List of mathematical symbols by subject

This list of mathematical symbols by subject shows a selection of the most common symbols that are used in modern mathematical notation within formulas, grouped by mathematical topic. As it is virtually impossible to list all the symbols ever used in mathematics, 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 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.
;Interpretation: A short textual description of the meaning of the formula in the previous column.
;Article: The Wikipedia article that discusses the meaning of the symbol.
;LaTeX: The LaTeX command that creates the icon. Characters from the ASCII character set can be used directly, with a few exceptions. High-and low-position is indicated via the characters ^ and _ 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>.
;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 the opening and the closing forms are specified.

Set theory

Definition symbols

Symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
		is defined by	Definition	`\colon`	`∶`	`U+003A`
		is defined as equal to	Definition	`\colon`	`∶`	`U+003A`
		is defined as equivalent to	Definition	`\colon`	`∶`	`U+003A`

Set construction

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∅		Empty set	Empty set	`\varnothing`, `\emptyset`	`∅`	`U+2205`
			Set consisting of the elements and so on	Set	`\`		`U+007B/D`
			Set of elements, that satisfy the condition	Set	`\mid`		`U+007C`
	:		Set of elements, that satisfy the condition	Set	`\colon`		`U+003A`

Set operations

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∪		Union of the sets and	Union	`\cup`	`∪`	`U+222A`
	∩		Intersection of the sets and	Intersection	`\cap`	`∩`	`U+2229`
	∖		Difference of sets and	Difference	`\setminus`		`U+2216`
	∆		Symmetric difference of sets and	Symmetric difference	`\triangle`	`Δ`	`U+2206`
	⨯		Cartesian product of sets and	Cartesian product	`\times`	`×`	`U+2A2F`
	⊍		Disjoint union of sets and	Disjoint union	`\dot\cup`		`U+228D`
	⊎		Disjoint union of sets and	Disjoint union	`\uplus`	`&uplus;`	`U+228E`
	⊔		Disjoint union of sets and	Disjoint union	`\sqcup`		`U+2294`
	∁		Complement of the set	Complement	`\mathrm`		`U+2201`
	◌̅		Complement of the set	Complement	`\overline`		`U+0305`
	?		Power set of the set	Power set	`\mathcal`		`U+1D4AB`
	?		Power set of the set	Power set	`\mathfrak`		`U+1D513`
	℘		Power set of the set	Power set	`\wp`		`U+2118`
	⋀		This is the greatest lower bound, infimum, or meet of all elements operated on.	Infimum and supremum	`\bigwedge`		`U+22C0`
	⋁		This is the least upper bound, supremum, or join of all elements operated on.	Infimum and supremum	`\bigvee`		`U+22C1`

Set relations

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	⊂		is a proper subset of	Subset	`\subset`	`⊂`	`U+2282`
	⊊		is a proper subset of	Subset	`\subsetneq`		`U+228A`
	⊆		is a subset of	Subset	`\subseteq`	`&sube;`	`U+2286`
	⊃		is a proper superset of	Superset	`\supset`	`⊃`	`U+2283`
	⊋		is a proper superset of	Superset	`\supsetneq`		`U+228B`
	⊇		is a superset of	Superset	`\supseteq`	`&supe;`	`U+2287`
	⊄		is not a proper subset of		`\not\subset`		`U+2284`
	⊅		is not a proper superset of	Superset	`\not\supset`		`U+2285`
	⊈		is not a subset of		`\not\subseteq`		`U+2288`
	⊉		is not a superset of	Superset	`\not\supseteq`		`U+2289`
	∈		Element is in the set	Element	`\in`	`∈`	`U+2208`
	∋		Element is in the set	Element	`\ni`, `\owns`	`&ni;`	`U+220B`
	∉		Element is not in the set	Element	`\notin`	`∉`	`U+2209`
	∌		Element is not in the set	Element	`\not\ni`		`U+220C`

Note: The symbols and are used inconsistently and often do not exclude the equality of the two quantities.

Number sets

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	?		Algebraic numbers	Algebraic number	`\mathbb`		`U+1D538`
	ℂ		Complex numbers	Complex number	`\mathbb`		`U+2102`
	ℍ		Quaternions	Quaternion	`\mathbb`		`U+210D`
	ℕ		Natural numbers	Natural number	`\mathbb`		`U+2115`
	?		Nonnegative numbers	Natural number	`\mathbb`		`U+1D541`
	?		Nonnegative numbers	Natural number	`\mathbb`		`U+1D54E`
	ℚ		Rational numbers	Rational number	`\mathbb`		`U+211A`
	ℝ		Real numbers	Real number	`\mathbb`		`U+211D`
	ℤ		Integers	Integer	`\mathbb`		`U+2124`

Cardinality

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
			Cardinality of the set	Cardinality	`\vert`		`U+007C`
	#		Cardinality of the set	Cardinality	`\#`		`U+0023`
	?		Cardinality of the continuum	Cardinality of the continuum	`\mathfrak`		`U+1D520`
	ℵ	,,...	Infinite cardinals	Aleph number	`\aleph`		`U+2135`
	ℶ	,,...	Beth numbers	Beth number	`\beth`		`U+2136`

Arithmetic

Arithmetic operators

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	+		added to	Addition	`+`	`+`	`U+002B`
	−		subtracted to	Subtraction	`-`	`−`	`U+2212`
	⋅		multiplied by	Multiplication	`\cdot`	`·`	`U+22C5`
	⨯		multiplied by	Multiplication	`\times`	`×`	`U+2A2F`
	:		divided by	Division	`:`:	`∶`	`U+003A`
	∕		divided by	Division	`/`	`&frasl;`	`U+2215`
	÷		divided by	Division	`\div`	`÷`	`U+00F7`
	⁄		divided by	Division	`\frac`		`U+2044`
	−		Negative of the number or the additive inverse of	Unary minus	`-`	`−`	`U+2212`
	±		Plus or minus	Plus or minus sign	`\pm`	`±`	`U+00B1`
	∓		Minus or plus	Plus or minus sign	`\mp`	`∓`	`U+2213`
			Term is evaluated first	Bracket			`U+0028/9`
			Term is evaluated first	Bracket			`U+005B/D`

Equality signs

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	=		equals	Equality	`=`		`U+003D`
	≠		does not equal	Inequality	`\neq`	`≠`	`U+2260`
	≡		is identical to	Identity	`\equiv`	`&equiv;`	`U+2261`
	≈		is approximately equal to	Approximation	`\approx`	`≈`	`U+2248`
	∼		is similar to	Equivalence class	`\sim`	`&sim;`	`U+223C`
	∝		is proportional to	Proportionality	`\propto`	`&prop;`	`U+221D`
	≙		corresponds to		`\widehat`		`U+2259`
	≟		is equal to ?	Questioning equal sign	`\overset`		`U+225F`

Comparison

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	<		is less than	Comparison	`<`	`<`	`U+003C`
	>		is greater than	Comparison	`>`	`>`	`U+003E`
	≤		is less than or equal to	Comparison	`\le`, `\leq`	`≤`	`U+2264`
	≦		is less than or equal to	Comparison	`\leqq`	`≦`	`U+2266`
	≥		is greater than or equal to	Comparison	`\ge`, `\geq`	`≥`	`U+2265`
	≧		is greater than or equal to	Comparison	`\geqq`	`≧`	`U+2267`
	≪		is much smaller than	Comparison	`\ll`	`≪`	`U+226A`
	≫		is much bigger than	Comparison	`\gg`	`≫`	`U+226B`
	≷		is greater than or less than or is different than		`\gtrless`	`≷`	`U+2277`

Divisibility

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∣		divides	Divisibility	`\mid`		`U+2223`
	∤		does not divide	Divisibility	`\nmid`		`U+2224`
	⊥		and are relatively prime	Relatively prime	`\perp`	`&perp;`	`U+22A5`
	⊓		Greatest common divisor of and	Greatest common divisor	`\sqcap`		`U+2293`
	∧		Greatest common divisor of and	Greatest common divisor	`\wedge`	`&and;`	`U+2227`
	⊔		Least common multiple of and	Least common multiple	`\sqcup`	`&and;`	`U+2294`
	∨		Least common multiple of and	Least common multiple	`\vee`	`&or;`	`U+2228`
	≡		and are congruent modulo	Modular arithmetic	`\equiv`	`&equiv;`	`U+2261`

Intervals

Symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
		Closed interval between and	Interval			`U+0028/9` `U+005B/D`
		Open interval between and	Interval			`U+0028/9` `U+005B/D`
		Open interval between and	Interval			`U+0028/9` `U+005B/D`
		Right-open interval between and	Interval			`U+0028/9` `U+005B/D`
		Right-open interval between and	Interval			`U+0028/9` `U+005B/D`
		Left-open interval between and	Interval			`U+0028/9` `U+005B/D`
		Left-open interval between and	Interval			`U+0028/9` `U+005B/D`

Elementary functions

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
			Absolute value of	Absolute value	`\vert`		`U+007C`
			Biggest whole number less than or equal to	Floor and ceiling functions			`U+005B/D`
	⌊ ⌋		Biggest whole number less than or equal to	Floor and ceiling functions	`\lfloor \rfloor`	`&lfloor;` `&rfloor;`	`U+230A/B`
	⌈ ⌉		Smallest whole number greater than or equal to	Floor and ceiling functions	`\lceil \rceil`	`&lceil;` `&rceil;`	`U+2308/9`
	√		Square root of	Square root	`\sqrt`	`√`	`U+221A`
			-th root of	nth root	`\sqrt`	`√`	`U+221A`
	%		percent	Percent	`\%`		`U+0025`

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

Complex numbers

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	ℜ		Real part of complex number	Complex number	`\Re`		`U+211C`
	ℑ		Imaginary part of complex number	Complex number	`\Im`		`U+2111`
	◌̅		Complex conjugate of	Complex conjugate	`\bar`		`U+0305`
	*		Complex conjugate of	Complex conjugate	`\ast`	`&lowast;`	`U+002A`
			Absolute value of complex number	Absolute value	`\vert`		`U+007C`
			Argument of	Argument	`\arg`

Mathematical constants

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	π		Pi, or Archimedes' constant	Pi	`\pi`		`U+03C0`
or	e		Euler's constant	e	`e` or `\rm`	or	`U+0065`
	φ		Golden ratio	Golden ratio	`\varphi`	`φ`	`U+03C6`
or	i		Imaginary unit	Imaginary unit	`i` or `\rm`	or	`U+0069`

See also: mathematical constant for symbols of additional mathematical constants.

Calculus

Sequences and series

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∑		Sum from to or over all elements in set	Summation	`\sum`	`∑`	`U+2211`
	∏		Product from to or over all elements in set	Product	`\prod`	`∏`	`U+220F`
	∐		Coproduct from to or over all elements in set	Coproduct	`\coprod`		`U+2210`
			Sequence of elements	Sequence			`U+0028/9`
	→		Sequence tends to limit	Limit of a sequence	`\to`	`→`	`U+2192`
	∞		tends to infinity	Infinity	`\infty`	`∞`	`U+221E`

Functions

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	→		Function maps from set to set	Function	`\to`	`→`	`U+2192`
	→		Function maps from set to set	Function	`\to`	`→`	`U+2192`
	↦		Function maps element to element	Function	`\mapsto`	`&mapstoright;`	`U+21A6`
	↦		Function maps element to element	Function	`\mapsto`	`&mapstoright;`	`U+21A6`
			Image of element under function	Image		`(` or `)`	`U+0028/9`
			Image of set under function	Image		`(` or `)`	`U+0028/9`
			Image of set under function	Image		`[` or `]`	`U+005B/D`
			Restriction of function to set	Restriction	`\vert`	`\|`	`U+007C`
	⋅		Placeholder for a variable as argument of function	Free variable	`\cdot`		`U+22C5`
	⁻		Inverse function of	Inverse function	`-1`		`U+207B`
	∘		Composition of functions and ;	Function composition	`\circ`	`∘`	`U+2218`
	∗		Convolution of functions and	Convolution	`\ast`	`&lowast;`	`U+2217`
	◌̂		Fourier transform of function	Fourier transform	`\hat`		`U+0302`

Limits

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	↑		Limit of function as approaches from below	Limit of a function	`\uparrow`	`↑`	`U+2191`
	↗		Limit of function as approaches from below	Limit of a function	`\nearrow`		`U+2197`
	→		Limit of function as approaches	Limit of a function	`\to`	`→`	`U+2192`
	↘		Limit of function as approaches from above	Limit of a function	`\searrow`		`U+2198`
	↓		Limit of function as approaches from above	Limit of a function	`\downarrow`	`↓`	`U+2193`
	⁺		Limit of a function as approaches from the right	Limit of a function	`^+`	`⁺`	`U+207A`
	⁻		Limit of a function as approaches from the left	Limit of a function	`^-`	`⁻`	`U+207B`

Asymptotic behaviour

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∼		Function is asymptotically equal to function	Asymptotic analysis	`\sim`	`&sim;`	`U+223C`
	o		Function grows slower than	Big O notation	`o`		`U+006F`
	?		Function grows not substantially faster than	Big O notation	`\mathcal`		`U+1D4AA`
	Θ		Function grows as fast as	Big O notation	`\Theta`	`Θ`	`U+0398`
	Ω		Function grows not substantially slower than	Big O notation	`\Omega`	`Ω`	`U+03A9`
	ω		Function grows faster than	Big O notation	`\omega`	`ω`	`U+03C9`

Differential calculus

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	′ ″		First or second derivative of function	Lagrange's notation	`\prime`	`′`	`U+2032,U+2033`
			Alternative notation for fourth, fifth, or sixth derivative of function	Lagrange's notation	`^`	`^Ⅳ`
			Alternative notation for fourth, fifth, or -th derivative of function	Lagrange's notation			`U+0028/9`
	◌̇		First or second derivative of function with respect to time	Newton's notation	`\dot`, `\ddot`		`U+0307`
	d		An infinitesimally small change in	Leibniz's notation	`d`	`d`	`U+0064`
	d		Derivative of function with respect to variable	Leibniz's notation	`d`	`d`	`U+0064`
	d		Derivative of function with respect to variable	Leibniz's notation	`d`	`d`	`U+0064`
	d		Second derivative of function with respect to variable	Leibniz's notation	`d`	`d`	`U+0064`
	d		Total differential of function	Leibniz's notation	`d`	`d`	`U+0064`
	∂		Partial derivative of function with respect to variable	Partial derivative	`\partial`	`∂`	`U+2202`

Integral calculus

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∫	,	Definite integral between and or over set	Integral	`\int`	`∫`	`U+222B`
	∮		Curve integral along curve	Curve integral	`\oint`		`U+222E`
	∬		Surface integral over surface	Surface integral	`\iint`		`U+222C`
	∭		Volume integral over volume	Volume integral	`\iiint`		`U+222D`

Vector calculus

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∇		Gradient of function	Gradient	`\nabla`	`∇`	`U+2207`
	∇		Divergence of vector field	Divergence	`\nabla`	`∇`	`U+2207`
	∇		Curl of vector field	Curl	`\nabla`	`∇`	`U+2207`
	∆		Laplace operator of function	Laplace operator	`\Delta`	`Δ`	`U+2206`
	□		D'Alembert operator of function	D'Alembert operator	`\square`		`U+25A1`

Topology

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∂		Boundary of set	Boundary	`\partial`	`∂`	`U+2202`
	˚		Interior of set	Interior	`\circ`	`°`	`U+02DA`
	◌̅		Closure of set	Closure	`\overline`		`U+0305`
	◌̇		Punctured neighbourhood of point	Punctured neighbourhood	`\dot`		— `U+0307`

Functional analysis

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	′		Topological dual space of topological vector space	Dual space	`\prime`	`′`	`U+2032/3`
	″		Bidual space of normed vector space	Dual space	`\prime`	`′`	`U+2032/3`
	◌̂		Completion of metric space	Complete metric space	`\hat`		`U+0302`
	↪		Embedding of topological vector space into	Embedding	`\hookrightarrow`		`U+21AA`

Linear algebra and geometry

Elementary geometry

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	[ ]		Line segment between points and	Line segment			`U+005B/D`
			Length of line segment between points and	Line segment	`\vert`		`U+007C`
	̅		Length of line segment between points and	Line segment	`\overline`		`U+0305`
	⃗		Vector between points and	Euclidean vector and Affine space	`\vec`		`U+20D7`
	∠		Angle between line segments and	Angle	`\angle`	`&ang;`	`U+2220`
	△		Triangle with vertices, and	Triangle	`\triangle`		`U+25B3`
	□		Quadrilateral with vertices,, and	Quadrilateral	`\square`		`U+25A1`
	∥		Lines and are parallel	Parallel	`\parallel`		`U+2225`
	∦		Lines and are not parallel	Parallel	`\nparallel`		`U+2226`
	⟂		Lines and are orthogonal	Orthogonality	`\perp`	`&perp;`	`U+27C2`

Vectors and matrices

Symbol	Usage	Article	LaTeX
	Row vector comprising elements through	Vector	`\begin` `...` `\end` or `\left`
	Column vector comprising elements through	Vector	`\begin` `...` `\end` or `\left`
	Matrix comprising elements through	Matrix	`\begin` `...` `\end` or `\left`

Vector calculus

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	⋅		Dot product of vectors and	Dot product	`\cdot`	`·`	`U+22C5`
			Dot product of vectors and	Dot product			`U+0028/9`
	⟨ ⟩		Dot product of vectors and	Dot product	`\langle \rangle`	`&lang;` `&rang;`	`U+27E8/9`
	⨯		Cross product of vectors and	Cross product	`\times`	`×`	`U+2A2F`
	[ ]		Cross product of vectors and	Cross product			`U+005B/D`
			Triple product of vectors, and	Triple product			`U+0028/9`
	⊗		Dyadic product of vectors and	Dyadic product	`\otimes`	`&otimes;`	`U+2297`
	∧		Exterior product of vectors and	Exterior algebra	`\wedge`	`&and;`	`U+2227`
			Length of vector	Euclidean norm	`\vert`		`U+007C`
	‖		Norm of vector	Norm	`\Vert`, `\\|`		`U+2016`
	̂		Normalized vector of vector	Unit vector	`\hat`		`U+0302`

Matrix calculus

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	⋅		Product of matrices and	Matrix multiplication	`\cdot`	`·`	`U+22C5`
	∘		Hadamard product of matrices and	Hadamard product	`\circ`		`U+2218`
	⊘		Hadamard division of matrices and	Hadamard product	`\oslash`		`U+2298`
	⊗		Kronecker product of matrices and	Kronecker product	`\otimes`	`&otimes;`	`U+2297`
	T		Transposed matrix of matrix	Transposed matrix	`^T`		`U+0054`
	⊺		Transposed matrix of matrix	Transposed matrix	`\intercal`		`U+22BA`
	H		Conjugate transpose of matrix	Conjugate transpose	`^H`		`U+0048`
	*		Conjugate transpose of matrix	Conjugate transpose	`\ast`	`&lowast;`	`U+002A`
	†		Conjugate transpose of matrix	Conjugate transpose	`\dagger`	`&dagger;`	`U+2020`
	⁻		Inverse matrix of matrix	Inverse matrix	`-1`		`U+207B`
	+		Moore–Penrose pseudoinverse of matrix	Moore–Penrose pseudoinverse	`+`	`+`	`U+002B`
			Determinant of Matrix	Determinant	`\vert`		`U+007C`
	‖		Norm of matrix	Matrix norm	`\Vert`, `\\|`		`U+2016`

Vector spaces

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	+		Sum of vector spaces and	Direct sum of modules	`+`	`+`	`U+002B`
	⊕		Direct sum of vector spaces and	Direct sum of modules	`\oplus`	`&oplus;`	`U+2295`
	⨯		Direct product of vector spaces and	Direct product	`\times`	`×`	`U+2A2F`
	⊗		Tensor product of vector spaces and	Tensor product	`\otimes`	`&otimes;`	`U+2297`
	/		Quotient space of vector space by subspace	Quotient space	`/`	`&frasl;`	`U+002F`
	⟂		Orthogonal complement of subspace	Orthogonal complement	`\perp`	`&perp;`	`U+27C2`
	*		Dual space of vector space	Dual space	`\ast`	`&lowast;`	`U+002A`
	0		Annihilator space of the set of vectors	Dual space	`0`		`U+0030`
	⟨ ⟩		Linear hull of the set of vectors	Linear hull	`\langle \rangle`	`&lang;` `&rang;`	`U+27E8/9`

Algebra

Relations

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∘		Composition of relations and	Composition of relations	`\circ`		`U+2218`
	∘		Operation of elements and	Operation	`\circ`		`U+2218`
	•		Operation of elements and	Operation	`\bullet`	`•`	`U+2219`
	∗		Operation of elements and	Operation	`\ast`	`&lowast;`	`U+2217`
	≤		Order relation between elements and	Order relation	`\leq`	`≤`	`U+2264`
	≺		Element is a predecessor of element	Successor ordinal	`\prec`		`U+227A`
	≻		Element is a successor of element	Successor ordinal	`\succ`		`U+227B`
	∼		Equivalence relation between elements and	Equivalence relation	`\sim`	`&sim;`	`U+223C`
	[ ]		Equivalence class of element	Equivalence class			`U+005B/D`
	/		Quotient set of set by equivalence relation	Quotient set	`/`	`&frasl;`	`U+002F`
	⁻		Inverse relation of relation	Inverse relation	`-1`		`U+207B`
	+		Transitive closure of relation	Transitive closure	`+`		`U+002B`
	*		Reflexive closure of relation	Reflexive closure	`\ast`	`&lowast;`	`U+002A`

Group theory

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	≃		Groups and are isomorphic	Group isomorphism	`\simeq`		`U+2243`
	≅		Groups and are isomorphic	Group isomorphism	`\cong`	`&cong;`	`U+2245`
	⨯		Direct product of groups and	Direct product	`\times`	`×`	`U+2A2F`
	⋊		Semidirect product of groups and	Semidirect product	`\rtimes`		`U+22CA`
	≀		Wreath product of groups and	Wreath product	`\wr`		`U+2240`
	≤		is a subgroup of group	Subgroup	`\leq`	`≤`	`U+2264`
	<		is a proper subgroup of group	Subgroup	`\lt`	`<`	`U+003C`
	⊲		is a normal subgroup of group	Normal subgroup	`\vartriangleleft`		`U+22B2`
	/		Quotient group of group by normal subgroup	Quotient group	`/`	`&frasl;`	`U+002F`
	:		Index of subgroup in group	Index of a subgroup	`\colon`		`U+003A`
	⟨ ⟩		Subgroup generated by set	Generating set of a group	`\langle \rangle`	`&lang;` `&rang;`	`U+27E8/9`
	[ ]		Commutator of elements and	Commutator			`U+005B/D`

Field theory

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	/		Extension of field over field	Field extension	`/`	`&frasl;`	`U+002F`
			Extension of field over field	Field extension	`\mid`		`U+007C`
	:		Extension of field over field	Field extension	`\colon`		`U+003A`
			Degree of field extension over	Degree of a field extension	`\colon`		`U+003A`
	̅		Algebraic closure of field	Algebraic closure	`\overline`		`U+0305`
			Extension of a field by adding an algebraic element	Field extension, Algebraic number field			U+0028/9
	?		Field of real or complex numbers	Field	`\mathbb`		`U+1D542`
	?		Finite field	Finite field	`\mathbb`		`U+1D53D`

Ring theory

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∗		Group of units of ring	Group of units	`\ast`	`&lowast;`	`U+2217`
	⨯		Group of units of ring	Group of units	`\times`	`×`	`U+2A2F`
	⊲		is an ideal of ring	Ideal	`\vartriangleleft`		`U+22B2`
	/		Quotient ring of ring by ideal	Quotient ring	`/`	`&frasl;`	`U+002F`
	[ ]		Polynomial ring over ring with variable	Polynomial ring			`U+005B/D`
	[ ]		Ring of formal power series and ring of formal Laurent series	Formal power series			`U+005B/D`

Combinatorics

Symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
		Number of permutations of elements	Factorial	`!`		`U+0021`
		Number of derangements of elements	Derangement	`!`		`U+0021`
		Number of involutions without fixed points	Double factorial	`!`		`U+0021`
		Number of -combinations of elements without repetition	Combination	`\binom`		`U+0028/9`
		Number of permutations of elements of which are identical	Multinomial coefficient	`\binom`		`U+0028/9`
		Number of -combinations of elements with repetition	Multiset	)		`U+0028/9`
		Rising factorial from with factors	Pochhammer symbol	`\overline`		`U+0305`
		Falling factorial from with factors	Pochhammer symbol	`\underline`		`U+0332`
		Product of all primes up to	Primorial	`\#`		`U+0023`

Stochastics

Probability theory

Symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
		Probability of event	Probability measure	`P`		`U+2119`
		Probability of event given event	Conditional probability	`\mid`		`U+007C`
		Expected value of the random variable	Expected value	`E`		`U+1D53C`
		Variance of the random variable	Variance	`V`		`U+1D54D`
		Standard deviation of the random variable	Standard deviation	`\sigma`	`σ`	`U+03C3`
		Covariance of random variables and	Covariance	`\sigma`	`σ`	`U+03C3`
		Correlation of random variables and	Correlation	`\rho`	`ρ`	`U+03C1`
		Random variable has distribution	Probability distribution	`\sim`	`&sim;`	`U+223C`
		Random variable has distribution approximately	Probability distribution	`\approx`	`≈`	`U+2248`
		Event is independent from event	Independence	`\perp`	`&perp;`	`U+22A5`

Statistics

Symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
		Average of the values	Average	`\bar`	`̅`	`U+0305`
		Average over all values in the set	Average	`\langle \rangle`	`&lang;` `&rang;`	`U+27E8/9`
		Estimator for parameter	Estimator	`\hat`	`̂`	`U+0302`

Logic

Operators

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∧		Proposition and proposition	Logical conjunction	`\land`	`&and;`	`U+2227`
	∨		Proposition or proposition	Logical disjunction	`\lor`	`&or;`	`U+2228`
	⇔		Proposition follows from proposition and vice versa	Logical equivalence	`\Leftrightarrow`	`⇔`	`U+21D4`
	↔		Proposition follows from proposition and vice versa	Logical equivalence	`\leftrightarrow`	`↔`	`U+2194`
	⇒		From proposition follows proposition	Logical consequence	`\Rightarrow`	`⇒`	`U+21D2`
	→		From proposition follows proposition	Logical consequence	`\rightarrow`	`→`	`U+2192`
	⊕		Either proposition or proposition	Exclusive or	`\oplus`	`&oplus;`	`U+2295`
	⊻		Either proposition or proposition	Exclusive or	`\veebar`		`U+22BB`
	⩒		Either proposition or proposition	Exclusive or	`\dot\lor`		`U+2A52`
	¬		Not proposition	Logical negation	`\lnot`	`¬`	`U+00AC`
	̅		Not proposition	Logical negation	`\bar`		`U+0305`
	←		If B then A, or not B without A. It is not to be confused with the assignment operator in computer science.	Converse implication	`\leftarrow`	`←`	`U+2190`

Quantifiers

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	∀		For all elements	Universal quantification	`\forall`	`∀`	`U+2200`
	⋀		For all elements	Universal quantification	`\bigwedge`		`U+22C0`
	∃		At least one element exists	Existential quantification	`\exists`	`∃`	`U+2203`
	⋁		At least one element exists	Existential quantification	`\bigvee`		`U+22C1`
	∃!		Exactly one element exists	Uniqueness quantification	`\exists!`	`∃!`	`U+2203`!
	⩒		Exactly one element exists	Uniqueness quantification	`\dot\bigvee`		`U+2A52`
	∄		No element exists	Existential quantification	`\nexists`		`U+2204`

Deduction symbols

Symbol	Unicode symbol	Usage	Interpretation	Article	LaTeX	HTML	Unicode
	⊢		Proposition can be syntactically derived from proposition	Propositional calculus, Turnstile	`\vdash`		`U+22A2`
	⊨		Proposition follows semantically from proposition	Inference	`\models`		`U+22A8`
	⊨		Proposition is universally true	Tautology	`\models`		`U+22A8`
	⊤		Proposition is universally true	Tautology	`\top`		`U+22A4`
	⊥		Proposition is contradictory	Contradiction	`\bot`	`&perp;`	`U+22A5`
	∴		Proposition is true, therefore proposition is true	Deductive reasoning	`\therefore`		`U+2234`
	∵		Proposition is true, because is true	Deductive reasoning	`\because`		`U+2235`
	∎		End of proof	Q.E.D.	`\blacksquare`		`U+220E`
	□		End of proof	Q.E.D.	`\Box`		`U+25A1`

Alphanumeric Symbols

Digits

Alphabets

Name	Sub-type	Alphabet
Double-struck		? ? ℂ ? ? ? ? ℍ ? ? ? ? ? ℕ ? ℙ ℚ ℝ ? ? ? ? ? ? ? ℤ
Double-struck		? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Script/Calligraphy		? ℬ ? ? ℰ ℱ ? ℋ ℐ ? ? ℒ ℳ ? ? ? ? ℛ ? ? ? ? ? ? ? ?
Script/Calligraphy		? ? ? ? ℯ ? ℊ ? ? ? ? ? ? ? ℴ ? ? ? ? ? ? ? ? ? ? ?
Script/Calligraphy	Bold	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Script/Calligraphy	Bold	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Fraktur		? ? ℭ ? ? ? ? ℌ ℑ ? ? ? ? ? ? ? ? ℜ ? ? ? ? ? ? ? ℨ
Fraktur		? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Fraktur	Bold	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Fraktur	Bold	? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Mono-space		? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Mono-space		? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek		Α Β Γ ᴦ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Ῥ ☧ Σ Ϲ Τ Υ υ Φ Χ Ψ Ω
Greek		α β ᵝ ᵦ γ ᵞ ᵧ δ ᵟ ε ϵ ϶ ζ η Ͱ ͱ θ ϑ ϴ ᶿ ι ᶥ ℩ κ ϰ λ ᴧ μ µ ν ξ ο π ϖ ρ ῥ ῤ ϱ ϼ ᴩ ᵨ σ ς ϲ Ͻ ͻ Ͼ ͼ Ͽ ͽ τ ϒ φ ϕ χ ᵡ ᵪ ψ ᴪ ω
Greek	Italic	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Italic	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Non-Latin Italic	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Bold	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Bold	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Bold Italic	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
Greek	Bold Italic	? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?

Greek Letters

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