List of mathematical symbols by subject

Short description: none

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

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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.

## Contents

* 1 Guide
* 2 Numbers
* 2.1 Number sets
* 2.1.1 Intervals
* 2.2 Mathematical constants
* 2.3 Complex numbers
* 2.4 Elementary arithmetic operations
* 2.4.1 Elementary functions
* 2.4.2 Trigonometric functions
* 2.5 Arithmetic comparison
* 3 Number theory
* 3.1 Divisibility and modulo
* 3.2 Combinatorics
* 4 Stochastics
* 4.1 Probability theory
* 4.2 Statistics
* 5 Calculus
* 5.1 Sequences and series
* 5.2 Limits
* 5.3 Differential calculus
* 5.4 Integral calculus
* 5.5 Vector calculus
* 5.6 Asymptotic behaviour
* 6 Linear algebra
* 6.1 Vectors and matrices
* 6.2 Vector operations
* 6.3 Matrix operations
* 6.4 Vector spaces
* 6.5 Functional analysis
* 7 Logic
* 7.1 Equality signs
* 7.2 Logical operators
* 7.3 Quantifiers
* 7.4 Deduction symbols
* 7.5 End of proof symbols
* 7.6 Formal language and strings
* 8 Functions and category theory
* 8.1 Functions
* 8.2 Morphisms
* 8.3 Constructions
* 9 Set theory
* 9.1 Definition symbols
* 9.2 Set construction
* 9.3 Set operations
* 9.4 Set relations
* 9.5 Cardinality
* 9.6 Equivalence classes/relations
* 10 Order theory
* 10.1 Comparisons
* 10.2 Binary relations
* 11 Algebra
* 11.1 Group theory
* 11.2 Field theory
* 11.3 Ring theory
* 12 Geometry
* 12.1 Euclidean geometry
* 12.2 Differential geometry
* 12.3 Topology
* 13 See also
* 13.1 By type of symbol
* 13.2 By topic area
* 13.3 General
* 13.4 Unicode
* 14 Bibliography
* 15 External links

## 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.mbf
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 `<mbf></mbf>` and `<MBF></MBF>`. The character × whose HTML code is Time 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

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𝔸 | 𝔸  | Algebraic number | `\mathbb{A}` | `&Aopf;` | `U+1D538`
ℂ | ℂ  | Complex number | `\mathbb{C}`, `\Complex` | `&Copf;` | `U+2102`
ℍ | ℍ  | Quaternion | `\mathbb{H}` | `&quaternions;` | `U+210D`
ℕ | ℕ  | Natural number | `\mathbb{N}`, `\N` | `&Nopf;` | `U+2115`
𝕆 | 𝕆  | Octonion | `\mathbb{O}` | `&Oopf;` | `U+1D546`
ℚ | ℚ  | Rational number | `\mathbb{Q}`, `\Q` | `&Qopf;` | `U+211A`
ℝ | ℝ  | Real number | `\mathbb{R}`, `\R`, `\Reals` | `&Ropf;` | `U+211D`
𝕊 | 𝕊  | Sedenion | `\mathbb{S}` | `&Sopf;` | `U+1D54A`
ℤ | ℤ  | Integer | `\mathbb{Z}`, `\Z` | `&Zopf;` | `U+2124`

#### Intervals

Symbol  | Usage  | LaTeX  | HTML  | Unicode Hex

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[] | [a,b] | `( )`
`[ ]` | `&lpar;` `&rpar;`
`&lsqb;` `&rsqb;` | `U+0028/9`
`U+005B/D`
][ | ]a,b[
() | (a,b)
[[ | [a,b[
[) | [a,b)
]] | ]a,b]
(] | (a,b]

### Mathematical constants

Symbol  | Unicode character  | Articles with usage  | LaTeX  | HTML  | Template  | Unicode Hex  | Note

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π | π  | Pi | `\pi` | `&pi;` | `{{pi}}` | `U+03C0` |
e or e | e  | e (mathematics)  | `e` or `\mathrm{e}` | `e` |  | `U+0065` | Recommend `{{mvar|e}}` or `{{math|e}}` over `e`
ϕ | ϕ  | Golden ratio | `\phi` | `&phi;` | `{{phi}}` | `U+03C6` |
φ | φ  | `\varphi` | `&straightphi;` | `{{varphi}}` | `U+03D5` |
i or i | i  | Imaginary unit | `i` or `\mathrm{i}` | `i` |  | `U+0069` | Recommend `{{mvar|i}}` or `{{math|i}}` over `i`
γ | γ  | Euler–Mascheroni constant | `\gamma` | `&gamma;` | `{{gamma}}` | `U+03B3` |
ϵ | ε  | Vacuum permittivity | `\epsilon` | `&epsi;` | `{{epsilon}}` | `U+03B5` |
ε | ϵ  | Dual number | `\varepsilon` | `&varepsilon;` | `{{varepsilon}}` | `U+03F5` |
θ | θ  | Mills' constant | `\theta` | `&theta;` | `{{theta}}` | `U+03B8` |
ϑ | ϑ  | `\vartheta` | `&vartheta;` | `{{vartheta}}` | `U+03D1` |
σ | σ  | Somos' quadratic recurrence constant | `\sigma` | `&sigma;` | `{{sigma}}` | `U+03C3` |
ς | ς  | `\varsigma` | `&varsigma;` | `{{varsigma}}` | `U+03C2` |
κ | κ  | Einstein gravitational constant  | `\kappa` | `&kappa;` | `{{kappa}}` | `U+03BA` |
λ | λ  | Prouhet–Thue–Morse constant | `\lambda` | `&lambda;` | `{{lambda}}` | `U+03BB` |
μ | μ  | Ramanujan–Soldner constant | `\mu` | `&mu;` | `{{mu}}` | `U+03BC` |
τ | τ  | Prouhet–Thue–Morse constant | `\tau` | `&tau;` | `{{tau}}` | `U+03C4` |

### Complex numbers

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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ℑ | ℑ  | ℑ(2+i)=1 | Complex number | `\Im` | `&image;` | `U+2111`
Im | Im  | Im⁡(2+i)=1 | `\operatorname{Im}` | `Im` |
ℜ | ℜ  | ℜ(2+i)=2 | `\Re` | `&Rfr;` | `U+211C`
Re | Re  | Re⁡(2+i)=2 | `\operatorname{Re}` | `Re` |
¯ | ◌̄  | z¯ | Complex conjugate | `\bar` | `&#x304;` | `U+0304`
¯¯ | ◌̄̄ | z¯¯ | `\bar{\bar{}}` | `&#x304;&#x304;`
‾ | ◌̅  | z‾ | `\overline` | `&#x305;` | `U+0305`
‾‾ | ◌̅̅ | z‾‾ | `\overline{\overline{}}` | `&#x305;&#x305;`
∗ | *  | z∗ | `{}^\ast` | `&ast;` | `U+002A`
|| | |  | |z| | Absolute value | `\vert` | `&VerticalLine;` | `U+007C`
arg⁡ |  | arg⁡(z) | Polar coordinate system | `\arg` |  |

Remark: real and imaginary parts of a complex number are often also denoted by Re and Im.

### Elementary arithmetic operations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex  | Notes

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+ | \+  | a+b | Addition | `+` | `&plus;` | `U+002B` |
− | −  | a−b | Subtraction | `-` | `&minus;` | `U+2212` |
⋅ | ⋅  | a⋅b | Multiplication | `\cdot` | `&sdot;` | `U+22C5` |
× | ⨯  | a×b | `\times` | `&times;` | `U+2A2F` |
: | ∶ or :  | a:b | Division (mathematics) | `:`, `\colon` | `&ratio;` or `&colon;` | `U+003A` or `U+2236` | In LaTeX, `:` added space around the colon a:b that `\colon` does not a:b.
/ | ∕  | a/b | `/` | `&#x2215;` | `U+2215` |
÷ | ÷  | a÷b | `\div` | `&divide;` | `U+00F7` |
| ⁄  | ab | `\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: a⁄b
−1 | ⁻  | a−1 | Multiplicative inverse | `^{-1}` |  | `U+207B` |
− | −  | −a | Additive inverse | `-` | `&minus;` | `U+2212` |
± | ±  | ±a | Plus or minus sign  | `\pm` | `&plusmn;` | `U+00B1` |
∓ | ∓  | ∓a | `\mp` | `&mnplus;` | `U+2213` |

#### Elementary functions

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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| √  | x | Square root | `\sqrt{}` | `&radic;` | `U+221A`
3 | ∛  | x3 | Cube root | `\sqrt[3]{x}` | `&x221B;` | `U+221B`
4 | ∜  | x4 | Fourth root  | `\sqrt[4]{x}` | `&x221C;` | `U+221C`
n |  | xn | nth root | `\sqrt[n]{}` |  |
% | %  | x% | Percentage | `\%` | `&percnt;` | `U+0025`
() | ( )  | (x) | Order of operations | `(` `)` | `&lpar;` `&rpar;` | `U+0028/9`
(12) | `\left( \right)`
[] | [ ]  | [x] | Bracket | `[` `]` | `&lsqb;` `&rsqb;` | `U+005B/D`
|| | | |  | |x| | Absolute value | `|`, `\vert` | `&VerticalLine;` | `U+007C`
{} | { }  | {x} | Fractional part | `\{` `\}`
`\lbrace` `\rbrace` | `&lcub;` `&rcub;` | `U+007B/D`
⌈⌉ | ⌈ ⌉  | ⌈x⌉ | Floor and ceiling functions | `\lceil` `\rceil` | `&lceil;` `&rceil;` | `U+2308/9`
⌊⌋ | ⌊ ⌋  | ⌊x⌋ | `\lfloor` `\rfloor` | `&lfloor;` `&rfloor;` | `U+230A/B`
⌜⌝ | ⌜ ⌝  | ⌜x⌝ | `\ulcorner` `\urcorner` | `&ulcorner;` `&urcorner;` | `U+231C/D`
⌞⌟ | ⌞ ⌟  | ⌞x⌟ | `\llcorner` `\lrcorner` | `&llcorner;` `&lrcorner;` | `U+231E/F`
⌢ |  ⌢​ | x⌢ | Cap product | `\frown` | `&frown;` | `U+2322`
⌣ |  ⌣​ | x⌣ | Cup product | `\smile` | `&smile;` | `U+2323`
exp | exp  | exp⁡x | Exponential function | `\exp` | `exp` |
log | log  | logbx | Logarithm | `\log` or `\log_{}` | `log` or `log<sub></sub>` |
ln | ln  | ln⁡x | Natural logarithm | `\ln` | `ln` |
lg | lg  | lg⁡x | Binary logarithm | `\lg` | `lg` |
min | min  | min⁡{1,2} | Maxima and minima | `\min` | `min` |
max | max  | max⁡{1,2} | `\max` | `max` |
inf | inf  | inf⁡{1,2} | Infimum and supremum | `\inf` | `inf` |
sup | sup  | sup⁡{1,2} | `\sup` | `sup` |
lim inf | liminf  | lim infn->∞xn | Limit inferior and limit superior | `\liminf` | `liminf` |
lim― | lim | lim―xn | `\varliminf` | `<u>lim</u>`
lim sup | limsup  | lim supn->∞xn | `\limsup` | `limsup` |
lim― | lim | lim―xn | `\varlimsup` | `<span style="text-decoration:overline;">lim</span>`
gcd | gcd  | 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

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sin | sin  | sin⁡x | Sine and cosine | `\sin` | `sin` |
cos | cos  | cos⁡x | `\cos` | `cos` |
tan | tan  | tan⁡x | Tangent | `\tan` | `tan` |
sec | sec  | sec⁡x | Trigonometric functions | `\sec` | `sec` |
csc | csc  | csc⁡x | `\csc` | `csc` |
cot | cot  | cot⁡x | `\cot` | `cot` |
arcsin | sin  | arcsin⁡x | Inverse trigonometric functions | `\arcsin` | `arcsin` |
arccos | arccos  | arccos⁡x | `\arccos` | `arccos` |
arctan | arctan  | arctan⁡x | `\arctan` | `arctan` |
arcsec | arcsec  | arcsec⁡x | `\arcsec` | `arcsec` |
arccsc | arccsc  | arccsc⁡x | `\arccsc` | `arccsc` |
arccot | arccot  | arccot⁡x | `\arccot` | `arccot` |
sinh | sinh  | sinh⁡x | Hyperbolic functions | `\sinh` | `sinh` |
cosh | cosh  | cosh⁡x | `\cosh` | `cosh` |
tanh | tanh  | tanh⁡x | `\tanh` | `tanh` |
coth | coth  | coth⁡x | `\coth` | `coth` |

### Arithmetic comparison

See also: Order relations, Set relations
Symbol  | Unicode character  | Usage  | LaTeX  | HTML  | Unicode Hex

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< | < | a<b | `<` | `&lt;` | `U+003C`
> | > | a>b | `>` | `&gt;` | `U+003E`
≤ | ≤  | a≤b | `\le`, `\leq` | `&le;` | `U+2264`
≥ | ≥  | a≥b | `\ge`, `\geq` | `&ge;` | `U+2265`
≦ | ≦  | a≦b | `\leqq` | `&LessFullEqual;` | `U+2266`
≧ | ≧  | a≧b | `\geqq` | `&GreaterFullEqual;` | `U+2267`
⩽ | ⩽  | a⩽b | `\leqslant` | `&LessSlantEqual` | `U+2A7D`
⩾ | ⩾  | a⩾b | `\geqslant` | `&GreaterSlantEqual` | `U+2A7E`
≪ | ≪  | a≪b | `\ll` | `&NestedLessLess;` | `U+226A`
≫ | ≫  | a≫b | `\gg` | `&NestedGreaterGreater;` | `U+226B`
≲ | ≲  | a≲b | `\lesssim` | `&lsim;` | `U+2272`
≳ | ≳  | a≳b | `\gtrsim` | `&GreaterTilde;` | `U+2273`
⪅ | ⪅  | a⪅b | `\lessapprox` | `&lessapprox;` | `U+2A85`
⪆ | ⪆  | a⪆b | `\gtrapprox` | `&gap;` | `U+2A86`
Symbol  | Unicode character  | Usage  | LaTeX  | HTML  | Unicode Hex

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≶ | ≶  | a≶b | `\lessgtr` | `&LessGreater` | `U+2276`
≷ | ≷  | a≷b | `\gtrless` | `&GreaterLess;` | `U+2277`
⋚ | ⋚  | a⋚b | `\lesseqgtr` | `&LessEqualGreater;` | `U+22DA`
⋛ | ⋛  | a⋛b | `\gtreqless` | `&GreaterEqualLess;` | `U+22DB`
⪋ | ⪋  | a⪋b | `\lesseqqgtr` | `&lesseqqgtr;` | `U+2A8B`
⪌ | ⪌  | a⪌b | `\gtreqqless` | `&gtreqqless;` | `U+2A8C`

## Number theory

### Divisibility and modulo

Symbol  | Unicode character  | Usage  | LaTeX  | HTML  | Unicode Hex

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∣ | ∣  | a∣b | `\mid` | `&VerticalBar;` | `U+2223`
∤ | ∤  | a∤b | `\nmid` | `&NotVerticalBar;` | `U+2224`
⊥ | ⊥  | a⊥b | `\perp` | `&perp;` | `U+22A5`
⊓ | ⊓  | a⊓b | `\sqcap` | `&SquareIntersection;` | `U+2293`
∧ | ∧  | a∧b | `\wedge` | `&and;` | `U+2227`
⊔ | ⊔  | a⊔b | `\sqcup` | `&SquareUnion;` | `U+2294`
∨ | ∨  | a∨b | `\vee` | `&or;` | `U+2228`
Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex  | Other information

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≡ | ≡  | a≡b | Modulo operation | `\equiv` | `&equiv;` | `U+2261` |
modm | mod  | amodm | `\mod m` | `mod` |  | `<math>\mod</math>` without a trailing symbol (e.g. m) will produce an error.
(modm) | (mod)  | a(modm) | `\pmod m` | `(mod)` |  | `<math>\pmod</math>` without a trailing symbol (e.g. m) will produce an error.
gcd | gcd  | gcd⁡(1,2) | Greatest common divisor  | `\gcd` | `gcd` |  |

### Combinatorics

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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! | !  | n! | Factorial | `!` | `&excl;` | `U+0021`
!n | Derangement
n!! | Double factorial
() | ( )  | (nk) | Combination | `\binom` | `&lpar;` `&rpar;` | `U+0028/9`
(nk1,…,kr) | Multinomial coefficient
(()) | (( ))  | ((nk)) | Multiset | (( ))  | `&lpar;` `&rpar;` | `U+0028/9`
‾ | ◌̄  | nm¯ | Pochhammer symbol  | `\bar` | `&#x304;` | `U+0304`
◌̅  | nm‾ | `\overline` | `&#x305;` | `U+0305`
◌̲  | nm_ | `\underline` | `&#x332;` | `U+0332`
# | #  | n# | Primorial | `\#` | `&num;` | `U+0023`

## Stochastics

### Probability theory

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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P |  | P(A) | Probability measure | `P` |  | `U+2119`
∣ |  | P(A∣B) | Conditional probability | `\mid` | `&VerticalLine;` | `U+007C`
/ |  | P(A/B) | `/` |  | `U+2215`
E | 𝔼  | E(X) | Expected value | `E` | `&Eopf;` | `U+1D53C`
V | 𝕍  | V(X) | Variance | `V` | `&Vopf;` | `U+1D54D`
σ | σ  | σ(X) | Standard deviation | `\sigma` | `&sigma;` | `U+03C3`
σ(X,Y) | Covariance
ρ | ρ  | ρ(X,Y) | Correlation | `\rho` | `&rho;` | `U+03C1`
∼ | ∼  | X∼F | Probability distribution | `\sim` | `&sim;` | `U+223C`
≈ | ≈  | X≈F | `\approx` | `&asymp;` | `U+2248`
⊥ | ⊥  | A⊥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

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¯ | ◌̅  | x¯ | Average | `\bar` | `&#x304;` | `U+0304`
‾ | ◌̅  | m‾ | `\overline` | `&#x305;` | `U+0305`
⟨⟩ | ⟨ ⟩  | ⟨X⟩ | `\langle \rangle` | `&lang;` `&rang;` | `U+27E8/9`
^ | ◌̂  | p^ | Estimator | `\hat` | `̂` | `U+0302`

## Calculus

### Sequences and series

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∑ | ∑  | ∑i=1n,∑i∈I | Summation | `\sum` | `&sum;` | `U+2211`
∏ | ∏  | ∏i=1n,∏i∈I | Multiplication | `\prod` | `&prod;` | `U+220F`
∐ | ∐  | ∐i=1n,∐i∈I | Coproduct | `\coprod` | `&Coproduct;` | `U+2210`
() | ( )  | (an) | Sequence | `( )` | `&lpar;` `&rpar;` | `U+0028/9`
-> | →  | an->a | Limit of a sequence | `\to` `\rarr` | `&rarr;` | `U+2192`
∞ | ∞  | n->∞ | Infinity | `\infty` | `&infin;` | `U+221E`

### Limits

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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-> | →  | limx->af(x) | Limit of a function | `\to`
`\rightarrow` | `&rarr;`
`&rightarrow;` | `U+2192`
⟶ | ⟶  | x⟶a | `\longrightarrow` | `&LongRightArrow;` | `U+27F6`
↑ | ↑  | limx↑af(x) | `\uparrow` | `&uarr;`
`&ShortUpArrow;` | `U+2191`
↗ | ↗  | limx↗af(x) | `\nearrow` | `&UpperRightArrow;` | `U+2197`
↘ | ↘  | limx↘af(x) | `\searrow` | `&LowerRightArrow;` | `U+2198`
↓ | ↓  | limx↓af(x) | `\downarrow` | `&darr;`
`&ShortDownArrow;` | `U+2193`
↙ | ↙  | a↙x | `\swarrow` | `&LowerLeftArrow;` | `U+2199`
<- | ←  | a<-x | `\leftarrow` | `&larr;`
`&ShortLeftArrow;` | `U+2190`
⟵ | ⟵  | a⟵x | `\longleftarrow` | `&longleftarrow;` | `U+27F5`
↖ | ↖  | a↖x | `\nwarrow` | `&UpperLeftArrow;` | `U+2196`
+ | ⁺  | limx->a+f(x) | `^+` | `&#8314;` | `U+207A`
− | ⁻  | limx->a−f(x) | `^-` | `&#8315;` | `U+207B`
lim |  | limn->∞xn | `\lim` |  |
lim inf |  | lim infn->∞xn | Limit inferior and limit superior | `\liminf` |  |
lim sup |  | lim supn->∞xn | `\limsup` |  |

### Differential calculus

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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′ | ′  | f′
f′ | Lagrange's notation
Prime (symbol) | `'`
`^\prime` | `&prime;` | `U+2032`

′′ | ″  | f″
f′′ | `''`
`^{\prime\prime}` | `&Prime;` | `U+2033`

′′′ | ‴  | f‴
f′′′ | `'''`
`^{\prime\prime\prime}` | `&tprime;` | `U+2034`

′′′′ | ⁗  | f⁗
f′′′′ | `''''`
`^{\prime\prime\prime\prime}` | `&qprime;` | `U+2057`
IVVVI |  | fIV,fV,fVI | `^{IV}` `^V` `^{VI}` | `<sup>IV</sup>` |
ivvvi |  | fiv,fv,fvi | `^{iv}` `^v` `^{vi}` | `<sup>iv</sup>` |
() | ⁽ ⁾  | f(4),f(5),f(n) | `^{( )}` | `<sup>( )</sup>` | `U+207D/E`
˙ | ◌̇  | f˙ | Newton's notation  | `\dot` | `&#x0307;` | `U+0307`
¨ | ◌̈  | f¨ | `\ddot` | `&#x0308;` | `U+0308`
d | d  | dx | Leibniz's notation | `d` | `d` | `U+0064`

dfdx
ddxf
d2dx2f
∂ | ∂  | ∂xf | Partial derivative | `\partial` | `&part;` | `U+2202`
∂∂x|x | ∂ and |  | ∂f∂x|x=x0 | `\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

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∫ | ∫  | ∫ab , ∫G | Integral | `\int` | `&int;` | `U+222B`
∬ | ∬  | ∬ℱ | Surface integral | `\iint` | `&Int;` | `U+222C`
∭ | ∭  | ∭V | Volume integral | `\iiint` | `&tint;` | `U+222D`
∮ | ∮  | ∮γ | Curve integral  | `\oint` | `&ContourIntegral;` | `U+222E`
| ∯  |  γ | Surface integral | `\oiint` | `&DoubleContourIntegral;` | `U+222F`
Template:Oiiint | ∰  | Template:Oiiint | Volume integral | `\oiiint` | `&Cconint;` | `U+2230`

### Vector calculus

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∇ | ∇  | ∇f | Gradient | `\nabla` | `&nabla;` | `U+2207`
∇⋅F | Divergence
∇×F | Curl (mathematics)
Δ | ∆  | Δf | Laplace operator | `\Delta` | `&Delta;` | `U+2206`
◻ | □  | ◻f | D'Alembert operator | `\square` | `&#9633;` | `U+25A1`

### Asymptotic behaviour

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∼ | ∼  | f∼ | Asymptotic analysis | `\sim` | `&sim;` | `U+223C`
o | o  | f∈o(g) | Big O notation | `o` |  | `U+006F`
𝒪 | 𝒪  | f∈𝒪(g) | `\mathcal{O}` | `&Oscr;` | `U+1D4AA`
Θ | Θ  | f∈Θ(g) | `\Theta` | `&Theta;` | `U+0398`
Ω | Ω  | f∈Ω(g) | `\Omega` | `&Omega;` | `U+03A9`
ω | ω  | f∈ω(g) | `\omega` | `&omega;` | `U+03C9`

## Linear algebra

### Vectors and matrices

Symbol  | Articles with usage  | LaTeX

|
|

(v1,…,vn) | Vector (mathematics and physics) | `\begin{pmatrix}`
`...`
`\end{pmatrix}`

`\left(`
`\begin{array}{...}`
`...`
`\end{array}`
`\right)`
(v1⋮vm)
(a11…a1n⋮⋱⋮am1…amn) | Matrix (mathematics)

### Vector operations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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⋅ | ⋅  | v⋅w | Dot product

Inner product space

| `\cdot` | `&sdot;` | `U+22C5`
() | ( )  | (v,w) | `( )` | `&lpar;` `&rpar;` | `U+0028/9`
⟨⟩ | ⟨ ⟩  | ⟨v,w⟩
⟨v|w⟩ | `\langle \rangle` | `&lang;` `&rang;` | `U+27E8/9`
× | ⨯  | v×w | Cross product | `\times` | `&times;` | `U+2A2F`
[] | [ ] | [v,w] | `[ ]` | `&lsqb;` `&rsqb;` | `U+005B/D`
() | ( )  | (u,v,w) | Triple product | `( )` | `&lpar;` `&rpar;` | `U+0028/9`
⊗ | ⊗  | v⊗w | Dyadic product  | `\otimes` | `&otimes;` | `U+2297`
∧ | ∧  | v∧w | Exterior algebra | `\wedge` | `&and;` | `U+2227`
|| | | |  | |v| | Euclidean norm  | `\vert` | `&VerticalLine;` | `U+007C`
‖‖ | ‖  | ‖v‖
‖v‖ | Norm (mathematics) | `\Vert`, `\|`
`\lVert` `\rVert` | `&Vert;` | `U+2016`
^ | ̂ | v^ | Unit vector | `\hat{}` | `&#x302;` | `U+0302`

### Matrix operations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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⋅ | ⋅  | A⋅B | Matrix multiplication | `\cdot` | `&sdot;` | `U+22C5`
∘ | ∘  | A∘B | Hadamard product | `\circ` | `&SmallCircle;` | `U+2218`
⊘ | ⊘  | A⊘B | Hadamard division  | `\oslash` | `&osol;` | `U+2298`
* | *  | A*B | Khatri-Rao product | `*` | `&ast;` | `U+002A`
⊗ | ⊗  | A⊗B | Kronecker product | `\otimes` | `&otimes;` | `U+2297`
⊺ | ⊺  | A⊺ | Transposed matrix  | `^\intercal` | `&intercal;` | `U+22BA`
⊤ | ⊤  | A⊤ | `^\top` | `&top;` | `U+22A4`
T | T  | AT | `^{\mathrm T}` |  | `U+0054`
∗ | *  | A∗ | Conjugate transpose | `^\ast` | `&ast;` | `U+002A`
† | †  | A† | `^\dagger` | `&dagger;` | `U+2020`
H | H  | AH | `^H` |  | `U+0048`
−1 | ⁻  | A−1 | Inverse matrix  | `^{-1}` |  | `U+207B`
+ | \+  | A+ | Moore–Penrose pseudoinverse  | `^+` | `&plus;` | `U+002B`
|| | | A |  | |A| | Determinant | `|`, `\vert` | `&VerticalLine;` | `U+007C`
det | det  | det⁡A | `\det` | `det` |
‖‖ | ‖  | ‖A‖ | Matrix norm | `\|`, `\Vert` | `&Vert;` | `U+2016`

### Vector spaces

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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+ | \+  | V+W | Direct sum of modules

Linear subspace

| `+` | `&plus;` | `U+002B`
⊕ | ⊕  | V⊕W | `\oplus` | `&oplus;` | `U+2295`
× | ⨯  | V×W | Direct product | `\times` | `&times;` | `U+2A2F`
⊗ | ⊗  | V⊗W | Tensor product | `\otimes` | `&otimes;` | `U+2297`
/ | /  | V/U | Quotient space (linear algebra) | `/` | `&frasl;` | `U+002F`
⊥ | ⟂  | U⊥ | Orthogonal complement | `^\perp` | `&perp;` | `U+27C2`
∗ | *  | V∗ | Dual space | `^\ast` | `&lowast;` | `U+002A`
0 | 0  | X0 | `^0` |  | `U+0030`
⟨⟩ | ⟨ ⟩  | ⟨X⟩ | Linear hull  | `\langle` `\rangle` | `&lang;` `&rang;` | `U+27E8/9`
dim | dim  | dim⁡X | Dimension (linear algebra)  | `\dim` | `dim` |
ker | ker  | ker⁡L | Kernel (linear algebra) | `\ker` | `ker` |
Pr | Pr  | Pr⁡1(x,y) | Projection (linear algebra) | `\Pr` | `Pr` |

### Functional analysis

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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' | ′  | V′ | Dual space | `^\prime` | `&prime;` | `U+2032/3`
'′ | ″  | V″
^ | ◌̂  | X^ | Complete metric space | `\hat{}` |  | `U+0302`
↪ | ↪  | X↪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

| Look up Appendix:Variations of "=", Appendix:Variations of "≡", or Appendix:Variations of the number sign in Wiktionary, the free dictionary.

|

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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= | = | a=b | Equality | `=` | `&equals;` | `U+003D`
# | #  | a#b | Apartness relation | `\#` | `&num;` | `U+0023`
≠ | ≠  | a≠b | Inequality | `\neq`
`\ne`
`\not=` | `&ne;` | `U+2260`
≡ | ≡ | a≡b | Identity | `\equiv` | `&equiv;` | `U+2261`
≈ | ≈  | a≈b | Approximation | `\approx` | `&asymp;` | `U+2248`
∼ | ∼  | a∼b | Equivalence class | `\sim` | `&sim;` | `U+223C`
∝ | ∝  | a∝b | Proportionality | `\propto` | `&prop;` | `U+221D`
=^ | ≙  | a=^b | Bijection | `\widehat{=}` | `&wedgeq;` | `U+2259`
=? | ≟  | a=?b | Asks "is it equal to"  | `\overset{?}{=}` | `&questeq;` | `U+225F`
=def | ≝  | a=defb | Equal to by definition  | `\overset{\operatorname{def}}{=}` | `&#x225D;` | `U+225D`
≜ | ≜  | a≜b | `\triangleq` | `&trie;` | `U+225C`
:= | ≔  | a:=b | Assignment | `:=` | `&coloneq;` | `U+2254`
=: | ≕  | a=:b | `=:` | `&eqcolon;` | `U+2255`
≐ | ≐  | xn≐b | Approaches the limit | `\doteq` | `&esdot;` | `U+2250`
== | ⩵  | x==y | Relational operator | `==` | `&Equal;` | `U+2A75`

### Logical operators

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∧ | ∧  | A∧B | Logical conjunction | `\land` | `&and;` | `U+2227`
∨ | ∨  | A∨B | Logical disjunction | `\lor` | `&or;` | `U+2228`
⇔ | ⇔  | A⇔B | Logical equivalence | `\Leftrightarrow` | `&hArr;` | `U+21D4`
↔ | ↔  | A↔B | `\leftrightarrow` | `&harr;` | `U+2194`
⟺ | ⟺  | A⟺B | `\iff` | `&Longleftrightarrow;` | `U+27FA`
⇒ | ⇒  | A⇒B | Logical consequence | `\Rightarrow` | `&rArr;` | `U+21D2`
-> | →  | A->B | `\rightarrow` | `&rarr;` | `U+2192`
⟹ | ⟹  | A⟹B | `\implies` | `&DoubleLongRightArrow;` | `U+27F9`
⟹ | A⟹B | `\Longrightarrow`
⊕ | ⊕  | A⊕B | Exclusive or | `\oplus` | `&oplus;` | `U+2295`
⊻ | ⊻  | A⊻B | `\veebar` | `&veebar;` | `U+22BB`
∨˙ | ⩒  | A∨˙B | `\dot\lor` |  | `U+2A52`
¬ | ¬  | ¬A | Logical negation  | `\lnot` | `&not;` | `U+00AC`
¯ | ◌̄  | A¯ | `\bar` | `&#x304;` | `U+0304`
‾ | ̅ | A‾ | `\overline` | `&#x305;` | `U+0305`
| ◌̸ | =
∉ | `\not`
(ex: `\not=` `\not\in`)  | `&#x338;`
(ex: `=&#x338;` `&isin;&#x338;`)  | `U+0338`
<- | ←  | A<-B | Converse implication | `\leftarrow` | `&ShortLeftArrow;` | `U+2190`
⊸ | ⊸  | A⊸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

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∀ | ∀  | ∀x | Universal quantification | `\forall` | `&forall;` | `U+2200`
⋀ | ⋀  | ⋀x | `\bigwedge` | `&Wedge;` | `U+22C0`
∃ | ∃  | ∃x | Existential quantification | `\exists` | `&exist;` | `U+2203`
⋁ | ⋁  | ⋁x | `\bigvee` | `&xvee;` | `U+22C1`
∃! | ∃!  | ∃!x | Uniqueness quantification | `\exists!` | `&exist;!` | `U+2203`!
⋁⋅ | ⩒  | ⋁x⋅ | `\dot\bigvee` |  | `U+2A52`
∄ | ∄  | ∄x | Existential quantification | `\nexists` | `&NotExists;` | `U+2204`

### Deduction symbols

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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⊢ | ⊢ | A⊢B | Logical consequence, Propositional calculus | `\vdash` | `&vdash;` | `U+22A2`
⊨ | ⊨ | A⊨B | Logical consequence, Inference | `\models` | `&DoubleRightTee;` | `U+22A8`
⊨A | Tautology (logic)
⊤ | ⊤  | A⊤ | `\top` | `&top;` | `U+22A4`
⊥ | ⊥  | A⊥ | Contradiction | `\bot` | `&perp;` | `U+22A5`
∴ | ∴  | A∴B | Deductive reasoning | `\therefore` | `&therefore;` | `U+2234`
∵ | ∵  | A∵B | `\because` | `&because;` | `U+2235`

### End of proof symbols

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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◼ | ■  | ...as desired. ◼ | Q.E.D. | `\blacksquare` | `&#x25A0;` | `U+25A0`
◻ | □  | `\Box` | `&squ;` | `U+25A1`
| ∎  | Tombstone | `` | `&#x220E;` | `U+220E`

### Formal language and strings

Main article: Formal language

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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ε | ε  | εs=s | Empty string | `\varepsilon` | `&epsi;` | `U+03B5`
|| | | |  | |s| | String length  | `\vert` | `&VerticalLine;` | `U+007C`
+ | \+  | s+t | Concatenation | `+` | `&plus;` | `U+002B`
⋅ | ⋅  | s⋅t | `\cdot` | `&sdot;` | `U+22C5`
¬ | ¬  | ¬L | Formal language | `\lnot` | `&not;` | `U+00AC`
∗ | *  | V∗ | Kleene star | `^\ast` | `&lowast;` | `U+002A`
+ | \+  | V+ | Free monoid | `^+` | `&plus;` | `U+002B`
∼ | ∼  | a∼b | Squiggle operator  | `\sim` | `&sim;` | `U+223C`
[[]] | ⟦⟧  | [[s]] | Squiggle operator  | `[\![` `]\!]` | `&LeftDoubleBracket;` `&RightDoubleBracket;` | `U+27E6/7`

## Functions and category theory

### Functions

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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-> | →  | f:A->B | Function (mathematics) | `\to` | `&rarr;` | `U+2192`
A->fB
↦ | ↦  | f:x↦y | `\mapsto` | `&mapstoright;` | `U+21A6`
x↦fy
() | ( )  | f(x) | Image (mathematics) | `( )` | `&lpar;` `&rpar;` | `U+0028/9`
f(X)
[] | [ ]  | f[X] | `[ ]` | `&lbrack;` or `&rbrack;` | `U+005B/D`
| | |  | f|X | Restriction (mathematics) | `\vert` | `&VerticalLine;` | `U+007C`
⋅ | ⋅  | f(⋅) | Free variable  | `\cdot` | `&sdot;` | `U+22C5`
−1 | ⁻  | f−1 | Inverse function | `-1` |  | `U+207B`
∘ | ∘  | f∘g | Function composition | `\circ` | `&#8728;` | `U+2218`
∗ | ∗  | f∗g | Convolution | `\ast` | `&lowast;` | `U+2217`
^ | ◌̂  | f^ | Fourier transform | `\hat` |  | `U+0302`
⊸ | ⊸  | f:X⊸Y | Multimap | `\multimap` | `&mumap;` | `U+22B8`

### Morphisms

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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-> | →  | f:X->Y | Morphism | `\to` | `&rarr;` | `U+2192`
X->fY
↦ | ↦  | f:x↦y | `\mapsto` | `&mapstoright;` | `U+21A6`
x↦fy
->∼ | ⥲  | f:X->∼Y | Isomorphism | `\tilde{\rightarrow}` |  | `U+2972`
↪ | ↪  | f:X↪Y | Monomorphism | `\hookrightarrow` | `&#8618` | `U+21AA`
X↪fY
↠ | ↠  | f:X↠Y | Epimorphism | `\twoheadrightarrow` | `&#8608` | `U+21A0`
X↠f Y
hom | hom  | homC(X,Y) | Morphism | `\hom` | `hom` |

### Constructions

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∏ | ∏  | ∏Xi | Product (category theory) | `\prod` | `&prod;` | `U+220F`
∐ | ∐  | ∐Xi | Coproduct | `\coprod` | `&Coproduct;` | `U+2210`
⊕ | ⊕  | ⊕Xi | Biproduct | `\oplus` | `&CirclePlus;` | `U+2295`
× | ×  | A×CB | Pullback (category theory) | `\times` | `&times;` | `U+00D7`
lim | lim  | lim⁡F | Limit (category theory) | `\lim` | `lim` |
proj lim | projlim  | proj limF | Inverse limit | `\projlim` | `projlim` |
lim<- |  | lim<-F | `\varprojlim` |  |
inj lim | injlim  | inj limF | Direct limit | `\injlim` | `injlim` |
lim-> |  | lim->F | `\varinjlim` |  |

## Set theory

### Definition symbols

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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: | :  | A:B | Definition | `\colon` | `&colon;` | `U+003A`
A:=B
A:⇔B

### Set construction

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∅ | ∅  | ∅={} | Empty set | `\varnothing` | `&varnothing;`
`&empty;` | `U+2205`
∅ |  |  | `\emptyset` |  |
{} | { }  | {a,b,…} | Set (mathematics) | `\{` `\}`
`\lbrace` `\rbrace` | `&lcub;` `&rcub;` | `U+007B/D`
∣ | |  | {a∣T(a)} | `\mid` | `&VerticalLine;` | `U+007C`
: | :  | {a:T(a)} | `\colon` | `&colon;` | `U+003A`
: | {a:T(a)} | `:`
Comparison of separators (the symbol between the variable and predicate)  Rendered result  | Latex code  | Notes on separator

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|

{x∈X:P(x)} | `\{x\in X : P(x)\}` | `:` inserts whitespace that `\colon` does not.
{x∈X:P(x)} | `\{x\in X \colon P(x)\}` |
{x∈X∣P(x)} | `\{x\in X \mid P(x)\}` | `\mid` inserts whitespace that `\vert` does not.
{x∈X|P(x)} | `\{x\in X \vert P(x)\}` | `\vert` and `|` are synonyms in LaTeX.
{x∈X\vline P(x)} | `\{x\in X \vline P(x)\}` | `\mid` inserts whitespace that `\vline` does not.
{∑n=1∞xn:|x|<1} | `\left\{\sum_{n=1}^{\infty} x^n : |x|<1\right\}` |
{∑n=1∞xn∣|x|<1} | `\left\{\sum_{n=1}^\infty x^n \mid |x|<1\right\}` |
{∑n=1∞xn||x|<1} | `\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.
{∑n=1∞xn||x|<1} | `\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

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∩ | ∩  | A∩B | Intersection (set theory) | `\cap` | `&cap;` | `U+2229`
⋂ | ⋂  | ⋂S∈PS | `\bigcap` | `&xcap;`
`&Intersection;` | `U+22C2`
∪ | ∪  | A∪B | Union (set theory) | `\cup` | `&cup;` | `U+222A`
⋃ | ⋃  | ⋃S∈PS | `\bigcup` | `&xcup;`
`&Union;` | `U+22C3`
∖ | ∖  | A∖B | Difference (set theory)  | `\setminus` | `&setminus;`
`&smallsetminus;` | `U+2216`
∖ | A∖B | `\smallsetminus`
△ | ∆ | A△B | Symmetric difference | `\triangle` | `&Delta;` | `U+2206`
⊖ | ⊖ | A⊖B | `\ominus` | `&CircleMinus;` | `U+2296`
× | ⨯  | A×B | Cartesian product | `\times` | `&times;` | `U+2A2F`
∩˙ | ⩀  | A∩˙B | Intersection (set theory) | `\dot\cap` | `&capdot;` | `U+2A40`
⊓ | ⊓  | A⊓B | `\sqcap` | `&SquareIntersection;` | `U+2293`
| ⩄  |  | `\capwedge` | `&capand;` | `U+2A44`
∪˙ | ⊍  | A∪˙B | Disjoint union | `\dot\cup` | `&cupdot;` | `U+228D`
⊎ | ⊎  | A⊎B | `\uplus` | `&uplus;` | `U+228E`
⊔ | ⊔  | A⊔B | `\sqcup` | `&SquareUnion;` | `U+2294`
| ⫛  |  | Transversal intersection | `\mlcp` | `&mlcp;` | `U+2ADB`
∁ | ∁  | A∁ | Complement (set theory) | `^\complement` | `&complement;` | `U+2201`
C | C | AC | `^{\mathrm C}` | `&complement;` | `U+2201`
¯ | ◌̄  | z¯ | `\bar{}` | `&#x304;` | `U+0304`
‾ | ◌̅  | A‾ | `\overline{}` |  | `U+0305`
℘ | ℘  | ℘(A) | Power set | `\wp` | `&wp;` | `U+2118`
𝒫 | 𝒫  | 𝒫(A) | `\mathcal{P}` | `&Pscr;` | `U+1D4AB`
𝔓 | 𝔓  | 𝔓(A) | `\mathfrak{P}` | `&Pfr;` | `U+1D513`
⋀ | ⋀  | ⋀x∈A | Infimum and supremum | `\bigwedge`
`\bigwedge\limits_{}` | `&Wedge;` | `U+22C0`
⋁ | ⋁  | ⋁x∈A | `\bigvee`
`\bigvee\limits_{}` | `&xvee;` | `U+22C1`

### Set relations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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⊂ | ⊂  | A⊂B | Subset | `\subset` | `&sub;` | `U+2282`
⊊ | ⊊  | A⊊B | `\subsetneq` | `&subne;` | `U+228A`
⊆ | ⊆  | A⊆B | `\subseteq` | `&sube;` | `U+2286`
| ⟃  | A ⟃ B |  | `\subsetcirc` | `&#x27C3;` | `U+27C3`
⊃ | ⊃ | A⊃B | Superset  | `\supset` | `&sup;` | `U+2283`
⊋ | ⊋  | A⊋B | `\supsetneq` | `&supne;` | `U+228B`
⊇ | ⊇  | A⊇B | `\supseteq` | `&supe;` | `U+2287`
| ⟄  | A ⟄ B |  | `\supsetcirc` | `&#x27C4;` | `U+27C4`
⊄ | ⊄  | A⊄B |  | `\not\subset` | `&nsub;` | `U+2284`
⊅ | ⊅  | A⊅B | Superset  | `\not\supset` | `&nsup;` | `U+2285`
⊈ | ⊈  | A⊈B |  | `\not\subseteq` | `&NotSubsetEqual;` | `U+2288`
⊉ | ⊉  | A⊉B | Superset  | `\not\supseteq` | `&NotSupersetEqual;` | `U+2289`
∈ | ∈  | a∈A | Element (mathematics) | `\in` | `&isin;` | `U+2208`
∋ | ∋  | A∋a | `\ni`, `\owns` | `&ni;` | `U+220B`
∉ | ∉  | a∉A | `\notin`, `\not\in` | `&notin;` | `U+2209`
∌ | ∌  | A∌a | `\not\ni` | `&NotReverseElement;` | `U+220C`
⊏ | ⊏  | A⊏B | Substring | `\sqsubset` | `&SquareSubset;` | `U+228F`
⊐ | ⊐  | A⊐B | `\sqsupset` | `&SquareSuperset;` | `U+2290`
⊑ | ⊑  | A⊑B | `\sqsubseteq` | `&sqsubseteq;` | `U+2291`
⊒ | ⊒  | A⊒B | `\sqsupseteq` | `&SquareSupersetEqual;` | `U+2292`

Note: The symbols ⊂ and ⊃ 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

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|| | | |  | |A| | Cardinality | `\vert` | `&VerticalLine;` | `U+007C`
# | #  | #A | `\#` | `&num;` | `U+0023`
𝔠 | 𝔠  |  | Cardinality of the continuum | `\mathfrak{c}` | `&cfr;` | `U+1D520`
ℵ | ℵ  | ℵ0, ℵ1, ...  | Aleph number | `\aleph` | `&aleph;` | `U+2135`
ℶ | ℶ  | ℶ0, ℶ1, ...  | Beth number | `\beth` | `&beth;` | `U+2136`

### Equivalence classes/relations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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[] | [ ] | [a] | Equivalence class | `[ ]` | `&lsqb;` `&rsqb;` | `U+005B/D`
/ | /  | M/∼ | Quotient set | `/` | `&sol;` | `U+002F`
∼ | ∼  | a∼b | Equivalence relation | `\sim` | `&sim;`, `&Tilde;` | `U+223C`
∽ | ∽ | a∽b | `\backsim` | `&bsim;` | `U+223D`
≁ | ≁  | a≁b | `\not\sim`, `\nsim` | `&nsim;` | `U+2241`
≂ | ≂  | a≂b | `\eqsim` | `&EqualTilde;` | `U+2242`
≃ | ≃  | a≃b | `\simeq` | `&TildeEqual;` | `U+2243`
≅ | ≅ | a≅b | `\cong` | `&TildeFullEqual;` | `U+2245`
≆ | ≇  | a≆b | `\not\cong`, `\ncong` | `&NotTildeFullEqual;` | `U+2247`

## Order theory

### Comparisons

See also: Arithmetic comparison, Set relations
Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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≤ | ≤  | a≤b | Order relation  | `\leq`, `\le` | `&leq;`, `&le;` | `U+2264`
≥ | ≥  | a≥b | `\geq`, `\ge` | `&geq;`, `&ge;` | `U+2265`
≮ | ≮  | a≮b | `\nless` | `&nlt;`, `&NotLess;` | `U+226E`
≯ | ≯  | a≯b | `\ngtr` | `&ngt;`, `&NotGreater;` | `U+226F`
≰ | ≰  | a≰b | `\not\leq`, `\nleq` | `&nle;`, `&NotLessEqual;` | `U+2270`
≱ | ≱  | a≱b | `\not\geq`, `\ngeq` | `&nge;`, `&NotGreaterEqual;` | `U+2271`
≲ | ≲  | a≲b | Inequality (mathematics) | `\lesssim` | `&lsim;`, `&LessTilde;` | `U+2272`
≳ | ≳  | a≳b | `\gtrsim` | `&gsim;`, `&GreaterTilde;` | `U+2273`
≴ | ≴  | a≴b | `\not\lesssim` | `&NotLessTilde;` | `U+2274`
≵ | ≵  | a≵b | `\not\gtrsim` | `&NotGreaterTilde;` | `U+2275`
≺ | ≺  | a≺b | Successor ordinal | `\prec` | `&prec;` | `U+227A`
≻ | ≻  | a≻b | `\succ` | `&succ;` | `U+227B`
≼ | ≼  | a≼b | `\preccurlyeq` | `&PrecedesSlantEqual;` | `U+227C`
≽ | ≽  | a≽b | `\succcurlyeq` | `&SucceedsSlantEqual;` | `U+227D`
≾ | ≾  | a≾b | `\precsim` | `&PrecedesTilde;` | `U+227E`
≿ | ≿  | a≿b | `\succsim` | `&SucceedsTilde;` | `U+227F`
⪯ | ⪯  | a⪯b | `\preceq` | `&PrecedesEqual;` | `U+2AAF`
⪰ | ⪰  | a⪰b | `\succeq` | `&SucceedsEqual;` | `U+2AB0`
⋞ | ⋞  | a⋞b | `\curlyeqprec` | `&curlyeqprec;` | `U+22DE`
⋟ | ⋟  | a⋟b | `\curlyeqsucc` | `&curlyeqsucc;` | `U+22DF`
⪯̸ | Partially ordered set | `\sqsubset` | `&sqsubset;`
`&SquareSubset;` | `U+228F`
⊐ | ⊐  | a⊐b | `\sqsupset` | `&sqsupset;`
`&SquareSuperset;` | `U+2290`
⊑ | ⊑  | a⊑b | `\sqsubseteq` | `&sqsubseteq;`
`&SquareSubsetEqual;` | `U+2291`
⊒ | ⊒  | a⊒b | `\sqsupseteq` | `&sqsupseteq;`
`&SquareSupersetEqual;` | `U+2292`
⋢ | ⋢  | a⋢b | `\not\sqsubseteq` | `&NotSquareSubsetEqual;` | `U+22E2`
⋣ | ⋣  | a⋣b | `\not\sqsupseteq` | `&NotSquareSupersetEqual;` | `U+22E3`

### Binary relations

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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;  | ;  | R;S | Composition of relations | `;` | `&semi;` | `U+003B`
∙ | •  | a∙b | Operation (mathematics) | `\bullet` | `&bull;` | `U+2219`
∗ | ∗  | a∗b | `\ast` | `&lowast;` | `U+2217`
T | ⁻  | RT | Converse relation | `T` |  |
¯ | ⁻  | R¯ | Complementary relation  | `\bar{R}` |  |
+ | \+  | R+ | Transitive closure | `+` |  | `U+002B`
∗ | *  | R∗ | Reflexive closure | `\ast` | `&lowast;` | `U+002A`

## Algebra

### Group theory

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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≃ | ≃  | G≃H | Group isomorphism | `\simeq` |  | `U+2243`
≅ | ≅  | G≅H | `\cong` | `&cong;` | `U+2245`
× | ⨯  | G×H | Direct product | `\times` | `&times;` | `U+2A2F`
⋊ | ⋊  | G⋊H | Semidirect product | `\rtimes` | `&rtimes;` | `U+22CA`
≀ | ≀  | G≀H | Wreath product | `\wr` | `&VerticalTilde;` | `U+2240`
≤ | ≤  | U≤G | Subgroup | `\leq` | `&le;` | `U+2264`
< | < | U<G | `\lt` | `&lt;` | `U+003C`
⊲ | ⊲  | N⊲G | Normal subgroup | `\vartriangleleft` | `&RightTriangle;` | `U+22B3`
⊴ | ⊴  | N⊴G | `\trianglelefteq` | `&LeftTriangleEqual;` | `U+22B4`
⋪ | ⋪  | N⋪G | `\not\vartriangleleft` | `&ntriangleleft;` | `U+22EA`
⋬ | ⋬  | N⋬G | `\not\trianglelefteq` | `&NotLeftTriangleEqual;` | `U+22EC`
⊳ | ⊳  | G⊳N | `\vartriangleright` | `&RightTriangle;` | `U+22B3`
⊵ | ⊵  | G⊵N | `\trianglerighteq` | `&RightTriangleEqual;` | `U+22B5`
⋫ | ⋫  | G⋫N | `\not\vartriangleright` | `&NotRightTriangle;` | `U+22EB`
⋭ | ⋭  | G⋭N | `\not\trianglerighteq` | `&NotRightTriangleEqual;` | `U+22ED`
/ | /  | G/N | Quotient group | `/` | `&frasl;` | `U+002F`
: | :  | (G:U) | Index of a subgroup | `\colon` | `&colon;` | `U+003A`
⟨⟩ | ⟨ ⟩  | ⟨E⟩ | Generating set of a group | `\langle \rangle` | `&lang;` `&rang;` | `U+27E8/9`
[] | [ ] | [g,h] | Commutator | `[ ]` | `&lsqb;` `&rsqb;` | `U+005B/D`

### Field theory

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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/ | /  | L/K | Field extension  | `/` | `&frasl;` | `U+002F`
∣ | |  | L∣K | `\mid` | `&VerticalLine;` | `U+007C`
: | :  | L:K | `\colon` | `&colon;` | `U+003A`
| [L:K] | Degree of a field extension
¯ | ◌̄  | K¯ | Algebraic closure  | `\bar` | `&#x304;` | `U+0304`
‾ | ◌̅  | K‾ | `\overline` | `&#x305;` | `U+0305`
() | ( )  | K(α) | Field extension, Algebraic number field | `( )` | `&lpar;` `&rpar;` | `U+0028/9`
𝔽 | 𝔽  |  | Finite field | `\mathbb{F}` | `&Fopf;` | `U+1D53D`
𝕂 | 𝕂  |  | Field (mathematics) | `\mathbb{K}` | `&Kopf;` | `U+1D542`

### Ring theory

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∗ | ∗  | R∗ | Group of units  | `\ast` | `&lowast;` | `U+2217`
× | ⨯  | R× | `\times` | `&times;` | `U+2A2F`
⊲ | ⊲  | I⊲R | Ideal (ring theory) | `\vartriangleleft` | `&LeftTriangle;` | `U+22B2`
/ | /  | R/I | Quotient ring | `/` | `&frasl;` | `U+002F`
[] | [ ] | R[X] | Polynomial ring | `[ ]` | `&lsqb;` `&rsqb;` | `U+005B/D`
| [ ] | RX,R((X)) | Formal power series | `[[ ]] ` | `&lsqb;` `&rsqb;` | `U+005B/D`
deg | deg  | deg⁡p(x) | Degree of a polynomial | `\deg` | `deg;` |

## Geometry

### Euclidean geometry

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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[] | [ ] | [AB] | Line segment | `[ ]` `\left[ \right]` | `&lsqb;` `&rsqb;` | `U+005B/D`
|| | | | | |AB| | `\vert` | `&VerticalLine;` | `U+007C`
‾ | ̅ | AB‾ | `\overline` | `&#x305;` | `U+0305`
_ | ̲ | AB_ | `\underline` | `&#x332;` | `U+0332`
-> | ⃗ | AB-> | Euclidean vector
and Affine space | `\vec` | `&#x20D7;` | `U+20D7`
∠ | ∠  | ∠ABC | Angle | `\angle` | `&ang;` | `U+2220`
| ∡  | ∡ABC  | Angle measure  | `` | `&measuredangle;` | `U+2221`
| ∟  | ∟ABC  | Right angle | `` | `&angrt;` | `U+221F`
| ⦜  | ⦜ABC  | Right angle | `` | `&vangrt;` | `U+299C`
| ⦟  | ⦟ABC  | Acute angle  | `` | `&#x299F;` | `U+299F`
| ⦦  | ⦦ABC  | Obtuse angle, Oblique angle  | `` | `&dwangle;` | `U+29A6`
| ⦞  | ⦞ABC  | Angles | `` | `&#x299E;` | `U+299E`
∥ | ∥  | g∥h | Parallel (geometry) | `\parallel` | `&shortparallel;` | `U+2225`
∦ | ∦  | g∦h | `\nparallel` | `&NotDoubleVerticalBar;` | `U+2226`
⊥ | ⟂  | g⊥h | Orthogonality | `\perp` | `&perp;` | `U+27C2`
△ | △  | △ABC | Triangle | `\triangle` | `&bigtriangleup;` | `U+25B3`
| ⊿  | ⊿ABC  | Right triangle | `` | `&lrtri;` | `U+22BF`
◻ | □  | ◻ABCD | Quadrilateral | `\square` | `&squ;` | `U+25A1`
| ▭  | ▭ABCD  | Rectangle | `` | `&rect;` | `U+25AD`
| ⏢  | ⏢ABCD  | Trapezium  | `` | `&trpezium;` | `U+23E2`
| ▱  | ▱ABCD  | Parallelogram | `` | `&fltns;` | `U+25B1`
| ◊  | ◊ABCD  | Rhombus, Lozenge | `` | `&loz;` | `U+25CA`
| ⬠  | ⬠ABCDE  | Pentagon | `` | `&#x2B20;` | `U+2B20`
| ⬡  | ⬡ABCDEF  | Hexagon | `` | `&#x2B21;` | `U+2B21`
| ⬢  | ⬢ABCDEF  | Hexagon | `` | `&#x2B22;` | `U+2B22`
| ○  | ○S  | Circle | `` | `&cir;` | `U+25CB`
| ●  | ●S  | Disc  | `` | `&#x25CF;` | `U+25CF`

### Differential geometry

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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ℒ | ℒ  | ℒXω | Lie derivative | `\mathcal{L}` | `&#x2112;` | `U+2112`
⌟ | ⌟  | X⌟ω | Interior product | `\mathbin{\lrcorner}` | `&lrcorner;` | `U+231F`
ι | 𝜄  | ιXω | `\iota` | `&#x1D704;` | `U+1D704`
∧ | ∧  | ω∧η | Wedge product  | `\wedge` | `&wedge;` | `U+2227`
⋀ | ⋀  | ⋀kA | `\bigwedge` | `&Wedge;` | `U+22C0`

### Topology

Symbol  | Unicode character  | Usage  | Articles with usage  | LaTeX  | HTML  | Unicode Hex

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∂ | ∂  | ∂U | Boundary (topology) | `\partial` | `&part;` | `U+2202`
∘ | ˚  | U∘ | Interior (topology) | `\circ` | `&deg;` | `U+02DA`
¯ | ◌̄  | z¯ | Closure (topology) | `\bar` | `&#x304;` | `U+0304`
‾ | ◌̅  | z‾ | `\overline` | `&#x305;` | `U+0305`
˙ | ◌̇  | U˙(x) | Punctured neighbourhood  | `\dot` |  | `U+0307`

## See also

### By type of symbol

* List of letters used in mathematics, science, and engineering
* Greek letters used in mathematics, science, and engineering
* Latin letters used in mathematics, science, and engineering
* Blackboard bold
* Diacritic

### By topic area

* Glossary of mathematical symbols
* List of logic symbols
* APL syntax and symbols
* List of common physics notations
* Notation in probability and statistics
* Physical constants

### General

* List of mathematical abbreviations
* Mathematical notation
* Language of mathematics

### Unicode

* Lists of Mathematical operators and symbols in Unicode
* Mathematical Operators and Supplemental Mathematical Operators
* List of mathematical symbols
* Miscellaneous Math Symbols: A, B, Technical
* Arrow (symbol) and Miscellaneous Symbols and Arrows and arrow symbols
* ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
* Number Forms
* Geometric Shapes
* Mathematical Alphanumeric Symbols, a Unicode block
* Mathematical constants and functions
* Table of mathematical symbols by introduction date
* List of Unicode characters
* Letterlike Symbols
* Unicode block

## Bibliography

* Tilo Arens; Frank Hettlich; Christian Karpfinger; Ulrich Kockelkorn; Klaus Lichtenegger; Hellmuth Stachel (2011) (in German), Mathematik (2. ed.), Spektrum Akademischer Verlag, pp. 1483ff, ISBN 978-3-827-42347-4
* Wolfgang Hackbusch (2010) (in German), Taschenbuch der Mathematik, Band 1 (3. ed.), Springer, pp. 1275ff, ISBN 978-3-835-10123-4
* Deutsches Institut für Normung: DIN 1302: Allgemeine mathematische Zeichen und Begriffe, Beuth-Verlag, 1999.
* Deutsches Institut für Normung: DIN 1303: Vektoren, Matrizen, Tensoren; Zeichen und Begriffe, Beuth-Verlag, 1987.
* International Standards Organisation: DIN EN ISO 80000-2: Größen und Einheiten – Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik, 2013.

## External links

LaTeX and Unicode

* Symbols defined by unicode-math - Lists LaTeX and corresponding Unicode symbols
* Unicode characters and corresponding LaTeX math mode command

LaTeX

* Scott Pakin (25 June 2020). "The Comprehensive LaTeX Symbol List" (PDF; 4,4 MB). The Comprehensive TeX Archive Network (CTAN). http://mirrors.ctan.org/info/symbols/comprehensive/symbols-a4.pdf.
* Detexify − Online tool: Find LaTeX code for a symbol by drawing it.

Unicode

* Symbols defined by unicode-math
* "Mathematical Operators – Unicode" (PDF). Retrieved 2013-07-20.
* Lists Unicode Block "Mathematical Operators"
* Lists Unicode Block "Supplemental Mathematical Operators"
* Lists Unicode Block "Miscellaneous Mathematical Symbols-A"
* Lists Unicode Block "Miscellaneous Mathematical Symbols-B"
* Lists Unicode Block "Mathematical Alphanumeric Symbols
* Shapecatcher − Online tool: Find Unicode and HTML codes for a symbol by drawing it.

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