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 Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms ...

. 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

command that creates the icon. Characters from the

ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...

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 The HyperText Markup Language or HTML is the standard markup language for documents designed to be displayed in a web browser. It can be assisted by technologies such as Cascading Style Sheets (CSS) and scripting languages such as JavaScri ...

, 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 and . The character × whose HTML code is times can be displayed by typing ×. ;Unicode: The

code point In character encoding terminology, a code point, codepoint or code position is a numerical value that maps to a specific character. Code points usually represent a single grapheme—usually a letter, digit, punctuation mark, or whitespace—but ...

of the corresponding

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology Technical standard, standard for the consistent character encoding, encoding, representation, and handling of Character (computing), text expre ...

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 In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, hexa ...

value is U+2A2F can be displayed by typing ⨯ where #x indicates that the value in hexadecimal.

Numbers

Number sets

Intervals

Mathematical constants

Complex numbers

:''Remark:'' real and imaginary parts of a complex number are often also denoted by

\operatorname

and

\operatorname

Elementary arithmetic operations

Elementary functions

''Note:'' the

power function Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to re ...

is not represented by its own icon, but by the positioning of the exponent as a

superscript A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, whil ...

Arithmetic comparison

:''See also'': Order relations, Set relations

Number theory

Divisibility and modulo

Combinatorics

Stochastics

Probability theory

:''Remark:'' for operators there are several notational variants; instead of round brackets also square brackets are used

Statistics

Calculus

Sequences and series

Limits

Differential calculus

Integral calculus

Vector calculus

Asymptotic behaviour

Linear algebra

Vectors and matrices

Vector operations

Matrix operations

Vector spaces

Functional analysis

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 In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bicon ...

", "s.t.", and "

WLOG ''Without loss of generality'' (often abbreviated to WOLOG, WLOG or w.l.o.g.; less commonly stated as ''without any loss of generality'' or ''with no loss of generality'') is a frequently used expression in mathematics. The term is used to indicate ...

Equality signs

Logical operators

Quantifiers

Deduction symbols

End of proof symbols

Formal language and strings

Functions and category theory

Functions

Morphisms

Constructions

Set theory

Definition symbols

Set construction

Separator symbols To scale a set's braces \ to the size of the set's content, use \left\. Wikipedia does not support \middle as that requires

e-TeX TeX Live is a cross-platform, free software distribution for the TeX typesetting system that includes major TeX-related programs, macro packages, and fonts. It is the replacement of its no-longer supported counterpart teTeX. It is now the defau ...

, although \big, , \Big, , \bigg, , or \Bigg, can be used in place of \middle, . However, unlike with \mid, whitespace \; around the bar , must be inserted manually; for example: \;\big, \; or \mathrel\big, \mathrel.

Set operations

Set relations

''Note:'' The symbols

\subset

and

\supset

are used inconsistently and often do not exclude the equality of the two quantities.

Cardinality

Equivalence classes/relations

Order theory

Comparions

:''See also'': Arithmetic comparison, Set relations

Binary relations

Algebra

Group theory

Field theory

Ring theory

Geometry

Euclidean geometry

Differential geometry

Topology

Alphanumeric Symbols

Digits

Alphabets

Greek Letters

Bibliography

* * *

Deutsches Institut für Normung ' (DIN; in English, the German Institute for Standardisation Registered Association) is the German national organization for standardization and is the German ISO member body. DIN is a German Registered Association ('' e.V.'') headquartered in ...

: ''DIN 1302: Allgemeine mathematische Zeichen und Begriffe'', Beuth-Verlag, 1999. *

: ''DIN 1303: Vektoren, Matrizen, Tensoren; Zeichen und Begriffe'', Beuth-Verlag, 1987. *

International Standards Organisation The International Organization for Standardization (ISO ) is an international standard development organization composed of representatives from the national standards organizations of member countries. Membership requirements are given in Art ...

: ''DIN EN ISO 80000-2: Größen und Einheiten – Teil 2: Mathematische Zeichen für Naturwissenschaft und Technik'', 2013. ''Note: This article is a translation of the German Wikipedia article :de:Liste mathematischer Symbole.''

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 *

− 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. {{DEFAULTSORT:Mathematical Symbols

Mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

Symbols A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...