List of mathematical symbols by subject

List of mathematical symbols by subject
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
Intervals
Mathematical constants
Complex numbers
Remark: real and imaginary parts of a complex number are often also denoted by and .
Elementary arithmetic operations
Elementary functions
Note: the power function is not represented by its own icon, but by the positioning of the exponent as a superscript.
Trigonometric functions
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", "s.t.", and "WLOG".
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\{ \right\}.
Wikipedia does not support \middle as that requires e-TeX, 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 and are used inconsistently and often do not exclude the equality of the two quantities.
Cardinality
Equivalence classes/relations
Order theory
Comparisons
See also: Arithmetic comparison, Set relations
Binary relations
Algebra
Group theory
Field theory
Ring theory
Geometry
Euclidean geometry
Differential geometry
Topology
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
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
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.
Mathematics
Symbols
Symbols
Symbols