending on the context and appear accordingly several times in the list. Further information on the symbols and their meaning can also be found in the respective linked articles.

## Guide

The following information is provided for each mathematical symbol:

Symbol
The symbol as it is represented by LaTeX. If there are several typographic variants, only one of the variants is shown.
Usage
An exemplary use of the symbol in a formula. Letters here stand as a placeholder for numbers, variables or complex expressions. Different possible applications are listed separately.
Articles with usage
Examples of Wikipedia articles in which the symbol is used.
LaTeX
The LaTeX command that creates the icon. Characters from the ASCII character set can be used directly, with a few exceptions (e.g., pound sign #, backslash \, braces {}, and percent sign %). High-and low-position is indicated via the ^ and _ characters, and is not explicitly specified.
HTML
The icon in HTML, if it is defined as a named mark. Non-named characters can be indicated in the form &#xnnnn by specifying the Unicode code point of the next column. High-and low-position can be indicated via <sup></sup> and <sub></sub>. The character × whose HTML code is times can be displayed by typing &times;.
Unicode
The code point of the corresponding Unicode character. Some characters are combining and require the entry of additional characters. For brackets, the code points of opening and closing forms are specified. The Unicode character ⨯ whose hexadecimal value is U+2A2F can be displayed by typing &#x2A2F; where #x indicates that the value in hexadecimal.

## Numbers

### Number sets

Symbol Unicode character Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \mathbb {A} }$ 𝔸 Algebraic number \mathbb{A} &Aopf; U+1D538
${\displaystyle \mathbb {C} }$ Complex number \mathbb{C}, \Complex &Copf; U+2102
${\displaystyle \mathbb {H} }$ Quaternion \mathbb{H} &quaternions; U+210D
${\displaystyle \mathbb {N} }$ Natural number \mathbb{N}, \N &Nopf; U+2115
${\displaystyle \mathbb {O} }$ 𝕆 Octonion \mathbb{O} &Oopf; U+1D546
${\displaystyle \mathbb {Q} }$ Rational number \mathbb{Q}, \Q &Qopf; U+211A
${\displaystyle \mathbb {R} }$ Real number \mathbb{R}, \R, \Reals &Ropf; U+211D
${\displaystyle \mathbb {S} }$ 𝕊 Sedenion \mathbb{S} &Sopf; U+1D54A
${\displaystyle \mathbb {Z} }$ Integer \mathbb{Z}, \Z &Zopf; U+2124

#### Intervals

Symbol Usage LaTeX HTML Unicode Hex
${\displaystyle [~~]}$ ${\displaystyle [a,b]}$ ( )
[ ]
&lpar; &rpar;
&lsqb; &rsqb;
U+0028/9
U+005B/D
${\displaystyle ]~~[}$ ${\displaystyle ]a,b[}$
${\displaystyle (~~)}$ ${\displaystyle (a,b)}$
${\displaystyle [~~[}$ ${\displaystyle [a,b[}$
${\displaystyle [~~)}$ ${\displaystyle [a,b)}$
${\displaystyle ]~~]}$ ${\displaystyle ]a,b]}$
${\displaystyle (~~]}$ ${\displaystyle (a,b]}$

### Mathematical constants

 For symbols of additional mathematical constants, see Mathematical constant.
Symbol Unicode character Articles with usage LaTeX HTML Template Unicode Hex Note
${\displaystyle \pi }$ π Pi \pi &pi; ((pi)) U+03C0
${\displaystyle e}$ or ${\displaystyle \mathrm {e} }$ e e (mathematics) e or \mathrm{e} e U+0065 Recommend ((mvar|e)) or ((math|e)) over e
${\displaystyle \phi }$ ϕ Golden ratio \phi &phi; ((phi)) U+03C6
${\displaystyle \varphi }$ φ \varphi &straightphi; ((varphi)) U+03D5
${\displaystyle i}$ or ${\displaystyle \mathrm {i} }$ i Imaginary unit i or \mathrm{i} i U+0069 Recommend ((mvar|i)) or ((math|i)) over i
${\displaystyle \gamma }$ γ Euler–Mascheroni constant \gamma &gamma; ((gamma)) U+03B3
${\displaystyle \epsilon }$ ε Vacuum permittivity \epsilon &epsi; ((epsilon)) U+03B5
${\displaystyle \varepsilon }$ ϵ Dual number \varepsilon &varepsilon; ((varepsilon)) U+03F5
${\displaystyle \theta }$ θ Mills' constant \theta &theta; ((theta)) U+03B8
${\displaystyle \vartheta }$ ϑ \vartheta &vartheta; ((vartheta)) U+03D1
${\displaystyle \sigma }$ σ Somos' quadratic recurrence constant \sigma &sigma; ((sigma)) U+03C3
${\displaystyle \varsigma }$ ς \varsigma &varsigma; ((varsigma)) U+03C2
${\displaystyle \kappa }$ κ Einstein gravitational constant \kappa &kappa; ((kappa)) U+03BA
${\displaystyle \lambda }$ λ Prouhet–Thue–Morse constant \lambda &lambda; ((lambda)) U+03BB
${\displaystyle \mu }$ μ Ramanujan–Soldner constant \mu &mu; ((mu)) U+03BC
${\displaystyle \tau }$ τ Prouhet–Thue–Morse constant \tau &tau; ((tau)) U+03C4

### Complex numbers

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \Im }$ ${\displaystyle \Im (2+i)=1}$ Complex number \Im &image; U+2111
${\displaystyle \operatorname {Im} }$ Im ${\displaystyle \operatorname {Im} (2+i)=1}$ \operatorname{Im} Im
${\displaystyle \Re }$ ${\displaystyle \Re (2+i)=2}$ \Re &Rfr; U+211C
${\displaystyle \operatorname {Re} }$ Re ${\displaystyle \operatorname {Re} (2+i)=2}$ \operatorname{Re} Re
${\displaystyle {\bar {~))}$ ◌̄ ${\displaystyle {\bar {z))}$ Complex conjugate \bar &#x304; U+0304
${\displaystyle {\bar {\bar {~))))$ ◌̄̄ ${\displaystyle {\bar {\bar {z))))$ \bar{\bar{)) &#x304;&#x304;
${\displaystyle {\overline {~~))}$ ◌̅ ${\displaystyle {\overline {z))}$ \overline &#x305; U+0305
${\displaystyle {\overline {\overline {~~))))$ ◌̅̅ ${\displaystyle {\overline {\overline {z))))$ \overline{\overline{)) &#x305;&#x305;
${\displaystyle {}^{\ast ))$ * ${\displaystyle z^{\ast ))$ {}^\ast &ast; U+002A
${\displaystyle |~~|}$ | ${\displaystyle |z|}$ Absolute value \vert &VerticalLine; U+007C
${\displaystyle \arg {))$ ${\displaystyle \arg(z)}$ Polar coordinate system \arg
Remark: real and imaginary parts of a complex number are often also denoted by ${\displaystyle \operatorname {Re} }$ and ${\displaystyle \operatorname {Im} }$.

### Elementary arithmetic operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex Notes
${\displaystyle +}$ + ${\displaystyle a+b}$ Addition + &plus; U+002B
${\displaystyle -}$ ${\displaystyle a-b}$ Subtraction - &minus; U+2212
${\displaystyle \cdot }$ ${\displaystyle a\cdot b}$ Multiplication \cdot &sdot; U+22C5
${\displaystyle \times }$ ${\displaystyle a\times b}$ \times &times; U+2A2F
${\displaystyle :}$ ∶  or  : ${\displaystyle a:b}$ Division (mathematics) :\colon &ratio; or &colon; U+003A or U+2236 In LaTeX, : added space around the colon ${\displaystyle a:b}$ that \colon does not ${\displaystyle a\colon b}$.
${\displaystyle /}$ ${\displaystyle a/b}$ / &#x2215; U+2215
${\displaystyle \div }$ ÷ ${\displaystyle a\div b}$ \div &divide; U+00F7
${\displaystyle {\frac {~~}{~~))}$ ${\displaystyle {\frac {a}{b))}$ \frac{a}{b}
\tfrac{a}{b} (inline)
\dfrac{a}{b} (display)
\cfrac{a}{b} (continued fraction)
&frasl; U+2044 <sup>a</sup>⁄<sub>b</sub> renders as: ab
${\displaystyle {}^{-1))$ ${\displaystyle a^{-1))$ Multiplicative inverse ^{-1} U+207B
${\displaystyle -}$ ${\displaystyle -a}$ Additive inverse - &minus; U+2212
${\displaystyle \pm }$ ± ${\displaystyle \pm a}$ Plus or minus sign \pm &plusmn; U+00B1
${\displaystyle \mp }$ ${\displaystyle \mp a}$ \mp &mnplus; U+2213

#### Elementary functions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle {\sqrt {\,))}$ ${\displaystyle {\sqrt {x))}$ Square root \sqrt{} &radic; U+221A
${\displaystyle {\sqrt[{3}]{\,))}$ ${\displaystyle {\sqrt[{3}]{x))}$ Cube root \sqrt[3]{x} &x221B; U+221B
${\displaystyle {\sqrt[{4}]{\,))}$ ${\displaystyle {\sqrt[{4}]{x))}$ Fourth root \sqrt[4]{x} &x221C; U+221C
${\displaystyle {\sqrt[{n}]{\,))}$ ${\displaystyle {\sqrt[{n}]{x))}$ nth root \sqrt[n]{}
${\displaystyle \%}$ % ${\displaystyle x\,\%}$ Percentage \% &percnt; U+0025
${\displaystyle (~~)}$ ( ) ${\displaystyle (x)}$ Order of operations ( ) &lpar; &rpar; U+0028/9
${\displaystyle \left({\frac {1}{2))\right)}$ \left( \right)
${\displaystyle [~~]}$ [ ] ${\displaystyle [x]}$ Bracket [ ] &lsqb; &rsqb; U+005B/D
${\displaystyle |~~|}$ | | ${\displaystyle |x|}$ Absolute value |, \vert &VerticalLine; U+007C
${\displaystyle \left\{~~\right\))$ { } ${\displaystyle \left\{x\right\))$ Fractional part \{ \}
\lbrace \rbrace
&lcub; &rcub; U+007B/D
${\displaystyle \lceil ~~\rceil }$ ⌈ ⌉ ${\displaystyle \lceil x\rceil }$ Floor and ceiling functions \lceil \rceil &lceil; &rceil; U+2308/9
${\displaystyle \lfloor ~~\rfloor }$ ⌊ ⌋ ${\displaystyle \lfloor x\rfloor }$ \lfloor \rfloor &lfloor; &rfloor; U+230A/B
${\displaystyle \ulcorner ~~\urcorner }$ ⌜ ⌝ ${\displaystyle \ulcorner x\urcorner }$ \ulcorner \urcorner &ulcorner; &urcorner; U+231C/D
${\displaystyle \llcorner ~~\lrcorner }$ ⌞ ⌟ ${\displaystyle \llcorner x\lrcorner }$ \llcorner \lrcorner &llcorner; &lrcorner; U+231E/F
${\displaystyle \frown }$  ⌢​ ${\displaystyle {\stackrel {\frown }{x))}$ Cap product \frown &frown; U+2322
${\displaystyle \smile }$  ⌣​ ${\displaystyle {\stackrel {\smile }{x))}$ Cup product \smile &smile; U+2323
${\displaystyle \exp }$ exp ${\displaystyle \exp x}$ Exponential function \exp exp
${\displaystyle \log }$ log ${\displaystyle \log _{b}x}$ Logarithm \log or \log_{} log or log<sub></sub>
${\displaystyle \ln }$ ln ${\displaystyle \ln x}$ Natural logarithm \ln ln
${\displaystyle \lg }$ lg ${\displaystyle \lg x}$ Binary logarithm \lg lg
${\displaystyle \min }$ min ${\displaystyle \min\{1,2\))$ Maxima and minima \min min
${\displaystyle \max }$ max ${\displaystyle \max\{1,2\))$ \max max
${\displaystyle \inf }$ inf ${\displaystyle \inf\{1,2\))$ Infimum and supremum \inf inf
${\displaystyle \sup }$ sup ${\displaystyle \sup\{1,2\))$ \sup sup
${\displaystyle \liminf }$ liminf ${\displaystyle \liminf _{n\to \infty }x_{n))$ Limit inferior and limit superior \liminf liminf
${\displaystyle \varliminf }$ lim ${\displaystyle \varliminf x_{n))$ \varliminf <u>lim</u>
${\displaystyle \limsup }$ limsup ${\displaystyle \limsup _{n\to \infty }x_{n))$ \limsup limsup
${\displaystyle \varlimsup }$ lim ${\displaystyle \varlimsup x_{n))$ \varlimsup <span style="text-decoration:overline;">lim</span>
${\displaystyle \gcd }$ gcd ${\displaystyle \gcd(1,2)}$ Greatest common divisor \gcd gcd

Note: the power function is not represented by its own icon, but by the positioning of the exponent as a superscript.

#### Trigonometric functions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \sin }$ sin ${\displaystyle \sin x}$ Sine and cosine \sin sin
${\displaystyle \cos }$ cos ${\displaystyle \cos x}$ \cos cos
${\displaystyle \tan }$ tan ${\displaystyle \tan x}$ Tangent \tan tan
${\displaystyle \sec }$ sec ${\displaystyle \sec x}$ Trigonometric functions \sec sec
${\displaystyle \csc }$ csc ${\displaystyle \csc x}$ \csc csc
${\displaystyle \cot }$ cot ${\displaystyle \cot x}$ \cot cot
${\displaystyle \arcsin }$ sin ${\displaystyle \arcsin x}$ Inverse trigonometric functions \arcsin arcsin
${\displaystyle \arccos }$ arccos ${\displaystyle \arccos x}$ \arccos arccos
${\displaystyle \arctan }$ arctan ${\displaystyle \arctan x}$ \arctan arctan
${\displaystyle \operatorname {arcsec} }$ arcsec ${\displaystyle \operatorname {arcsec} x}$ \arcsec arcsec
${\displaystyle \operatorname {arccsc} }$ arccsc ${\displaystyle \operatorname {arccsc} x}$ \arccsc arccsc
${\displaystyle \operatorname {arccot} }$ arccot ${\displaystyle \operatorname {arccot} x}$ \arccot arccot
${\displaystyle \sinh }$ sinh ${\displaystyle \sinh x}$ Hyperbolic functions \sinh sinh
${\displaystyle \cosh }$ cosh ${\displaystyle \cosh x}$ \cosh cosh
${\displaystyle \tanh }$ tanh ${\displaystyle \tanh x}$ \tanh tanh
${\displaystyle \coth }$ coth ${\displaystyle \coth x}$ \coth coth

### Arithmetic comparison

Symbol Unicode character Usage LaTeX HTML Unicode Hex
${\displaystyle <}$ < ${\displaystyle a < &lt; U+003C
${\displaystyle >}$ > ${\displaystyle a>b}$ > &gt; U+003E
${\displaystyle \leq }$ ${\displaystyle a\leq b}$ \le, \leq &le; U+2264
${\displaystyle \geq }$ ${\displaystyle a\geq b}$ \ge, \geq &ge; U+2265
${\displaystyle \leqq }$ ${\displaystyle a\leqq b}$ \leqq &LessFullEqual; U+2266
${\displaystyle \geqq }$ ${\displaystyle a\geqq b}$ \geqq &GreaterFullEqual; U+2267
${\displaystyle \leqslant }$ ${\displaystyle a\leqslant b}$ \leqslant &LessSlantEqual U+2A7D
${\displaystyle \geqslant }$ ${\displaystyle a\geqslant b}$ \geqslant &GreaterSlantEqual U+2A7E
${\displaystyle \ll }$ ${\displaystyle a\ll b}$ \ll &NestedLessLess; U+226A
${\displaystyle \gg }$ ${\displaystyle a\gg b}$ \gg &NestedGreaterGreater; U+226B
${\displaystyle \lesssim }$ ${\displaystyle a\lesssim b}$ \lesssim &lsim; U+2272
${\displaystyle \gtrsim }$ ${\displaystyle a\gtrsim b}$ \gtrsim &GreaterTilde; U+2273
${\displaystyle \lessapprox }$ ${\displaystyle a\lessapprox b}$ \lessapprox &lessapprox; U+2A85
${\displaystyle \gtrapprox }$ ${\displaystyle a\gtrapprox b}$ \gtrapprox &gap; U+2A86
Symbol Unicode character Usage LaTeX HTML Unicode Hex
${\displaystyle \lessgtr }$ ${\displaystyle a\lessgtr b}$ \lessgtr &LessGreater U+2276
${\displaystyle \gtrless }$ ${\displaystyle a\gtrless b}$ \gtrless &GreaterLess; U+2277
${\displaystyle \lesseqgtr }$ ${\displaystyle a\lesseqgtr b}$ \lesseqgtr &LessEqualGreater; U+22DA
${\displaystyle \gtreqless }$ ${\displaystyle a\gtreqless b}$ \gtreqless &GreaterEqualLess; U+22DB
${\displaystyle \lesseqqgtr }$ ${\displaystyle a\lesseqqgtr b}$ \lesseqqgtr &lesseqqgtr; U+2A8B
${\displaystyle \gtreqqless }$ ${\displaystyle a\gtreqqless b}$ \gtreqqless &gtreqqless; U+2A8C

## Number theory

### Divisibility and modulo

Symbol Unicode character Usage LaTeX HTML Unicode Hex
${\displaystyle \mid }$ ${\displaystyle a\mid b}$ \mid &VerticalBar; U+2223
${\displaystyle \nmid }$ ${\displaystyle a\nmid b}$ \nmid &NotVerticalBar; U+2224
${\displaystyle \perp }$ ${\displaystyle a\perp b}$ \perp &perp; U+22A5
${\displaystyle \sqcap }$ ${\displaystyle a\sqcap b}$ \sqcap &SquareIntersection; U+2293
${\displaystyle \wedge }$ ${\displaystyle a\wedge b}$ \wedge &and; U+2227
${\displaystyle \sqcup }$ ${\displaystyle a\sqcup b}$ \sqcup &SquareUnion; U+2294
${\displaystyle \vee }$ ${\displaystyle a\vee b}$ \vee &or; U+2228
Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex Other information
${\displaystyle \equiv }$ ${\displaystyle a\equiv b}$ Modulo operation \equiv &equiv; U+2261
${\displaystyle \mod m}$ mod ${\displaystyle a\mod m}$ \mod m mod $\mod$ without a trailing symbol (e.g. ${\displaystyle m}$) will produce an error.
${\displaystyle {\pmod {m))}$ (mod) ${\displaystyle a{\pmod {m))}$ \pmod m (mod) $\pmod$ without a trailing symbol (e.g. ${\displaystyle m}$) will produce an error.
${\displaystyle \gcd }$ gcd ${\displaystyle \gcd(1,2)}$ Greatest common divisor \gcd gcd

### Combinatorics

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle !}$ ! ${\displaystyle n!}$ Factorial ! &excl; U+0021
${\displaystyle !n}$ Derangement
${\displaystyle n!!}$ Double factorial
${\displaystyle {\tbinom {~}{~))}$ ( ) ${\displaystyle {\tbinom {n}{k))}$ Combination \binom &lpar; &rpar; U+0028/9
${\displaystyle {\tbinom {n}{k_{1},\ldots ,k_{r))))$ Multinomial coefficient
${\displaystyle \left(\!{\tbinom {~}{~))\!\right)}$ (( )) ${\displaystyle \left(\!{\tbinom {n}{k))\!\right)}$ Multiset (( )) &lpar; &rpar; U+0028/9
${\displaystyle {\overline {~))}$ ◌̄ ${\displaystyle n^{\bar {m))}$ Pochhammer symbol \bar &#x304; U+0304
◌̅ ${\displaystyle n^{\overline {m))}$ \overline &#x305; U+0305
◌̲ ${\displaystyle n^{\underline {m))}$ \underline &#x332; U+0332
${\displaystyle \#}$ # ${\displaystyle n\#}$ Primorial \# &num; U+0023

## Stochastics

### Probability theory

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle P}$ ${\displaystyle P(A)}$ Probability measure P U+2119
${\displaystyle \mid }$ ${\displaystyle P(A\mid B)}$ Conditional probability \mid &VerticalLine; U+007C
${\displaystyle /}$ ${\displaystyle P(A/B)}$ / U+2215
${\displaystyle E}$ 𝔼 ${\displaystyle E(X)}$ Expected value E &Eopf; U+1D53C
${\displaystyle V}$ 𝕍 ${\displaystyle V(X)}$ Variance V &Vopf; U+1D54D
${\displaystyle \sigma }$ σ ${\displaystyle \sigma (X)}$ Standard deviation \sigma &sigma; U+03C3
${\displaystyle \sigma (X,Y)}$ Covariance
${\displaystyle \rho }$ ρ ${\displaystyle \rho (X,Y)}$ Correlation \rho &rho; U+03C1
${\displaystyle \sim }$ ${\displaystyle X\sim F}$ Probability distribution \sim &sim; U+223C
${\displaystyle \approx }$ ${\displaystyle X\approx F}$ \approx &asymp; U+2248
${\displaystyle {\displaystyle \perp ))$ ${\displaystyle A\perp B}$ Independence (probability theory) \perp &perp; U+22A5
Remark: for operators there are several notational variants; instead of round brackets also square brackets are used

### Statistics

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle {\bar {~))}$ ◌̅ ${\displaystyle {\bar {x))}$ Average \bar &#x304; U+0304
${\displaystyle {\overline {~~))}$ ◌̅ ${\displaystyle {\overline {m))}$ \overline &#x305; U+0305
${\displaystyle \langle ~~\rangle }$ ⟨ ⟩ ${\displaystyle \langle X\rangle }$ \langle \rangle &lang; &rang; U+27E8/9
${\displaystyle {\hat {~))}$ ◌̂ ${\displaystyle {\hat {p))}$ Estimator \hat ̂ U+0302

## Calculus

### Sequences and series

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \sum }$ ${\displaystyle \sum _{i=1}^{n},\sum _{i\in I))$ Summation \sum &sum; U+2211
${\displaystyle \prod }$ ${\displaystyle \prod _{i=1}^{n},\prod _{i\in I))$ Multiplication \prod &prod; U+220F
${\displaystyle \coprod }$ ${\displaystyle \coprod _{i=1}^{n},\coprod _{i\in I))$ Coproduct \coprod &Coproduct; U+2210
${\displaystyle (~~)}$ ( ) ${\displaystyle (a_{n})}$ Sequence ( ) &lpar; &rpar; U+0028/9
${\displaystyle \to }$ ${\displaystyle a_{n}\to a}$ Limit of a sequence \to \rarr &rarr; U+2192
${\displaystyle \infty }$ ${\displaystyle n\to \infty }$ Infinity \infty &infin; U+221E

### Limits

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \to }$ ${\displaystyle \lim _{x\to a}f(x)}$ Limit of a function \to
\rightarrow
&rarr;
&rightarrow;
U+2192
${\displaystyle \longrightarrow }$ ${\displaystyle x\longrightarrow a}$ \longrightarrow &LongRightArrow; U+27F6
${\displaystyle \uparrow }$ ${\displaystyle \lim _{x\uparrow a}f(x)}$ \uparrow &uarr;
&ShortUpArrow;
U+2191
${\displaystyle \nearrow }$ ${\displaystyle \lim _{x\nearrow a}f(x)}$ \nearrow &UpperRightArrow; U+2197
${\displaystyle \searrow }$ ${\displaystyle \lim _{x\searrow a}f(x)}$ \searrow &LowerRightArrow; U+2198
${\displaystyle \downarrow }$ ${\displaystyle \lim _{x\downarrow a}f(x)}$ \downarrow &darr;
&ShortDownArrow;
U+2193
${\displaystyle \swarrow }$ ${\displaystyle a\swarrow x}$ \swarrow &LowerLeftArrow; U+2199
${\displaystyle \leftarrow }$ ${\displaystyle a\leftarrow x}$ \leftarrow &larr;
&ShortLeftArrow;
U+2190
${\displaystyle \longleftarrow }$ ${\displaystyle a\longleftarrow x}$ \longleftarrow &longleftarrow; U+27F5
${\displaystyle \nwarrow }$ ${\displaystyle a\nwarrow x}$ \nwarrow &UpperLeftArrow; U+2196
${\displaystyle ^{+))$ ${\displaystyle \lim _{x\to a^{+))f(x)}$ ^+ &#8314; U+207A
${\displaystyle ^{-))$ ${\displaystyle \lim _{x\to a^{-))f(x)}$ ^- &#8315; U+207B
${\displaystyle \lim }$ ${\displaystyle \lim _{n\to \infty }x_{n))$ \lim
${\displaystyle \liminf }$ ${\displaystyle \liminf _{n\to \infty }x_{n))$ Limit inferior and limit superior \liminf
${\displaystyle \limsup }$ ${\displaystyle \limsup _{n\to \infty }x_{n))$ \limsup

### Differential calculus

 Main article: Differential calculus
Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle {}'}$
${\displaystyle {}^{\prime ))$
${\displaystyle f'}$
${\displaystyle f^{\prime ))$
Lagrange's notation
Prime (symbol)
'
^\prime
&prime; U+2032
${\displaystyle {}''}$
${\displaystyle {}^{\prime \prime ))$
${\displaystyle f''}$
${\displaystyle f^{\prime \prime ))$
''
^{\prime\prime}
&Prime; U+2033
${\displaystyle {}'''}$
${\displaystyle {}^{\prime \prime \prime ))$
${\displaystyle f'''}$
${\displaystyle f^{\prime \prime \prime ))$
'''
^{\prime\prime\prime}
&tprime; U+2034
${\displaystyle {}''''}$
${\displaystyle {}^{\prime \prime \prime \prime ))$
${\displaystyle f''''}$
${\displaystyle f^{\prime \prime \prime \prime ))$
''''
^{\prime\prime\prime\prime}
&qprime; U+2057
${\displaystyle ^{IV}\;{}^{V}\;{}^{VI))$ ${\displaystyle f^{IV},f^{V},f^{VI))$ ^{IV} ^V ^{VI} <sup>IV</sup>
${\displaystyle ^{iv}\;{}^{v}\;{}^{vi))$ ${\displaystyle f^{iv},f^{v},f^{vi))$ ^{iv} ^v ^{vi} <sup>iv</sup>
${\displaystyle {}^{(~)))$ ⁽ ⁾ ${\displaystyle f^{(4)},f^{(5)},f^{(n)))$ ^{( )} <sup>( )</sup> U+207D/E
${\displaystyle {\dot {~~))}$ ◌̇ ${\displaystyle {\dot {f))}$ Newton's notation \dot &#x0307; U+0307
${\displaystyle {\ddot {~~))}$ ◌̈ ${\displaystyle {\ddot {f))}$ \ddot &#x0308; U+0308
${\displaystyle d}$ d ${\displaystyle dx}$ Leibniz's notation d d U+0064
${\displaystyle df}$
${\displaystyle {\frac {df}{dx))}$
${\displaystyle {\frac {d}{dx))f}$
${\displaystyle {\frac {d^{2)){dx^{2))}f}$
${\displaystyle \partial }$ ${\displaystyle \partial _{x}f}$ Partial derivative \partial &part; U+2202
${\displaystyle \left.{\frac {\partial }{\partial x))\right\vert _{x))$ ∂ and | ${\displaystyle \left.{\frac {\partial f}{\partial x))\right\vert _{x=x_{0))}$ \left. \frac{\partial }{\partial x} \right\vert_x &part; and
&VerticalLine;
U+2202 and
U+007C

### Integral calculus

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \int }$ ${\displaystyle \int _{a}^{b))$ , ${\displaystyle \int _{G))$ Integral \int &int; U+222B
${\displaystyle \iint }$ ${\displaystyle \iint _{\mathcal {F))}$ Surface integral \iint &Int; U+222C
${\displaystyle \iiint }$ ${\displaystyle \iiint _{V))$ Volume integral \iiint &tint; U+222D
${\displaystyle \oint }$ ${\displaystyle \oint _{\gamma ))$ Curve integral \oint &ContourIntegral; U+222E
${\displaystyle \gamma }$ Surface integral \oiint &DoubleContourIntegral; U+222F
${\displaystyle \gamma }$ Volume integral \oiiint &Cconint; U+2230

### Vector calculus

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \nabla }$ ${\displaystyle \nabla f}$ Gradient \nabla &nabla; U+2207
${\displaystyle \nabla \cdot F}$ Divergence
${\displaystyle \nabla \times F}$ Curl (mathematics)
${\displaystyle \Delta }$ ${\displaystyle \Delta f}$ Laplace operator \Delta &Delta; U+2206
${\displaystyle \square }$ ${\displaystyle \square f}$ D'Alembert operator \square &#9633; U+25A1

### Asymptotic behaviour

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \sim }$ ${\displaystyle f\sim }$ Asymptotic analysis \sim &sim; U+223C
${\displaystyle o}$ o ${\displaystyle f\in o(g)}$ Big O notation o U+006F
${\displaystyle {\mathcal {O))}$ 𝒪 ${\displaystyle f\in {\mathcal {O))(g)}$ \mathcal{O} &Oscr; U+1D4AA
${\displaystyle \Theta }$ Θ ${\displaystyle f\in \Theta (g)}$ \Theta &Theta; U+0398
${\displaystyle \Omega }$ Ω ${\displaystyle f\in \Omega (g)}$ \Omega &Omega; U+03A9
${\displaystyle \omega }$ ω ${\displaystyle f\in \omega (g)}$ \omega &omega; U+03C9

## Linear algebra

### Vectors and matrices

Symbol Articles with usage LaTeX
${\displaystyle {\begin{pmatrix}v_{1},\ldots ,v_{n}\end{pmatrix))}$ Vector (mathematics and physics) \begin{pmatrix}
...
\end{pmatrix}

or

\left(
\begin{array}{...}
...
\end{array}
\right)
${\displaystyle {\begin{pmatrix}v_{1}\\\vdots \\v_{m}\end{pmatrix))}$
${\displaystyle {\begin{pmatrix}a_{11}&\!\ldots \!&a_{1n}\\\vdots &\!\ddots \!&\vdots \\a_{m1}&\!\ldots \!&a_{mn}\end{pmatrix))}$ Matrix (mathematics)

### Vector operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \cdot }$ ${\displaystyle v\cdot w}$ Dot product \cdot &sdot; U+22C5
${\displaystyle (~~)}$ ( ) ${\displaystyle (v,w)}$ ( ) &lpar; &rpar; U+0028/9
${\displaystyle \langle ~~\rangle }$ ⟨ ⟩ ${\displaystyle \langle v,w\rangle }$
${\displaystyle \langle v\,|\,w\rangle }$
\langle \rangle &lang; &rang; U+27E8/9
${\displaystyle \times }$ ${\displaystyle v\times w}$ Cross product \times &times; U+2A2F
${\displaystyle [~~]}$ [ ] ${\displaystyle [v,w]}$ [ ] &lsqb; &rsqb; U+005B/D
${\displaystyle (~~)}$ ( ) ${\displaystyle (u,v,w)}$ Triple product ( ) &lpar; &rpar; U+0028/9
${\displaystyle \otimes }$ ${\displaystyle v\otimes w}$ Dyadic product \otimes &otimes; U+2297
${\displaystyle \wedge }$ ${\displaystyle v\wedge w}$ Exterior algebra \wedge &and; U+2227
${\displaystyle |~~|}$ | | ${\displaystyle |v|}$ Euclidean norm \vert &VerticalLine; U+007C
${\displaystyle \|~~\|}$ ${\displaystyle \|v\|}$
${\displaystyle \lVert v\rVert }$
Norm (mathematics) \Vert\|
\lVert \rVert
&Vert; U+2016
${\displaystyle {\hat {~))}$ ̂ ${\displaystyle {\hat {v))}$ Unit vector \hat{} &#x302; U+0302

### Matrix operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \cdot }$ ${\displaystyle A\cdot B}$ Matrix multiplication \cdot &sdot; U+22C5
${\displaystyle \circ }$ ${\displaystyle A\circ B}$ Hadamard product \circ &SmallCircle; U+2218
${\displaystyle \oslash }$ ${\displaystyle A\oslash B}$ Hadamard division \oslash &osol; U+2298
${\displaystyle *}$ * ${\displaystyle A*B}$ Khatri-Rao product * &ast; U+002A
${\displaystyle \otimes }$ ${\displaystyle A\otimes B}$ Kronecker product \otimes &otimes; U+2297
${\displaystyle {}^{\intercal ))$ ${\displaystyle A^{\intercal ))$ Transposed matrix ^\intercal &intercal; U+22BA
${\displaystyle {}^{\top ))$ ${\displaystyle A^{\top ))$ ^\top &top; U+22A4
${\displaystyle {}^{\mathrm {T} ))$ T ${\displaystyle A^{\mathrm {T} ))$ ^{\mathrm T} U+0054
${\displaystyle {}^{\ast ))$ * ${\displaystyle A^{\ast ))$ Conjugate transpose ^\ast &ast; U+002A
${\displaystyle {}^{\dagger ))$ ${\displaystyle A^{\dagger ))$ ^\dagger &dagger; U+2020
${\displaystyle {}^{\mathrm {H} ))$ H ${\displaystyle A^{\mathrm {H} ))$ ^H U+0048
${\displaystyle {}^{-1))$ ${\displaystyle A^{-1))$ Inverse matrix ^{-1} U+207B
${\displaystyle {}^{+))$ + ${\displaystyle A^{+))$ Moore–Penrose pseudoinverse ^+ &plus; U+002B
${\displaystyle |~~|}$ | A | ${\displaystyle |A|}$ Determinant |, \vert &VerticalLine; U+007C
${\displaystyle \det }$ det ${\displaystyle \det A}$ \det det
${\displaystyle \|~~\|}$ ${\displaystyle \|A\|}$ Matrix norm \|, \Vert &Vert; U+2016

### Vector spaces

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle +}$ + ${\displaystyle V+W}$ Direct sum of modules + &plus; U+002B
${\displaystyle \oplus }$ ${\displaystyle V\oplus W}$ \oplus &oplus; U+2295
${\displaystyle \times }$ ${\displaystyle V\times W}$ Direct product \times &times; U+2A2F
${\displaystyle \otimes }$ ${\displaystyle V\otimes W}$ Tensor product \otimes &otimes; U+2297
${\displaystyle /}$ / ${\displaystyle V\,/\,U}$ Quotient space (linear algebra) / &frasl; U+002F
${\displaystyle {}^{\perp ))$ ${\displaystyle U^{\perp ))$ Orthogonal complement ^\perp &perp; U+27C2
${\displaystyle {}^{\ast ))$ * ${\displaystyle V^{\ast ))$ Dual space ^\ast &lowast; U+002A
${\displaystyle {}^{0))$ 0 ${\displaystyle X^{0))$ ^0 U+0030
${\displaystyle \langle ~~\rangle }$ ⟨ ⟩ ${\displaystyle \langle X\rangle }$ Linear hull \langle \rangle &lang; &rang; U+27E8/9
${\displaystyle \dim }$ dim ${\displaystyle \dim X}$ Dimension (linear algebra) \dim dim
${\displaystyle \ker }$ ker ${\displaystyle \ker L}$ Kernel (linear algebra) \ker ker
${\displaystyle \Pr }$ Pr ${\displaystyle \Pr {}_{1}(x,y)}$ Projection (linear algebra) \Pr Pr

### Functional analysis

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle {}'}$ ${\displaystyle V'}$ Dual space ^\prime &prime; U+2032/3
${\displaystyle {}''}$ ${\displaystyle V''}$
${\displaystyle {\hat {~))}$ ◌̂ ${\displaystyle {\hat {X))}$ Complete metric space \hat{} U+0302
${\displaystyle \hookrightarrow }$ ${\displaystyle X\hookrightarrow Y}$ Embedding \hookrightarrow U+21AA

## Logic

The current Wikipedia guidelines advise against unnecessary use of ∀, ∃, and ⇔ and instead recommend writing out "for all", "there exists", and "if and only if." The same is true of abbreviations such as "iff", "s.t.", and "WLOG".

### Equality signs

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle =}$ = ${\displaystyle a=b}$ Equality = &equals; U+003D
${\displaystyle \#}$ # ${\displaystyle a\,\#\,b}$ Apartness relation \# &num; U+0023
${\displaystyle \neq }$ ${\displaystyle a\neq b}$ Inequality \neq
\ne
\not=
&ne; U+2260
${\displaystyle \equiv }$ ${\displaystyle a\equiv b}$ Identity \equiv &equiv; U+2261
${\displaystyle \approx }$ ${\displaystyle a\approx b}$ Approximation \approx &asymp; U+2248
${\displaystyle \sim }$ ${\displaystyle a\sim b}$ Equivalence class \sim &sim; U+223C
${\displaystyle \propto }$ ${\displaystyle a\propto b}$ Proportionality \propto &prop; U+221D
${\displaystyle {\widehat {=))}$ ${\displaystyle a\,{\widehat {=))\,b}$ Bijection \widehat{=} &wedgeq; U+2259
${\displaystyle {\overset {?}{=))}$ ${\displaystyle a\,{\overset {?}{=))\,b}$ Asks "is it equal to" \overset{?}{=} &questeq; U+225F
${\displaystyle {\overset {\operatorname {def} }{=))}$ ${\displaystyle a\,{\overset {\operatorname {def} }{=))\,b}$ Equal to by definition \overset{\operatorname{def)){=} &#x225D; U+225D
${\displaystyle \triangleq }$ ${\displaystyle a\,\triangleq \,b}$ \triangleq &trie; U+225C
${\displaystyle :=}$ ${\displaystyle a\,:=\,b}$ Assignment := &coloneq; U+2254
${\displaystyle =:}$ ${\displaystyle a\,=:\,b}$ =: &eqcolon; U+2255
${\displaystyle \doteq }$ ${\displaystyle x_{n}\doteq \,b}$ Approaches the limit \doteq &esdot; U+2250
${\displaystyle ==}$ ${\displaystyle x\,==\,y}$ Relational operator == &Equal; U+2A75

### Logical operators

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \land }$ ${\displaystyle A\land B}$ Logical conjunction \land &and; U+2227
${\displaystyle \lor }$ ${\displaystyle A\lor B}$ Logical disjunction \lor &or; U+2228
${\displaystyle \Leftrightarrow }$ ${\displaystyle A\Leftrightarrow B}$ Logical equivalence \Leftrightarrow &hArr; U+21D4
${\displaystyle \leftrightarrow }$ ${\displaystyle A\leftrightarrow B}$ \leftrightarrow &harr; U+2194
${\displaystyle \iff }$ ${\displaystyle A\iff B}$ \iff &Longleftrightarrow; U+27FA
${\displaystyle \Rightarrow }$ ${\displaystyle A\Rightarrow B}$ Logical consequence \Rightarrow &rArr; U+21D2
${\displaystyle \rightarrow }$ ${\displaystyle A\rightarrow B}$ \rightarrow &rarr; U+2192
${\displaystyle \implies }$ ${\displaystyle A\implies B}$ \implies &DoubleLongRightArrow; U+27F9
${\displaystyle \Longrightarrow }$ ${\displaystyle A\Longrightarrow B}$ \Longrightarrow
${\displaystyle \oplus }$ ${\displaystyle A\oplus B}$ Exclusive or \oplus &oplus; U+2295
${\displaystyle \veebar }$ ${\displaystyle A\,\veebar \,B}$ \veebar &veebar; U+22BB
${\displaystyle {\dot {\lor ))}$ ${\displaystyle A\,{\dot {\lor ))\,B}$ \dot\lor U+2A52
${\displaystyle \lnot }$ ¬ ${\displaystyle \lnot A}$ Logical negation \lnot &not; U+00AC
${\displaystyle {\bar {~))}$ ◌̄ ${\displaystyle {\bar {A))}$ \bar &#x304; U+0304
${\displaystyle {\overline {~~))}$ ̅ ${\displaystyle {\overline {A))}$ \overline &#x305; U+0305
${\displaystyle \not }$ ◌̸ ${\displaystyle \not =}$
${\displaystyle \not \in }$
\not
(ex: \not= \not\in)
&#x338;
(ex: =&#x338; &isin;&#x338;)
U+0338
${\displaystyle \leftarrow }$ ${\displaystyle A\leftarrow B}$ Converse implication \leftarrow &ShortLeftArrow; U+2190
${\displaystyle \multimap }$ ${\displaystyle A\multimap B}$ Linear logic \multimap &mumap; U+22B8
A ⅋ B Linear logic \upand (No Wikipedia support) &x214B; U+214B

### Quantifiers

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \forall }$ ${\displaystyle \forall \,x}$ Universal quantification \forall &forall; U+2200
${\displaystyle \bigwedge }$ ${\displaystyle \bigwedge _{x))$ \bigwedge &Wedge; U+22C0
${\displaystyle \exists }$ ${\displaystyle \exists \,x}$ Existential quantification \exists &exist; U+2203
${\displaystyle \bigvee }$ ${\displaystyle \bigvee _{x))$ \bigvee &xvee; U+22C1
${\displaystyle \exists !}$ ∃! ${\displaystyle \exists !\,x}$ Uniqueness quantification \exists! &exist;! U+2203!
${\displaystyle \bigvee ^{\centerdot ))$ ${\displaystyle \bigvee _{x}^{\centerdot ))$ \dot\bigvee U+2A52
${\displaystyle \nexists }$ ${\displaystyle \nexists \,x}$ Existential quantification \nexists &NotExists; U+2204

### Deduction symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \vdash }$ ${\displaystyle A\vdash B}$ Logical consequence, Propositional calculus \vdash &vdash; U+22A2
${\displaystyle \models }$ ${\displaystyle A\models B}$ Logical consequence, Inference \models &DoubleRightTee; U+22A8
${\displaystyle \models A}$ Tautology (logic)
${\displaystyle \top }$ ${\displaystyle A\top }$ \top &top; U+22A4
${\displaystyle \bot }$ ${\displaystyle A\bot }$ Contradiction \bot &perp; U+22A5
${\displaystyle \therefore }$ ${\displaystyle A\therefore B}$ Deductive reasoning \therefore &therefore; U+2234
${\displaystyle \because }$ ${\displaystyle A\because B}$ \because &because; U+2235

### End of proof symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \blacksquare }$ ...as desired. ${\displaystyle \blacksquare }$ Q.E.D. \blacksquare &#x25A0; U+25A0
${\displaystyle \Box }$ \Box &squ; U+25A1
${\displaystyle }$ Tombstone &#x220E; U+220E

### Formal language and strings

 Main article: Formal language
Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \varepsilon }$ ε ${\displaystyle \varepsilon s=s}$ Empty string \varepsilon &epsi; U+03B5
${\displaystyle |~~|}$ | | ${\displaystyle |s|}$ String length \vert &VerticalLine; U+007C
${\displaystyle +}$ + ${\displaystyle s+t}$ Concatenation + &plus; U+002B
${\displaystyle \cdot }$ ${\displaystyle s\cdot t}$ \cdot &sdot; U+22C5
${\displaystyle \lnot }$ ¬ ${\displaystyle \lnot L}$ Formal language \lnot &not; U+00AC
${\displaystyle {}^{\ast ))$ * ${\displaystyle V^{\ast ))$ Kleene star ^\ast &lowast; U+002A
${\displaystyle {}^{+))$ + ${\displaystyle V^{+))$ Free monoid ^+ &plus; U+002B
${\displaystyle \sim }$ ${\displaystyle a\sim b}$ Squiggle operator \sim &sim; U+223C
${\displaystyle [\![~~]\!]}$ ⟦⟧ ${\displaystyle [\![s]\!]}$ Squiggle operator [\![ ]\!] &LeftDoubleBracket; &RightDoubleBracket; U+27E6/7

## Functions and category theory

### Functions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \to }$ ${\displaystyle f\colon A\to B}$ Function (mathematics) \to &rarr; U+2192
${\displaystyle A\,{\stackrel {f}{\to ))\,B}$
${\displaystyle \mapsto }$ ${\displaystyle f\colon x\mapsto y}$ \mapsto &mapstoright; U+21A6
${\displaystyle x\,{\stackrel {f}{\mapsto ))\,y}$
${\displaystyle (~~)}$ ( ) ${\displaystyle f(x)}$ Image (mathematics) ( ) &lpar; &rpar; U+0028/9
${\displaystyle f(X)}$
${\displaystyle [~~]}$ [ ] ${\displaystyle f[X]}$ [ ] &lbrack; or &rbrack; U+005B/D
${\displaystyle \vert }$ | ${\displaystyle f\vert _{X))$ Restriction (mathematics) \vert &VerticalLine; U+007C
${\displaystyle \cdot }$ ${\displaystyle f(\cdot )}$ Free variable \cdot &sdot; U+22C5
${\displaystyle {}^{-1))$ ${\displaystyle f^{-1))$ Inverse function -1 U+207B
${\displaystyle \circ }$ ${\displaystyle f\circ g}$ Function composition \circ &#8728; U+2218
${\displaystyle \ast }$ ${\displaystyle f\ast g}$ Convolution \ast &lowast; U+2217
${\displaystyle {\hat {~))}$ ◌̂ ${\displaystyle {\hat {f))}$ Fourier transform \hat U+0302
${\displaystyle \multimap }$ ${\displaystyle f:X\multimap Y}$ Multimap \multimap &mumap; U+22B8

### Morphisms

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \to }$ ${\displaystyle f\colon X\to Y}$ Morphism \to &rarr; U+2192
${\displaystyle X\,{\stackrel {f}{\to ))\,Y}$
${\displaystyle \mapsto }$ ${\displaystyle f\colon x\mapsto y}$ \mapsto &mapstoright; U+21A6
${\displaystyle x\,{\stackrel {f}{\mapsto ))\,y}$
${\displaystyle {\overset {\sim }{\rightarrow ))}$ ${\displaystyle f\colon X{\overset {\sim }{\rightarrow ))Y}$ Isomorphism \tilde{\rightarrow} U+2972
${\displaystyle \hookrightarrow }$ ${\displaystyle f\colon X\hookrightarrow Y}$ Monomorphism \hookrightarrow &#8618 U+21AA
${\displaystyle X\,{\stackrel {f}{\hookrightarrow ))\,Y}$
${\displaystyle \twoheadrightarrow }$ ${\displaystyle f\colon X\twoheadrightarrow Y}$ Epimorphism \twoheadrightarrow &#8608 U+21A0
${\displaystyle X\,{\stackrel {f}{\twoheadrightarrow ))\ Y}$
${\displaystyle \hom }$ hom ${\displaystyle \hom _{C}(X,Y)}$ Morphism \hom hom

### Constructions

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \prod }$ ${\displaystyle \prod X_{i))$ Product (category theory) \prod &prod; U+220F
${\displaystyle \coprod }$ ${\displaystyle \coprod X_{i))$ Coproduct \coprod &Coproduct; U+2210
${\displaystyle \oplus }$ ${\displaystyle \oplus X_{i))$ Biproduct \oplus &CirclePlus; U+2295
${\displaystyle \times }$ × ${\displaystyle A\times _{C}B}$ Pullback (category theory) \times &times; U+00D7
${\displaystyle \lim }$ lim ${\displaystyle \lim F}$ Limit (category theory) \lim lim
${\displaystyle \projlim }$ projlim ${\displaystyle \projlim F}$ Inverse limit \projlim projlim
${\displaystyle \varprojlim }$ ${\displaystyle \varprojlim F}$ \varprojlim
${\displaystyle \injlim }$ injlim ${\displaystyle \injlim F}$ Direct limit \injlim injlim
${\displaystyle \varinjlim }$ ${\displaystyle \varinjlim F}$ \varinjlim

## Set theory

### Definition symbols

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \colon }$ : ${\displaystyle A\colon B}$ Definition \colon &colon; U+003A
${\displaystyle A\colon =B}$
${\displaystyle A\colon \Leftrightarrow B}$

### Set construction

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \varnothing }$ ${\displaystyle \varnothing =\{\;\))$ Empty set \varnothing &varnothing;
&empty;
U+2205
${\displaystyle \emptyset }$ \emptyset
${\displaystyle \{~\))$ { } ${\displaystyle \{a,b,\ldots \))$ Set (mathematics) \{ \}
\lbrace \rbrace
&lcub; &rcub; U+007B/D
${\displaystyle \mid }$ | ${\displaystyle \{a\mid T(a)\))$ \mid &VerticalLine; U+007C
${\displaystyle \colon }$ : ${\displaystyle \{a\colon T(a)\))$ \colon &colon; U+003A
${\displaystyle :}$ ${\displaystyle \{a:T(a)\))$ :
Comparison of separators (the symbol between the variable and predicate)
Rendered result Latex code Notes on separator
${\displaystyle \{x\in X:P(x)\))$ \{x\in X : P(x)\} : inserts whitespace that \colon does not.
${\displaystyle \{x\in X\colon P(x)\))$ \{x\in X \colon P(x)\}
${\displaystyle \{x\in X\mid P(x)\))$ \{x\in X \mid P(x)\} \mid inserts whitespace that \vert does not.
${\displaystyle \{x\in X\vert P(x)\))$ \{x\in X \vert P(x)\} \vert and | are synonyms in LaTeX.
${\displaystyle \{x\in X\vline P(x)\))$ \{x\in X \vline P(x)\} \mid inserts whitespace that \vline does not.
${\displaystyle \left\{\sum _{n=1}^{\infty }x^{n}:|x|<1\right\))$ \left\{\sum_{n=1}^{\infty} x^n : |x|<1\right\}
${\displaystyle \left\{\sum _{n=1}^{\infty }x^{n}\mid |x|<1\right\))$ \left\{\sum_{n=1}^\infty x^n \mid |x|<1\right\}
${\displaystyle \left\{\sum _{n=1}^{\infty }x^{n}\;{\Bigg |}\;|x|<1\right\))$ \left\{\sum_{n=1}^\infty x^n \;\Bigg|\; |x|<1\right\} \;\Bigg|\; is used since neither \middle\mid, \Bigg\mid, nor \Bigg\vline render in Wikipedia.
${\displaystyle \left\{\left.\sum _{n=1}^{\infty }x^{n}\;\right|\;|x|<1\right\))$ \left\{\left.\sum_{n=1}^\infty x^n \;\right|\; |x|<1\right\} Using \left. \right| or \left| \right. is potentially an alternative to manual scaling.

### Set operations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \cap }$ ${\displaystyle A\cap B}$ Intersection (set theory) \cap &cap; U+2229
${\displaystyle \bigcap }$ ${\displaystyle \bigcap _{S\in P}S}$ \bigcap &xcap;
&Intersection;
U+22C2
${\displaystyle \cup }$ ${\displaystyle A\cup B}$ Union (set theory) \cup &cup; U+222A
${\displaystyle \bigcup }$ ${\displaystyle \bigcup _{S\in P}S}$ \bigcup &xcup;
&Union;
U+22C3
${\displaystyle \setminus }$ ${\displaystyle A\setminus B}$ Difference (set theory) \setminus &setminus;
&smallsetminus;
U+2216
${\displaystyle \smallsetminus }$ ${\displaystyle A\smallsetminus B}$ \smallsetminus
${\displaystyle \triangle }$ ${\displaystyle A\,\triangle \,B}$ Symmetric difference \triangle &Delta; U+2206
${\displaystyle \ominus }$ ${\displaystyle A\ominus B}$ \ominus &CircleMinus; U+2296
${\displaystyle \times }$ ${\displaystyle A\times B}$ Cartesian product \times &times; U+2A2F
${\displaystyle {\dot {\cap ))}$ ${\displaystyle A\,{\dot {\cap ))\,B}$ Intersection (set theory) \dot\cap &capdot; U+2A40
${\displaystyle \sqcap }$ ${\displaystyle A\sqcap B}$ \sqcap &SquareIntersection; U+2293
${\displaystyle }$ ${\displaystyle }$ \capwedge &capand; U+2A44
${\displaystyle {\dot {\cup ))}$ ${\displaystyle A\,{\dot {\cup ))\,B}$ Disjoint union \dot\cup &cupdot; U+228D
${\displaystyle \uplus }$ ${\displaystyle A\uplus B}$ \uplus &uplus; U+228E
${\displaystyle \sqcup }$ ${\displaystyle A\sqcup B}$ \sqcup &SquareUnion; U+2294
${\displaystyle }$ ${\displaystyle }$ Transversal intersection \mlcp &mlcp; U+2ADB
${\displaystyle {}^{\complement ))$ ${\displaystyle A^{\complement ))$ Complement (set theory) ^\complement &complement; U+2201
${\displaystyle {}^{\mathrm {C} ))$ C ${\displaystyle A^{\mathrm {C} ))$ ^{\mathrm C} &complement; U+2201
${\displaystyle {\bar {~))}$ ◌̄ ${\displaystyle {\bar {z))}$ \bar{} &#x304; U+0304
${\displaystyle {\overline {~~))}$ ◌̅ ${\displaystyle {\overline {A))}$ \overline{} U+0305
${\displaystyle \wp }$ ${\displaystyle \wp (A)}$ Power set \wp &wp; U+2118
${\displaystyle {\mathcal {P))}$ 𝒫 ${\displaystyle {\mathcal {P))(A)}$ \mathcal{P} &Pscr; U+1D4AB
${\displaystyle {\mathfrak {P))}$ 𝔓 ${\displaystyle {\mathfrak {P))(A)}$ \mathfrak{P} &Pfr; U+1D513
${\displaystyle \bigwedge }$ ${\displaystyle \bigwedge \limits _{x\in A))$ Infimum and supremum \bigwedge
\bigwedge\limits_{}
&Wedge; U+22C0
${\displaystyle \bigvee }$ ${\displaystyle \bigvee \limits _{x\in A))$ \bigvee
\bigvee\limits_{}
&xvee; U+22C1

### Set relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \subset }$ ${\displaystyle A\subset B}$ Subset \subset &sub; U+2282
${\displaystyle \subsetneq }$ ${\displaystyle A\subsetneq B}$ \subsetneq &subne; U+228A
${\displaystyle \subseteq }$ ${\displaystyle A\subseteq B}$ \subseteq &sube; U+2286
${\displaystyle }$ AB \subsetcirc &#x27C3; U+27C3
${\displaystyle \supset }$ ${\displaystyle A\supset B}$ Superset \supset &sup; U+2283
${\displaystyle \supsetneq }$ ${\displaystyle A\supsetneq B}$ \supsetneq &supne; U+228B
${\displaystyle \supseteq }$ ${\displaystyle A\supseteq B}$ \supseteq &supe; U+2287
${\displaystyle }$ AB \supsetcirc &#x27C4; U+27C4
${\displaystyle \not \subset }$ ${\displaystyle A\not \subset B}$ \not\subset &nsub; U+2284
${\displaystyle \not \supset }$ ${\displaystyle A\not \supset B}$ Superset \not\supset &nsup; U+2285
${\displaystyle \not \subseteq }$ ${\displaystyle A\not \subseteq B}$ \not\subseteq &NotSubsetEqual; U+2288
${\displaystyle \not \supseteq }$ ${\displaystyle A\not \supseteq B}$ Superset \not\supseteq &NotSupersetEqual; U+2289
${\displaystyle \in }$ ${\displaystyle a\in A}$ Element (mathematics) \in &isin; U+2208
${\displaystyle \ni }$ ${\displaystyle A\ni a}$ \ni, \owns &ni; U+220B
${\displaystyle \notin }$ ${\displaystyle a\notin A}$ \notin, \not\in &notin; U+2209
${\displaystyle \not \ni }$ ${\displaystyle A\not \ni a}$ \not\ni &NotReverseElement; U+220C
${\displaystyle \sqsubset }$ ${\displaystyle A\sqsubset B}$ Substring \sqsubset &SquareSubset; U+228F
${\displaystyle \sqsupset }$ ${\displaystyle A\sqsupset B}$ \sqsupset &SquareSuperset; U+2290
${\displaystyle \sqsubseteq }$ ${\displaystyle A\sqsubseteq B}$ \sqsubseteq &sqsubseteq; U+2291
${\displaystyle \sqsupseteq }$ ${\displaystyle A\sqsupseteq B}$ \sqsupseteq &SquareSupersetEqual; U+2292

Note: The symbols ${\displaystyle \subset }$ and ${\displaystyle \supset }$ are used inconsistently and often do not exclude the equality of the two quantities.

### Cardinality

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle |~~|}$ | | ${\displaystyle |A|}$ Cardinality \vert &VerticalLine; U+007C
${\displaystyle \#}$ # ${\displaystyle \#A}$ \# &num; U+0023
${\displaystyle {\mathfrak {c))}$ 𝔠 Cardinality of the continuum \mathfrak{c} &cfr; U+1D520
${\displaystyle \aleph }$ ${\displaystyle \aleph _{0))$, ${\displaystyle \aleph _{1))$, ... Aleph number \aleph &aleph; U+2135
${\displaystyle \beth }$ ${\displaystyle \beth _{0))$, ${\displaystyle \beth _{1))$, ... Beth number \beth &beth; U+2136

### Equivalence classes/relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle [~~]}$ [ ] ${\displaystyle [a]}$ Equivalence class [ ] &lsqb; &rsqb; U+005B/D
${\displaystyle /}$ / ${\displaystyle M/\!\sim }$ Quotient set / &sol; U+002F
${\displaystyle \sim }$ ${\displaystyle a\sim b}$ Equivalence relation \sim &sim;, &Tilde; U+223C
${\displaystyle \backsim }$ ${\displaystyle a\backsim b}$ \backsim &bsim; U+223D
${\displaystyle \nsim }$ ${\displaystyle a\nsim b}$ \not\sim, \nsim &nsim; U+2241
${\displaystyle \eqsim }$ ${\displaystyle a\eqsim b}$ \eqsim &EqualTilde; U+2242
${\displaystyle \simeq }$ ${\displaystyle a\simeq b}$ \simeq &TildeEqual; U+2243
${\displaystyle \cong }$ ${\displaystyle a\cong b}$ \cong &TildeFullEqual; U+2245
${\displaystyle \ncong }$ ${\displaystyle a\ncong b}$ \not\cong, \ncong &NotTildeFullEqual; U+2247

## Order theory

### Comparisons

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \leq }$ ${\displaystyle a\leq b}$ Order relation \leq, \le &leq;, &le; U+2264
${\displaystyle \geq }$ ${\displaystyle a\geq b}$ \geq, \ge &geq;, &ge; U+2265
${\displaystyle \nless }$ ${\displaystyle a\nless b}$ \nless &nlt;, &NotLess; U+226E
${\displaystyle \ngtr }$ ${\displaystyle a\ngtr b}$ \ngtr &ngt;, &NotGreater; U+226F
${\displaystyle \nleq }$ ${\displaystyle a\nleq b}$ \not\leq, \nleq &nle;, &NotLessEqual; U+2270
${\displaystyle \ngeq }$ ${\displaystyle a\ngeq b}$ \not\geq, \ngeq &nge;, &NotGreaterEqual; U+2271
${\displaystyle \lesssim }$ ${\displaystyle a\lesssim b}$ Inequality (mathematics) \lesssim &lsim;, &LessTilde; U+2272
${\displaystyle \gtrsim }$ ${\displaystyle a\gtrsim b}$ \gtrsim &gsim;, &GreaterTilde; U+2273
${\displaystyle \not \lesssim }$ ${\displaystyle a\not \lesssim b}$ \not\lesssim &NotLessTilde; U+2274
${\displaystyle \not \gtrsim }$ ${\displaystyle a\not \gtrsim b}$ \not\gtrsim &NotGreaterTilde; U+2275
${\displaystyle \prec }$ ${\displaystyle a\prec b}$ Successor ordinal \prec &prec; U+227A
${\displaystyle \succ }$ ${\displaystyle a\succ b}$ \succ &succ; U+227B
${\displaystyle \preccurlyeq }$ ${\displaystyle a\preccurlyeq b}$ \preccurlyeq &PrecedesSlantEqual; U+227C
${\displaystyle \succcurlyeq }$ ${\displaystyle a\succcurlyeq b}$ \succcurlyeq &SucceedsSlantEqual; U+227D
${\displaystyle \precsim }$ ${\displaystyle a\precsim b}$ \precsim &PrecedesTilde; U+227E
${\displaystyle \succsim }$ ${\displaystyle a\succsim b}$ \succsim &SucceedsTilde; U+227F
${\displaystyle \preceq }$ ${\displaystyle a\preceq b}$ \preceq &PrecedesEqual; U+2AAF
${\displaystyle \succeq }$ ${\displaystyle a\succeq b}$ \succeq &SucceedsEqual; U+2AB0
${\displaystyle \curlyeqprec }$ ${\displaystyle a\curlyeqprec b}$ \curlyeqprec &curlyeqprec; U+22DE
${\displaystyle \curlyeqsucc }$ ${\displaystyle a\curlyeqsucc b}$ \curlyeqsucc &curlyeqsucc; U+22DF
${\displaystyle \not \preceq }$ ${\displaystyle a\sqsubset b}$ Partially ordered set \sqsubset &sqsubset;
&SquareSubset;
U+228F
${\displaystyle \sqsupset }$ ${\displaystyle a\sqsupset b}$ \sqsupset &sqsupset;
&SquareSuperset;
U+2290
${\displaystyle \sqsubseteq }$ ${\displaystyle a\sqsubseteq b}$ \sqsubseteq &sqsubseteq;
&SquareSubsetEqual;
U+2291
${\displaystyle \sqsupseteq }$ ${\displaystyle a\sqsupseteq b}$ \sqsupseteq &sqsupseteq;
&SquareSupersetEqual;
U+2292
${\displaystyle \not \sqsubseteq }$ ${\displaystyle a\not \sqsubseteq b}$ \not\sqsubseteq &NotSquareSubsetEqual; U+22E2
${\displaystyle \not \sqsupseteq }$ ${\displaystyle a\not \sqsupseteq b}$ \not\sqsupseteq &NotSquareSupersetEqual; U+22E3

### Binary relations

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
; ; ${\displaystyle R;S}$ Composition of relations ; &semi; U+003B
${\displaystyle \bullet }$ ${\displaystyle a\bullet b}$ Operation (mathematics) \bullet &bull; U+2219
${\displaystyle \ast }$ ${\displaystyle a\ast b}$ \ast &lowast; U+2217
${\displaystyle {}^{T))$ ${\displaystyle R^{T))$ Converse relation T
${\displaystyle {\bar {))}$ ${\displaystyle {\bar {R))}$ Complementary relation \bar{R}
${\displaystyle {}^{+))$ + ${\displaystyle R^{+))$ Transitive closure + U+002B
${\displaystyle {}^{\ast ))$ * ${\displaystyle R^{\ast ))$ Reflexive closure \ast &lowast; U+002A

## Algebra

### Group theory

Symbol Unicode character Usage Articles with usage LaTeX HTML Unicode Hex
${\displaystyle \simeq }$ ${\displaystyle G\simeq H}$ Group isomorphism \simeq U+2243
${\displaystyle \cong }$ ${\displaystyle G\cong H}$ \cong &cong; U+2245
${\displaystyle \times }$ ${\displaystyle G\times H}$ Direct product \times &times; U+2A2F
${\displaystyle \rtimes }$ ${\displaystyle G\rtimes H}$ Semidirect product \rtimes &rtimes; U+22CA
${\displaystyle \wr }$ ${\displaystyle G\,\wr \,H}$ Wreath product \wr &VerticalTilde; U+2240
${\displaystyle \leq }$ ${\displaystyle U\leq G}$ Subgroup \leq &le; U+2264
${\displaystyle <}$ < ${\displaystyle U