# List of math symbols

Some math symbols

This list of mathematical symbols shows a selection of the most common symbols used in modern mathematical notation within formulas . Since it is practically impossible to list all symbols ever used in mathematics, only those symbols are given in this list that appear frequently in mathematics class or in mathematics study . Many of the symbols are standardized , for example in DIN 1302 General mathematical symbols or DIN EN ISO 80000-2 sizes and units - Part 2: Mathematical symbols for science and technology .

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

## Explanation

The following information is provided for each math symbol:

symbol
The symbol as represented by LaTeX . If there are several typographical variants, only one of the variants is shown.
use
An exemplary use of the symbol within a formula. Letters are used as placeholders for numbers , variables or more complex expressions . Different uses are listed separately.
interpretation
A brief textual description of the meaning of the formula in the previous column.
items
The Wikipedia article that covers the meaning ( semantics ) of the symbol.
Latex
The LaTeX command used to create the symbol. Characters from the ASCII character set can with a few exceptions ( double cross , backslash , braces , percent sign be used directly). Superscripts and subscripts are made using the characters ^and _and are not explicitly specified.
HTML
The symbol in HTML if it is defined as a named character . Unnamed characters can be represented by specifying the Unicode code point in the following column in the form &#xnnnn;, where nnnnthe hexadecimal is Unicode. Superscripts and subscripts are made using <sup></sup>and <sub></sub>.
Unicode
The code point of the corresponding Unicode character. Some characters are combining and require additional characters to be entered. In the case of brackets, the code points of the opening and closing brackets are specified.

## Set theory

### Quantity construction

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ varnothing}$ ${\ displaystyle \ {\ \}}$ empty set Empty set \varnothing,
\emptyset
&empty; U+2205
${\ displaystyle \ {~ \}}$ ${\ displaystyle \ {a, b, \ ldots \}}$ Set consisting of the elements , and so on ${\ displaystyle a}$${\ displaystyle b}$ Set (mathematics) , class (set theory) \{ \} U+007B/D
${\ displaystyle \ mid}$ ${\ displaystyle \ {a \ mid T (a) \}}$ Set or class of elements that meet the condition${\ displaystyle a}$${\ displaystyle T (a)}$ \mid U+007C
${\ displaystyle \ colon}$ ${\ displaystyle \ {a: T (a) \}}$ : U+003A

### Set operations

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ cup}$ ${\ displaystyle A \ cup B}$ Union of sets and${\ displaystyle A}$${\ displaystyle B}$ Union set \cup &cup; U+222A
${\ displaystyle \ cap}$ ${\ displaystyle A \ cap B}$ Average of the quantities and${\ displaystyle A}$${\ displaystyle B}$ Intersection \cap &cap; U+2229
${\ displaystyle \ setminus}$ ${\ displaystyle A \ setminus B}$ Difference in quantities and${\ displaystyle A}$${\ displaystyle B}$ Difference amount \setminus U+2216
${\ displaystyle \ triangle}$ ${\ displaystyle A \, \ triangle \, B}$ symmetrical difference of the quantities and${\ displaystyle A}$${\ displaystyle B}$ Symmetrical difference \triangle &Delta; U+2206
${\ displaystyle \ times}$ ${\ displaystyle A \ times B}$ Cartesian product of the sets and${\ displaystyle A}$${\ displaystyle B}$ Cartesian product \times &times; U+2A2F
${\ displaystyle {\ dot {\ cup}}}$ ${\ displaystyle A \, {\ dot {\ cup}} \, B}$ Union of disjoint sets and${\ displaystyle A}$${\ displaystyle B}$ Disjoint union \dot\cup U+228D
${\ displaystyle \ sqcup}$ ${\ displaystyle A \ sqcup B}$ Disjoint union of the sets and${\ displaystyle A}$${\ displaystyle B}$ \sqcup U+2294
${\ displaystyle {} ^ {\ mathrm {C}}}$ ${\ displaystyle A ^ {\ mathrm {C}}}$ Complement of the crowd ${\ displaystyle A}$ Complement (set theory) \mathrm{C} U+2201
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle {\ overline {A}}}$ \bar U+0305
${\ displaystyle {\ mathcal {P}}}$ ${\ displaystyle {\ mathcal {P}} (A)}$ Power set of set ${\ displaystyle A}$ Power set \mathcal{P} U+1D4AB
${\ displaystyle {\ mathfrak {P}}}$ ${\ displaystyle {\ mathfrak {P}} (A)}$ \mathfrak{P} U+1D513

### Quantity relations

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ subset}$ ${\ displaystyle A \ subset B}$ ${\ displaystyle A}$ is a real subset of ${\ displaystyle B}$ Subset \subset &sub; U+2282
${\ displaystyle \ subsetneq}$ ${\ displaystyle A \ subsetneq B}$ \subsetneq U+228A
${\ displaystyle \ subseteq}$ ${\ displaystyle A \ subseteq B}$ ${\ displaystyle A}$ is a subset of ${\ displaystyle B}$ \subseteq &sube; U+2286
${\ displaystyle \ supset}$ ${\ displaystyle A \ supset B}$ ${\ displaystyle A}$ is proper superset of ${\ displaystyle B}$ Superset \supset &sup; U+2283
${\ displaystyle \ supsetneq}$ ${\ displaystyle A \ supsetneq B}$ \supsetneq U+228B
${\ displaystyle \ supseteq}$ ${\ displaystyle A \ supseteq B}$ ${\ displaystyle A}$ is a superset of ${\ displaystyle B}$ \supseteq &supe; U+2287
${\ displaystyle \ in}$ ${\ displaystyle a \ in A}$ the element is in the set contain ${\ displaystyle a}$${\ displaystyle A}$ Element (math) \in &isin; U+2208
${\ displaystyle \ ni}$ ${\ displaystyle A \ ni a}$ \ni, \owns &ni; U+220B
${\ displaystyle \ notin}$ ${\ displaystyle a \ notin A}$ the element is not in the set contain ${\ displaystyle a}$${\ displaystyle A}$ \notin &notin; U+2209
${\ displaystyle \ not \ ni}$ ${\ displaystyle A \ not \ ni a}$ \not\ni U+220C

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

### Sets of numbers

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ mathbb {P}}$ Prime numbers Prime number \mathbb{P} &Popf; U+2119
${\ displaystyle \ mathbb {N}}$ natural numbers Natural number \mathbb{N} &Nopf; U+2115
${\ displaystyle \ mathbb {Z}}$ whole numbers Integer \mathbb{Z} &Zopf; U+2124
${\ displaystyle \ mathbb {F} _ {p ^ {n}}}$ finite field with prime number characteristic ${\ displaystyle p}$ Finite body \mathbb{F} &Fopf; U+1D53D
${\ displaystyle \ mathbb {Q}}$ rational numbers Rational number \mathbb{Q} &Qopf; U+211A
${\ displaystyle \ mathbb {I}}$ irrational numbers (Real) irrational number \mathbb{I} &Iopf; U+1D540
${\ displaystyle \ mathbb {A}}$ algebraic numbers (Complex) algebraic number \mathbb{A} &Aopf; U+1D538
${\ displaystyle \ mathbb {T}}$ transcendent numbers Real transcendent number \mathbb{T} &Topf; U+1D54B
${\ displaystyle \ mathbb {R}}$ real numbers Real number \mathbb{R} &Ropf; U+211D
${\ displaystyle {} ^ {*} \ mathbb {R}}$ hyperreal numbers Hyper real number {}^*\mathbb{R} * &Ropf; U+211D
${\ displaystyle \ mathbb {C}}$ complex numbers Complex number \mathbb{C} &Copf; U+2102
${\ displaystyle \ mathbb {H}}$ Quaternions Quaternion \mathbb{H} &Hopf; U+210D
${\ displaystyle \ mathbb {O}}$ Octonions Octonion \mathbb{O} U+1D546
${\ displaystyle \ mathbb {S}}$ Sedenions Sedenion \mathbb{S} U+1D54A
${\ displaystyle \ mathbb {K}}$ Functional
analysis
${\ displaystyle \ mathbb {K} \ in \ {\ mathbb {R}, \ mathbb {C} \}}$ Algebras \mathbb{K} &Kopf; U+1D542

### Powers

symbol use interpretation items Latex HTML Unicode
${\ displaystyle | ~~ |}$ ${\ displaystyle | A |}$ Cardinality of a set ${\ displaystyle A}$ Power (mathematics) \vert U+007C
${\ displaystyle \ #}$ ${\ displaystyle \ #A}$ \# U+0023
${\ displaystyle {\ mathfrak {c}}}$ Thickness of the continuum Continuum (mathematics) \mathfrak{c} U+1D520
${\ displaystyle \ aleph}$ ${\ displaystyle \ aleph _ {0}}$, , ... ${\ displaystyle \ aleph _ {1}}$ Cardinal numbers Cardinal number (math) \aleph U+2135
${\ displaystyle \ beth}$ ${\ displaystyle \ beth _ {0}}$, , ... ${\ displaystyle \ beth _ {1}}$ Beth numbers Beth function \beth U+2136

## arithmetic

### Arithmetic symbol

symbol use interpretation items Latex HTML Unicode
${\ displaystyle +}$ ${\ displaystyle a + b}$ ${\ displaystyle a}$and are added ${\ displaystyle b}$ addition + U+002B
${\ displaystyle -}$ ${\ displaystyle from}$ ${\ displaystyle b}$is subtracted from ${\ displaystyle a}$ subtraction - &minus; U+2212
${\ displaystyle a}$ ${\ displaystyle b}$ U+2052
${\ displaystyle \ cdot}$ ${\ displaystyle a \ cdot b}$ ${\ displaystyle a}$and are multiplied ${\ displaystyle b}$ multiplication \cdot &middot; U+22C5
${\ displaystyle \ times}$ ${\ displaystyle a \ times b}$ \times &times; U+2A2F
${\ displaystyle:}$ ${\ displaystyle a: b}$ ${\ displaystyle a}$is divided by ${\ displaystyle b}$ Division (math) : U+003A
${\ displaystyle /}$ ${\ displaystyle a / b}$ / &frasl; U+2215
${\ displaystyle \ div}$ ${\ displaystyle a \ div b}$ \div &divide; U+00F7
${\ displaystyle {\ frac {~~} {~~}}}$ ${\ displaystyle {\ tfrac {a} {b}}}$ \frac U+2044
${\ displaystyle -}$ ${\ displaystyle -a}$ negative number or additive inverse of${\ displaystyle a}$${\ displaystyle a}$ Unary minus - &minus; U+2212
${\ displaystyle \ pm}$ ${\ displaystyle \ pm a}$ plus or minus ${\ displaystyle a}$ Plus minus sign \pm &plusmn; U+00B1
${\ displaystyle \ mp}$ ${\ displaystyle \ mp a}$ minus or plus ${\ displaystyle a}$ \mp U+2213
${\ displaystyle (~)}$ ${\ displaystyle (a)}$ the term is evaluated first ${\ displaystyle a}$ Bracket (character) ( ) U+0028/9
${\ displaystyle [~]}$ ${\ displaystyle [a]}$ [ ] U+005B/D

### Equal sign

symbol use interpretation items Latex HTML Unicode
${\ displaystyle =}$ ${\ displaystyle a = b}$ ${\ displaystyle a}$ is equal to ${\ displaystyle b}$ equation = U+003D
${\ displaystyle \ neq}$ ${\ displaystyle a \ neq b}$ ${\ displaystyle a}$ is not the same ${\ displaystyle b}$ Inequality \neq &ne; U+2260
${\ displaystyle \ equiv}$ ${\ displaystyle a \ equiv b}$ ${\ displaystyle a}$ is identical to ${\ displaystyle b}$ Identity equation \equiv &equiv; U+2261
${\ displaystyle \ approx}$ ${\ displaystyle a \ approx b}$ ${\ displaystyle a}$ is about the same ${\ displaystyle b}$ Rounding \approx &asymp; U+2248
${\ displaystyle \ sim}$ ${\ displaystyle a \ sim b}$ ${\ displaystyle a}$ is proportional to ${\ displaystyle b}$ Proportionality \sim &sim; U+223C
${\ displaystyle \ propto}$ ${\ displaystyle a \ propto b}$ \propto &prop; U+221D
${\ displaystyle {\ widehat {=}}}$ ${\ displaystyle a \, {\ widehat {=}} \, b}$ ${\ displaystyle a}$ corresponds ${\ displaystyle b}$ Matches sign \widehat{=} U+2259
${\ displaystyle \ sim}$ ${\ displaystyle a \ sim b}$ ${\ displaystyle a}$ is just as appreciated as ${\ displaystyle b}$ Preference relation \sim  -

### Comparison sign

symbol use interpretation items Latex HTML Unicode
${\ displaystyle <}$ ${\ displaystyle a ${\ displaystyle a}$ is smaller than ${\ displaystyle b}$ Comparison (numbers) < &lt; U+003C
${\ displaystyle>}$ ${\ displaystyle a> b}$ ${\ displaystyle a}$ is bigger than ${\ displaystyle b}$ > &gt; U+003E
${\ displaystyle \ leq}$ ${\ displaystyle a \ leq b}$ ${\ displaystyle a}$is less than or equal to${\ displaystyle b}$${\ displaystyle b}$ \le, \leq &le; U+2264
${\ displaystyle \ leqq}$ ${\ displaystyle a \ leqq b}$ \leqq U+2266
${\ displaystyle \ geq}$ ${\ displaystyle a \ geq b}$ ${\ displaystyle a}$is greater than or equal to${\ displaystyle b}$${\ displaystyle b}$ \ge, \geq &ge; U+2265
${\ displaystyle \ geqq}$ ${\ displaystyle a \ geqq b}$ \geqq U+2267
${\ displaystyle \ ll}$ ${\ displaystyle a \ ll b}$ ${\ displaystyle a}$ is much smaller than ${\ displaystyle b}$ \ll U+226A
${\ displaystyle \ gg}$ ${\ displaystyle a \ gg b}$ ${\ displaystyle a}$ is much bigger than ${\ displaystyle b}$ \gg U+226B
${\ displaystyle \ lll}$ ${\ displaystyle a \ lll b}$ ${\ displaystyle a}$ is much smaller than ${\ displaystyle b}$ \lll U+22D8
${\ displaystyle \ ggg}$ ${\ displaystyle a \ ggg b}$ ${\ displaystyle a}$ is much larger than ${\ displaystyle b}$ \ggg U+22D9
${\ displaystyle \ lessgtr}$ ${\ displaystyle a \ lessgtr b}$ ${\ displaystyle a}$ is less than or greater than ${\ displaystyle b}$ \lessgtr U+2276
${\ displaystyle \ gtrless}$ ${\ displaystyle a \ gtrless b}$ ${\ displaystyle a}$ is greater or less than ${\ displaystyle b}$ \gtrless U+2277
${\ displaystyle \ prec}$ ${\ displaystyle a \ prec b}$ ${\ displaystyle b}$is strictly preferred to ${\ displaystyle a}$ Preference relation \prec U+227A
${\ displaystyle \ succ}$ ${\ displaystyle a \ succ b}$ ${\ displaystyle a}$is strictly preferred to ${\ displaystyle b}$ \succ U+227B
${\ displaystyle \ preccurlyeq}$ ${\ displaystyle a \ preccurlyeq b}$ ${\ displaystyle b}$is preferred weakly or is at least as good as${\ displaystyle a}$${\ displaystyle b}$${\ displaystyle a}$ \preccurlyeq U+227C
${\ displaystyle \ succcurlyeq}$ ${\ displaystyle a \ succcurlyeq b}$ ${\ displaystyle a}$is preferred weakly or is at least as good as${\ displaystyle b}$${\ displaystyle a}$${\ displaystyle b}$ \succcurlyeq U+227D

### Divisibility

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ mid}$ ${\ displaystyle a \ mid b}$ ${\ displaystyle a}$ Splits ${\ displaystyle b}$ Divisibility \mid U+2223
${\ displaystyle \ parallel}$ ${\ displaystyle a \ parallel b}$ ${\ displaystyle a}$divides exactly ${\ displaystyle b}$ \parallel U+2225
${\ displaystyle \ nmid}$ ${\ displaystyle a \ nmid b}$ ${\ displaystyle a}$does not share${\ displaystyle b}$ \nmid U+2224
${\ displaystyle \ perp}$ ${\ displaystyle a \ perp b}$ ${\ displaystyle a}$and are coprime ${\ displaystyle b}$ Coprime \perp &perp; U+22A5
${\ displaystyle \ sqcap}$ ${\ displaystyle a \ sqcap b}$ greatest common factor of and${\ displaystyle a}$${\ displaystyle b}$ Greatest common divisor \sqcap U+2293
${\ displaystyle \ wedge}$ ${\ displaystyle a \ wedge b}$ \wedge &and; U+2227
${\ displaystyle \ sqcup}$ ${\ displaystyle a \ sqcup b}$ smallest common multiple of and${\ displaystyle a}$${\ displaystyle b}$ Least common multiple \sqcup U+2294
${\ displaystyle \ vee}$ ${\ displaystyle a \ vee b}$ \vee &or; U+2228
${\ displaystyle \ equiv}$ ${\ displaystyle a \ equiv b {\ bmod {m}}}$ ${\ displaystyle a}$and are congruent modulo${\ displaystyle b}$${\ displaystyle m}$ Congruence (number theory) \equiv &equiv; U+2261

### Intervals

symbol use interpretation items Latex HTML Unicode
${\ displaystyle [~~]}$ ${\ displaystyle [a, b]}$ completed interval between and${\ displaystyle a}$${\ displaystyle b}$ interval ( )
[ ]
U+0028/9
U+005B/D
${\ displaystyle] ~~ [}$ ${\ displaystyle] a, b [}$ open interval between and${\ displaystyle a}$${\ displaystyle b}$
${\ displaystyle (~~)}$ ${\ displaystyle (a, b)}$
${\ displaystyle [~~ [}$ ${\ displaystyle [a, b [}$ right half-open interval between and${\ displaystyle a}$${\ displaystyle b}$
${\ displaystyle [~~)}$ ${\ displaystyle [a, b)}$
${\ displaystyle] ~~]}$ ${\ displaystyle] a, b]}$ left half-open interval between and${\ displaystyle a}$${\ displaystyle b}$
${\ displaystyle (~~]}$ ${\ displaystyle (a, b]}$

### Elementary functions

symbol use interpretation items Latex HTML Unicode
${\ displaystyle | ~~ |}$ ${\ displaystyle | x |}$ amount of ${\ displaystyle x}$ Amount function \vert U+007C
${\ displaystyle \ left [~~ \ right]}$ ${\ displaystyle \ left [x \ right]}$ largest integer less than or equal to ${\ displaystyle x}$ Gaussian bracket [ ] U+005B/D
${\ displaystyle \ lfloor ~~ \ rfloor}$ ${\ displaystyle \ lfloor x \ rfloor}$ \lfloor \rfloor &lfloor; &rfloor; U+230A/B
${\ displaystyle \ lceil ~~ \ rceil}$ ${\ displaystyle \ lceil x \ rceil}$ smallest whole number greater than or equal to ${\ displaystyle x}$ \lceil \rceil &lceil; &rceil; U+2308/9
${\ displaystyle {\ sqrt {\,}}}$ ${\ displaystyle {\ sqrt {x}}}$ squareroot of ${\ displaystyle x}$ Root (math) \sqrt &radic; U+221A
${\ displaystyle {\ sqrt [{n}] {x}}}$ ${\ displaystyle n}$-th root ${\ displaystyle x}$
${\ displaystyle \%}$ ${\ displaystyle x \, \%}$ ${\ displaystyle x}$ percent percent \% U+0025

Note : the power function is not represented by its own symbol, but by superscripting the exponent .

### Complex numbers

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ Re}$ ${\ displaystyle \ Re (z)}$ Real part of the complex number ${\ displaystyle z}$ Complex number \Re U+211C
${\ displaystyle \ Im}$ ${\ displaystyle \ Im (z)}$ Imaginary part of the complex number ${\ displaystyle z}$ \Im U+2111
${\ displaystyle {\ bar {~}}}$ ${\ displaystyle {\ bar {z}}}$ Conjugates complex number of number ${\ displaystyle z}$ Conjugation (math) \bar U+0305
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle z ^ {\ ast}}$ \ast &lowast; U+002A
${\ displaystyle | ~~ |}$ ${\ displaystyle | z |}$ Complex number amount ${\ displaystyle z}$ Amount function \vert U+007C

Note: for the designation of the real and imaginary part of a complex number, the abbreviations and are the most common. ${\ displaystyle \ operatorname {Re}}$${\ displaystyle \ operatorname {Im}}$

### Mathematical constants

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ pi}$ Circle number Circle number \pi &pi; U+03C0
${\ displaystyle \ mathrm {e}}$ Euler's number Euler's number \mathrm{e} U+0065
${\ displaystyle \ Phi}$ Golden cut Golden cut \Phi &Phi; U+03A6
${\ displaystyle \ mathrm {i}}$ imaginary unit Imaginary number \mathrm{i} U+0069

## Analysis

### Sequences and ranks

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ sum}$ ${\ displaystyle \ sum _ {i = 1} ^ {n}, \ sum _ {i \ in I}}$ Sum of to or over all in the set${\ displaystyle i = 1}$${\ displaystyle n}$${\ displaystyle i}$${\ displaystyle I}$ total \sum &sum; U+2211
${\ displaystyle \ prod}$ ${\ displaystyle \ prod _ {i = 1} ^ {n}, \ prod _ {i \ in I}}$ Product of up to or over all in the amount${\ displaystyle i = 1}$${\ displaystyle n}$${\ displaystyle i}$${\ displaystyle I}$ Product (math) \prod &prod; U+220F
${\ displaystyle \ coprod}$ ${\ displaystyle \ coprod _ {i = 1} ^ {n}, \ coprod _ {i \ in I}}$ Coproduct of up to or over all in the set${\ displaystyle i = 1}$${\ displaystyle n}$${\ displaystyle i}$${\ displaystyle I}$ Coproduct \coprod U+2210
${\ displaystyle (~~)}$ ${\ displaystyle (a_ {n}) _ {n}}$ Follow with the sequence members ${\ displaystyle a_ {1}, a_ {2}, \ ldots}$ Episode (math) ( ) U+0028/9
${\ displaystyle \ to}$ ${\ displaystyle a_ {n} \ to a}$ the sequence converges towards the limit value${\ displaystyle (a_ {n})}$${\ displaystyle a}$ Limit value (sequence) \to &rarr; U+2192
${\ displaystyle \ infty}$ ${\ displaystyle n \ to \ infty}$ ${\ displaystyle n}$ strives for infinity infinity \infty &infin; U+221E

### Functions

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ to}$ ${\ displaystyle f \ colon A \ to B}$ the function is the amount in the amount from ${\ displaystyle f}$${\ displaystyle A}$${\ displaystyle B}$ Function (math) \to &rarr; U+2192
${\ displaystyle A \, {\ stackrel {f} {\ to}} \, B}$
${\ displaystyle \ mapsto}$ ${\ displaystyle f \ colon x \ mapsto y}$ the function of forming the element to the element from ${\ displaystyle f}$${\ displaystyle x}$${\ displaystyle y}$ \mapsto &mapsto; U+21A6
${\ displaystyle x \, {\ stackrel {f} {\ mapsto}} \, y}$
${\ displaystyle (~~)}$ ${\ displaystyle f (x)}$ Function value of for the element${\ displaystyle f}$${\ displaystyle x}$ Image (math) ( ) U+0028/9
${\ displaystyle f (X)}$ Image of the crowd under the function${\ displaystyle X}$${\ displaystyle f}$
${\ displaystyle [~~]}$ ${\ displaystyle f [X]}$ [ ] U+005B/D
${\ displaystyle \ vert}$ ${\ displaystyle f \ vert _ {X}}$ Restriction of the function to the quantity${\ displaystyle f}$${\ displaystyle X}$ Restriction \vert U+007C
${\ displaystyle \ cdot}$ ${\ displaystyle f (\ cdot)}$ Placeholder for a variable as an argument of the function ${\ displaystyle f}$ Variable (math) \cdot &middot; U+22C5
${\ displaystyle {} ^ {- 1}}$ ${\ displaystyle f ^ {- 1}}$ Inverse function to ${\ displaystyle f}$ Inverse function -1 U+207B
${\ displaystyle f ^ {- 1} (Y)}$ Archetype of the crowd under the function${\ displaystyle Y}$${\ displaystyle f}$ Archetype (mathematics)
${\ displaystyle \ circ}$ ${\ displaystyle f \ circ g}$ Concatenation of functions and${\ displaystyle f}$${\ displaystyle g}$ Composition (mathematics) \circ U+2218
${\ displaystyle \ ast}$ ${\ displaystyle f \ ast g}$ Convolution of functions and${\ displaystyle f}$${\ displaystyle g}$ Convolution (math) \ast &lowast; U+2217
${\ displaystyle {\ hat {~}}}$ ${\ displaystyle {\ hat {f}}}$ Fourier transform of the function ${\ displaystyle f}$ Fourier transform \hat U+0302

### Limit values

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ uparrow}$ ${\ displaystyle \ lim _ {x \ uparrow a} f (x)}$ left-hand limit of the function for against${\ displaystyle f}$${\ displaystyle x}$${\ displaystyle a}$ Limit value (function) \uparrow &uarr; U+2191
${\ displaystyle \ nearrow}$ ${\ displaystyle \ lim _ {x \ nearrow a} f (x)}$ \nearrow U+2197
${\ displaystyle \ to}$ ${\ displaystyle \ lim _ {x \ to a} f (x)}$ bilateral limit value of the function for against${\ displaystyle f}$${\ displaystyle x}$${\ displaystyle a}$ \to &rarr; U+2192
${\ displaystyle \ searrow}$ ${\ displaystyle \ lim _ {x \ searrow a} f (x)}$ right-hand limit of the function for against${\ displaystyle x}$${\ displaystyle a}$ \searrow U+2198
${\ displaystyle \ downarrow}$ ${\ displaystyle \ lim _ {x \ downarrow a} f (x)}$ \downarrow &darr; U+2193
${\ displaystyle X_ {n} {\ xrightarrow {p}} X}$ ${\ displaystyle \ operatorname {plim} (X_ {n}) = X}$ Convergence in probability for against${\ displaystyle X_ {n}}$${\ displaystyle X}$ Convergence (stochastics) \to &rarr; U+2192
${\ displaystyle X_ {n} {\ xrightarrow {d}} X}$ ${\ displaystyle x_ {n} {\ xrightarrow {d}} x}$ Convergence in distribution for against${\ displaystyle x_ {n}}$${\ displaystyle x}$ \to &rarr; U+2192
${\ displaystyle X_ {n} {\ xrightarrow {m}} X}$ ${\ displaystyle x_ {n} {\ xrightarrow {m}} x}$ Root mean square convergence for against${\ displaystyle x_ {n}}$${\ displaystyle x}$ \to &rarr; U+2192

### Asymptotic behavior

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ sim}$ ${\ displaystyle f \ sim g}$ the function is asymptotically equal to the function${\ displaystyle f}$${\ displaystyle g}$ Asymptotic analysis \sim &sim; U+223C
${\ displaystyle o}$ ${\ displaystyle f \ in o (g)}$ the function grows slower than${\ displaystyle f}$${\ displaystyle g}$ Landau symbols o U+006F
${\ displaystyle {\ mathcal {O}}}$ ${\ displaystyle f \ in {\ mathcal {O}} (g)}$ the function does not grow much faster than${\ displaystyle f}$${\ displaystyle g}$ \mathcal{O} U+1D4AA
${\ displaystyle \ Theta}$ ${\ displaystyle f \ in \ Theta (g)}$ the function grows as fast as${\ displaystyle f}$${\ displaystyle g}$ \Theta &Theta; U+0398
${\ displaystyle \ Omega}$ ${\ displaystyle f \ in \ Omega (g)}$ the function does not grow much slower than${\ displaystyle f}$${\ displaystyle g}$ \Omega &Omega; U+03A9
${\ displaystyle \ omega}$ ${\ displaystyle f \ in \ omega (g)}$ the function grows faster than${\ displaystyle f}$${\ displaystyle g}$ \omega &omega; U+03C9

### Differential calculus

symbol use interpretation items Latex HTML Unicode
${\ displaystyle {} '}$ ${\ displaystyle f ', f' '}$ first or second derivative of the function ${\ displaystyle f}$ Differential calculus \prime &prime; U+2032
${\ displaystyle \ cdot}$ ${\ displaystyle {\ dot {f}}, {\ ddot {f}}}$ first or second derivative of after time (in physics) ${\ displaystyle f}$ \dot, \ddot U+0307
${\ displaystyle {} ^ {(~)}}$ ${\ displaystyle f ^ {(n)}}$ ${\ displaystyle n}$-th derivative of the function ${\ displaystyle f}$ ( ) U+0028/9
${\ displaystyle \ mathrm {d}}$ ${\ displaystyle {\ frac {\ mathrm {d} f} {\ mathrm {d} x}}}$ Derivation of the function according to${\ displaystyle f}$${\ displaystyle x}$ \mathrm{d} U+0064
${\ displaystyle \ mathrm {d} f}$ total differential of function ${\ displaystyle f}$ Total differential
${\ displaystyle \ partial}$ ${\ displaystyle {\ frac {\ partial \! f} {\ partial x}}}$ partial derivative of the function to${\ displaystyle f}$${\ displaystyle x}$ Partial derivative \partial &part; U+2202

### Integral calculus

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ int}$ ${\ displaystyle \ int _ {a} ^ {b}}$, ${\ displaystyle \ displaystyle \ int _ {G}}$ definite integral between and or over the area${\ displaystyle a}$${\ displaystyle b}$${\ displaystyle G}$ Integral calculus \int &int; U+222B
${\ displaystyle \ oint}$ ${\ displaystyle \ oint _ {\ gamma}}$ Integral over the curve ${\ displaystyle \ gamma}$ Curve integral \oint U+222E
${\ displaystyle \ iint}$ ${\ displaystyle \ iint _ {\ mathcal {F}}}$ Integral over the area ${\ displaystyle {\ mathcal {F}}}$ Surface integral \iint U+222C
${\ displaystyle \ iiint}$ ${\ displaystyle \ iiint _ {V}}$ Integral over the volume ${\ displaystyle V}$ Volume integral \iiint U+222D

### Vector analysis

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ nabla}$ ${\ displaystyle \ nabla f}$ Gradient of function ${\ displaystyle f}$ Gradient (math) \nabla &nabla; U+2207
${\ displaystyle \ nabla \ cdot F}$ Divergence of the vector field ${\ displaystyle F}$ Divergence of a vector field
${\ displaystyle \ nabla \ times F}$ Rotation of the vector field ${\ displaystyle F}$ Rotation of a vector field
${\ displaystyle \ Delta}$ ${\ displaystyle \ Delta f}$ Laplace operator of the function ${\ displaystyle f}$ Laplace operator \Delta &Delta; U+2206
${\ displaystyle \ square}$ ${\ displaystyle \ square f}$ D'Alembert operator of the function ${\ displaystyle f}$ D'Alembert operator \square U+25A1

### topology

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ partial}$ ${\ displaystyle \ partial U}$ Edge of the crowd ${\ displaystyle U}$ Edge (topology) \partial &part; U+2202
${\ displaystyle {} ^ {\ circ}}$ ${\ displaystyle U ^ {\ circ}}$ Inside the crowd ${\ displaystyle U}$ Inner point \circ &deg; U+02DA
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle {\ overline {U}}}$ Completing the crowd ${\ displaystyle U}$ Degree (topology) \bar U+0305
${\ displaystyle {\ dot {~}}}$ ${\ displaystyle {\ dot {U}} (x)}$ Dotted neighborhood of the point${\ displaystyle U}$${\ displaystyle x}$ Dotted environment \dot U+0307

### Functional analysis

symbol use interpretation items Latex HTML Unicode
${\ displaystyle {} '}$ ${\ displaystyle V '}$ topological dual space of the topological vector space ${\ displaystyle V}$ Topological dual space \prime &prime; U+2032
${\ displaystyle {} ''}$ ${\ displaystyle V ''}$ Bidual space of the normalized vector space ${\ displaystyle V}$ Double room
${\ displaystyle {\ hat {~}}}$ ${\ displaystyle {\ hat {X}}}$ Completion of the metric space ${\ displaystyle X}$ Complete space \hat U+0302
${\ displaystyle \ hookrightarrow}$ ${\ displaystyle X \ hookrightarrow Y}$ Embedding the topological space in the space${\ displaystyle X}$${\ displaystyle Y}$ Embedding (mathematics) \hookrightarrow U+21AA
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle T ^ {\ ast}}$ Adjoint operator of the linear operator ${\ displaystyle T}$ Adjoint operator \ast &lowast; U+002A

### Measure theory

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ ll}$ ${\ displaystyle \ nu \ ll \ mu}$ The measure is absolutely constant regarding${\ displaystyle \ nu}$${\ displaystyle \ mu}$ Absolutely constant measure \ll U+226A
${\ displaystyle \ perp}$ ${\ displaystyle \ nu \ perp \ mu}$ The measure is singular in terms of${\ displaystyle \ nu}$${\ displaystyle \ mu}$ Singular measure \perp U+22A5
${\ displaystyle \ sigma}$ ${\ displaystyle \ sigma ({\ mathcal {M}})}$ The smallest algebra that contains ${\ displaystyle \ sigma}$${\ displaystyle {\ mathcal {M}}}$ σ-algebra \sigma U+03A3
${\ displaystyle \ delta}$ ${\ displaystyle \ delta ({\ mathcal {E}})}$ The smallest Dynkin system that contains ${\ displaystyle {\ mathcal {E}}}$ Dynkin system \delta U+0394

## Linear algebra and geometry

### Elementary geometry

symbol use interpretation items Latex HTML Unicode
${\ displaystyle [~~]}$ ${\ displaystyle [AB]}$ Distance between points and${\ displaystyle A}$${\ displaystyle B}$ Route (geometry) [ ] U+005B/D
${\ displaystyle | ~~ |}$ ${\ displaystyle | AB |}$ Length of the route between points and${\ displaystyle A}$${\ displaystyle B}$ \vert U+007C
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle {\ overline {AB}}}$ \overline U+0305
${\ displaystyle {\ overrightarrow {~~}}}$ ${\ displaystyle {\ overrightarrow {AB}}}$ Connection vector of points and${\ displaystyle A}$${\ displaystyle B}$ vector \vec U+20D7
${\ displaystyle (~~)}$ ${\ displaystyle (AB)}$ Line connecting the points and${\ displaystyle A}$${\ displaystyle B}$ Connecting line ( ) U+0028/9
${\ displaystyle \ angle}$ ${\ displaystyle \ angle ABC}$ Angle with the thighs and${\ displaystyle BA}$${\ displaystyle BC}$ angle \angle &ang; U+2220
${\ displaystyle \ triangle}$ ${\ displaystyle \ triangle ABC}$ Triangle with corner points , and${\ displaystyle A}$${\ displaystyle B}$${\ displaystyle C}$ triangle \triangle U+25B3
${\ displaystyle \ square}$ ${\ displaystyle \ square {\ mathit {ABCD}}}$ Rectangle with the corners , , and${\ displaystyle A}$${\ displaystyle B}$${\ displaystyle C}$${\ displaystyle D}$ square \square U+25A1
${\ displaystyle \ parallel}$ ${\ displaystyle g \ parallel h}$ the straight lines and are parallel to each other ${\ displaystyle g}$${\ displaystyle h}$ Parallelism (geometry) \parallel U+2225
${\ displaystyle \ nparallel}$ ${\ displaystyle g \ nparallel h}$ the straight lines and are not parallel to each other ${\ displaystyle g}$${\ displaystyle h}$ \nparallel U+2226
${\ displaystyle \ perp}$ ${\ displaystyle g \ perp h}$ the straight lines and are orthogonal to each other ${\ displaystyle g}$${\ displaystyle h}$ Orthogonality \perp &perp; U+22A5

### Vectors and matrices

symbol interpretation items Latex
${\ displaystyle {\ begin {pmatrix} v_ {1}, \ ldots, v_ {n} \ end {pmatrix}}}$ Line vector consisting of the elements to${\ displaystyle v_ {1}}$${\ displaystyle v_ {n}}$ vector \begin{pmatrix}
...
\end{pmatrix}

or

\left(
\begin{array}{...}
...
\end{array}
\right)
${\ displaystyle {\ begin {pmatrix} v_ {1} \\\ vdots \\ v_ {m} \ end {pmatrix}}}$ Column vector consisting of the elements to${\ displaystyle v_ {1}}$${\ displaystyle v_ {m}}$
${\ displaystyle {\ begin {pmatrix} a_ {11} & \! \ ldots \! & a_ {1n} \\\ vdots & \! \ ddots \! & \ vdots \\ a_ {m1} & \! \ ldots \ ! & a_ {mn} \ end {pmatrix}}}$ Matrix consisting of the elements to${\ displaystyle a_ {11}}$${\ displaystyle a_ {mn}}$ Matrix (math)

### Vector calculation

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ cdot}$ ${\ displaystyle v \ cdot w}$ Dot product of the vectors and${\ displaystyle v}$${\ displaystyle w}$ Scalar product \cdot &middot; U+22C5
${\ displaystyle (~~)}$ ${\ displaystyle (v, w)}$ ( ) U+0028/9
${\ displaystyle \ langle ~~ \ rangle}$ ${\ displaystyle \ langle v, w \ rangle}$
${\ displaystyle \ langle v \, | \, w \ rangle}$
\langle \rangle &lang; &rang; U+27E8/9
${\ displaystyle \ times}$ ${\ displaystyle v \ times w}$ Cross product (vector product) of the vectors and${\ displaystyle v}$${\ displaystyle w}$ Cross product \times &times; U+2A2F
${\ displaystyle [~~]}$ ${\ displaystyle [v, w]}$ [ ] U+005B/D
${\ displaystyle (~~)}$ ${\ displaystyle (u, v, w)}$ Late product of vectors , and${\ displaystyle u}$${\ displaystyle v}$${\ displaystyle w}$ Late product ( ) U+0028/9
${\ displaystyle \ otimes}$ ${\ displaystyle v \ otimes w}$ dyadic product of vectors and${\ displaystyle v}$${\ displaystyle w}$ Dyadic product \otimes &otimes; U+2297
${\ displaystyle \ wedge}$ ${\ displaystyle v \ wedge w}$ Umbrella product of vectors and${\ displaystyle v}$${\ displaystyle w}$ Roof product \wedge U+2227
${\ displaystyle | ~~ |}$ ${\ displaystyle | v |}$ Amount of the vector ${\ displaystyle v}$ vector \vert U+007C
${\ displaystyle \ | ~~ \ |}$ ${\ displaystyle \ | v \ |}$ Norm of the vector ${\ displaystyle v}$ Vector norm \Vert, \| U+2016
${\ displaystyle {\ hat {~}}}$ ${\ displaystyle {\ hat {v}}}$ Unit vector to vector ${\ displaystyle v}$ Unit vector \hat U+0302

### Matrix calculation

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ cdot}$ ${\ displaystyle A \ cdot B}$ Product of the matrices and${\ displaystyle A}$${\ displaystyle B}$ Matrix multiplication \cdot &middot; U+22C5
${\ displaystyle \ colon}$ ${\ displaystyle A \, \ colon \, B}$ Frobenius dot product of the matrices and (in physics) ${\ displaystyle A}$${\ displaystyle B}$ Frobenius dot product \colon U+003A
${\ displaystyle \ circ}$ ${\ displaystyle A \ circ B}$ Hadamard product of the matrices and${\ displaystyle A}$${\ displaystyle B}$ Hadamard product \circ U+2218
${\ displaystyle \ otimes}$ ${\ displaystyle A \ otimes B}$ Kronecker product of the dies and${\ displaystyle A}$${\ displaystyle B}$ Kronecker product \otimes &otimes; U+2297
${\ displaystyle {} ^ {T}}$ ${\ displaystyle A ^ {T}}$ transposed matrix of the matrix ${\ displaystyle A}$ Transposed matrix T U+0054
${\ displaystyle {} ^ {H}}$ ${\ displaystyle A ^ {H}}$ adjoint matrix of the matrix ${\ displaystyle A}$ Adjoint matrix H U+0048
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle A ^ {\ ast}}$ \ast &lowast; U+002A
${\ displaystyle {} ^ {\ dagger}}$ ${\ displaystyle A ^ {\ dagger}}$ \dagger &dagger; U+2020
${\ displaystyle {} ^ {- 1}}$ ${\ displaystyle A ^ {- 1}}$ inverse matrix of the matrix ${\ displaystyle A}$ Inverse matrix -1 U+207B
${\ displaystyle {} ^ {+}}$ ${\ displaystyle A ^ {+}}$ Moore-Penrose Inverse of the Matrix ${\ displaystyle A}$ Pseudoinverse + U+002B
${\ displaystyle | ~~ |}$ ${\ displaystyle | A |}$ Determinant of the matrix ${\ displaystyle A}$ Determinant (mathematics) \vert U+007C
${\ displaystyle \ | ~~ \ |}$ ${\ displaystyle \ | A \ |}$ Norm of the matrix ${\ displaystyle A}$ Matrix norm \Vert, \| U+2016

### Vector spaces

symbol use interpretation items Latex HTML Unicode
${\ displaystyle +}$ ${\ displaystyle V + W}$ Sum of the vector spaces and${\ displaystyle V}$${\ displaystyle W}$ Direct sum + U+002B
${\ displaystyle \ oplus}$ ${\ displaystyle V \ oplus W}$ direct sum of the vector spaces and${\ displaystyle V}$${\ displaystyle W}$ \oplus &oplus; U+2295
${\ displaystyle \ times}$ ${\ displaystyle V \ times W}$ direct product of the vector spaces and${\ displaystyle V}$${\ displaystyle W}$ Direct product \times &times; U+2A2F
${\ displaystyle \ otimes}$ ${\ displaystyle V \ otimes W}$ Tensor product of the vector spaces and${\ displaystyle V}$${\ displaystyle W}$ Tensor product \otimes &otimes; U+2297
${\ displaystyle /}$ ${\ displaystyle V \, / \, U}$ Factor space of the vector space after the sub-vector space${\ displaystyle V}$${\ displaystyle U}$ Factor space / &frasl; U+002F
${\ displaystyle {} ^ {\ perp}}$ ${\ displaystyle U ^ {\ perp}}$ orthogonal complement of subspace ${\ displaystyle U}$ Orthogonal complement \perp &perp; U+27C2
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle V ^ {\ ast}}$ Dual space of vector space ${\ displaystyle V}$ Dual space \ast &lowast; U+002A
${\ displaystyle {} ^ {0}}$ ${\ displaystyle X ^ {0}}$ Annihilator space of the set of vectors ${\ displaystyle X}$ Annihilator (mathematics) 0 U+0030
${\ displaystyle \ langle ~~ \ rangle}$ ${\ displaystyle \ langle X \ rangle}$ linear envelope of the set of vectors ${\ displaystyle X}$ Linear envelope \langle \rangle &lang; &rang; U+27E8/9

## algebra

### Relations

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ circ}$ ${\ displaystyle R \ circ S}$ Composition of relations and${\ displaystyle R}$${\ displaystyle S}$ Composition (mathematics) \circ U+2218
${\ displaystyle a \ circ b}$ Linking the elements and (in general) ${\ displaystyle a}$${\ displaystyle b}$ Linkage (math)
${\ displaystyle \ bullet}$ ${\ displaystyle a \ bullet b}$ \bullet &bull; U+2219
${\ displaystyle \ ast}$ ${\ displaystyle a \ ast b}$ \ast &lowast; U+2217
${\ displaystyle \ leq}$ ${\ displaystyle a \ leq b}$ Order relation between the elements and${\ displaystyle a}$${\ displaystyle b}$ Order relation \leq &le; U+2264
${\ displaystyle \ prec}$ ${\ displaystyle a \ prec b}$ the element is ancestor of the element${\ displaystyle a}$${\ displaystyle b}$ Successor (mathematics) \prec U+227A
${\ displaystyle \ succ}$ ${\ displaystyle a \ succ b}$ the element is the successor of the element${\ displaystyle a}$${\ displaystyle b}$ \succ U+227B
${\ displaystyle \ sim}$ ${\ displaystyle a \ sim b}$ Equivalence relation between the elements and${\ displaystyle a}$${\ displaystyle b}$ Equivalence relation \sim &sim; U+223C
${\ displaystyle [~~]}$ ${\ displaystyle [a]}$ Equivalence class of the element ${\ displaystyle a}$ Equivalence class [ ] U+005B/D
${\ displaystyle /}$ ${\ displaystyle M / \ sim}$ Factor set of the set according to the equivalence relation${\ displaystyle M}$${\ displaystyle \ sim}$ Set of factors (math) / &frasl; U+002F
${\ displaystyle {} ^ {- 1}}$ ${\ displaystyle R ^ {- 1}}$ Inverse relation of relation ${\ displaystyle R}$ Inverse relation -1 U+207B
${\ displaystyle {} ^ {+}}$ ${\ displaystyle R ^ {+}}$ Transitive envelope of the relation ${\ displaystyle R}$ Transitive envelope (relation) + U+002B
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle R ^ {\ ast}}$ Reflexive-transitive envelope of the relation ${\ displaystyle R}$ \ast &lowast; U+002A

### Group theory

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ simeq}$ ${\ displaystyle G \ simeq H}$ the groups and are isomorphic ${\ displaystyle G}$${\ displaystyle H}$ Group isomorphism \simeq U+2243
${\ displaystyle \ cong}$ ${\ displaystyle G \ cong H}$ \cong &cong; U+2245
${\ displaystyle \ times}$ ${\ displaystyle G \ times H}$ Direct product of groups and${\ displaystyle G}$${\ displaystyle H}$ Direct product \times &times; U+2A2F
${\ displaystyle \ rtimes}$ ${\ displaystyle G \ rtimes H}$ Semi-direct product of groups and${\ displaystyle G}$${\ displaystyle H}$ Semi-direct product \rtimes U+22CA
${\ displaystyle \ wr}$ ${\ displaystyle G \, \ wr \, H}$ Wreath product of groups and${\ displaystyle G}$${\ displaystyle H}$ Wreath product \wr U+2240
${\ displaystyle \ leq}$ ${\ displaystyle U \ leq G}$ ${\ displaystyle U}$ is a subgroup of the group ${\ displaystyle G}$ Subgroup \leq &le; U+2264
${\ displaystyle <}$ ${\ displaystyle U ${\ displaystyle U}$ is a real subgroup of the group ${\ displaystyle G}$ \lt &lt; U+003C
${\ displaystyle \ vartriangleleft}$ ${\ displaystyle N \ vartriangleleft G}$ ${\ displaystyle N}$ is a normal part of the group ${\ displaystyle G}$ Normal divider \vartriangleleft U+22B2
${\ displaystyle \ trianglelefteq}$ ${\ displaystyle N \ trianglelefteq G}$ \trianglelefteq
${\ displaystyle /}$ ${\ displaystyle G / N}$ Factor group of the group after the normal divisor${\ displaystyle G}$${\ displaystyle N}$ Factor group / &frasl; U+002F
${\ displaystyle \ colon}$ ${\ displaystyle (G \ colon U)}$ Index of the subgroup in the group${\ displaystyle U}$${\ displaystyle G}$ Index (group theory) \colon U+003A
${\ displaystyle \ langle ~~ \ rangle}$ ${\ displaystyle \ langle E \ rangle}$ Subgroup by the amount is generated ${\ displaystyle E}$ Producer (algebra) \langle \rangle &lang; &rang; U+27E8/9
${\ displaystyle (~~)}$ ${\ displaystyle (g, h)}$ Conjugation of group elements and${\ displaystyle g}$${\ displaystyle h}$ Conjugation (group theory) ( ) U+0028/9
${\ displaystyle [~~]}$ ${\ displaystyle [g, h]}$ Commutator of group elements and${\ displaystyle g}$${\ displaystyle h}$ Commutator (math) [ ] U+005B/D

### Body theory

symbol use interpretation items Latex HTML Unicode
${\ displaystyle /}$ ${\ displaystyle L / K}$ Extension of the body over the body${\ displaystyle L}$${\ displaystyle K}$ Body enlargement / &frasl; U+002F
${\ displaystyle \ mid}$ ${\ displaystyle L \ mid K}$ \mid U+007C
${\ displaystyle \ colon}$ ${\ displaystyle L \ colon K}$ \colon U+003A
${\ displaystyle [L \ colon K]}$ Degree of body enlargement over${\ displaystyle L}$${\ displaystyle K}$ Degree of expansion
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle {\ overline {K}}}$ Algebraic closure of the body ${\ displaystyle K}$ Algebraic degree \overline U+0305
${\ displaystyle \ mathbb {K}}$ Field of real or complex numbers Body (algebra) \mathbb{K} U+1D542
${\ displaystyle \ mathbb {F}}$ finite body Finite body \mathbb{F} U+1D53D

### Ring theory

symbol use interpretation items Latex HTML Unicode
${\ displaystyle {} ^ {\ ast}}$ ${\ displaystyle R ^ {\ ast}}$ Unit group of the ring ${\ displaystyle R}$ Unit group \ast &lowast; U+2217
${\ displaystyle {} ^ {\ times}}$ ${\ displaystyle R ^ {\ times}}$ \times &times; U+2A2F
${\ displaystyle \ vartriangleleft}$ ${\ displaystyle I \ vartriangleleft R}$ ${\ displaystyle I}$ is an ideal of the ring ${\ displaystyle R}$ Ideal (ring theory) \vartriangleleft U+22B2
${\ displaystyle /}$ ${\ displaystyle R / I}$ Factor ring of the ring according to the ideal${\ displaystyle R}$${\ displaystyle I}$ Factor ring / &frasl; U+002F
${\ displaystyle [~~]}$ ${\ displaystyle R [X]}$ Polynomial ring above the ring with the variable${\ displaystyle R}$${\ displaystyle X}$ Polynomial ring [ ] U+005B/D

## Stochastics

### Combinatorics

symbol use interpretation items Latex HTML Unicode
${\ displaystyle!}$ ${\ displaystyle n!}$ Number of permutations of elements ${\ displaystyle n}$ Faculty ! U+0021
${\ displaystyle! n}$ Number of fixed-point-free permutations of elements ${\ displaystyle n}$ Sub-faculty
${\ displaystyle n !!}$ Number of genuinely involutive permutations ( odd) ${\ displaystyle n}$ Double faculty
${\ displaystyle {\ tbinom {~} {~}}}$ ${\ displaystyle {\ tbinom {n} {k}}}$ Number of combinations without repetition of of elements ${\ displaystyle k}$${\ displaystyle n}$ Binomial coefficient \binom U+0028/9
${\ displaystyle {\ tbinom {n} {k_ {1}, \ ldots, k_ {r}}}}$ Number of arrangements of different elements ${\ displaystyle k_ {1}, \ ldots, k_ {r}}$ Multinomial coefficient
${\ displaystyle \ left (\! {\ tbinom {~} {~}} \! \ right)}$ ${\ displaystyle \ left (\! {\ tbinom {n} {k}} \! \ right)}$ Number of combinations with repetition of from elements ${\ displaystyle k}$${\ displaystyle n}$ Multiset U+0028/9
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle n ^ {\ overline {m}}}$ Increasing factorial from with factors ${\ displaystyle n}$${\ displaystyle m}$ Falling and rising factorial \overline U+0305
${\ displaystyle n ^ {\ underline {m}}}$ Falling factorial off with factors ${\ displaystyle n}$${\ displaystyle m}$ \underline U+0332
${\ displaystyle \ #}$ ${\ displaystyle n \ #}$ Product of the prime numbers less than or equal to ${\ displaystyle n}$ Primorial \# U+0023

### probability calculation

symbol use interpretation items Latex HTML Unicode
${\ displaystyle P}$ ${\ displaystyle P (A)}$ Probability of the event ${\ displaystyle A}$ Probability measure P U+2119
${\ displaystyle \ mid}$ ${\ displaystyle P (A \ mid B)}$ Probability of assuming${\ displaystyle A}$${\ displaystyle B}$ Conditional probability \mid U+007C
${\ displaystyle \ operatorname {E}}$ ${\ displaystyle \ operatorname {E} [X \ mid Y]}$ Expected value of the random variable due to${\ displaystyle X}$${\ displaystyle Y}$ Expected value - U+1D53C U+223C
${\ displaystyle \ operatorname {E}}$ ${\ displaystyle \ operatorname {E} [X]}$ Expected value of the random variable ${\ displaystyle X}$ - U+1D53C
${\ displaystyle \ operatorname {Var}}$ ${\ displaystyle \ operatorname {Var} [X]}$ Variance of the random variable ${\ displaystyle X}$ Variance (stochastics) - -
${\ displaystyle \ operatorname {sd}}$ ${\ displaystyle \ operatorname {sd} [X]}$ Standard deviation of the random variable ${\ displaystyle X}$ Standard deviation (probability theory) - -
${\ displaystyle \ operatorname {Cov}}$ ${\ displaystyle \ operatorname {Cov} [X, Y]}$ Covariance of the random variables and${\ displaystyle X}$${\ displaystyle Y}$ Covariance (stochastics)
${\ displaystyle \ rho}$ ${\ displaystyle \ rho (X, Y)}$ Correlation of the random variables and${\ displaystyle X}$${\ displaystyle Y}$ Correlation coefficient \rho &rho; U+03C1
${\ displaystyle R ^ {2}}$ ${\ displaystyle \ rho (X, Y) ^ {2}}$ Square of the correlation between the random variables and${\ displaystyle X}$${\ displaystyle Y}$ Coefficient of determination \rho &rho; U+03C1
${\ displaystyle \ sim}$ ${\ displaystyle X \ sim F}$ the random variable follows the distribution${\ displaystyle X}$${\ displaystyle F}$ Probability distribution \sim &sim; U+223C
${\ displaystyle \ nsim}$ ${\ displaystyle X \ nsim F}$ the random variable does not follow the distribution${\ displaystyle X}$${\ displaystyle F}$ \nsim &nsim; U+2241
${\ displaystyle {\ stackrel {as} {\ sim}}}$ ${\ displaystyle X \; {\ stackrel {as} {\ sim}} \; F}$ the random variable almost certainly follows the distribution${\ displaystyle X}$${\ displaystyle F}$ \approx &asymp; U+2248
${\ displaystyle {\ stackrel {a} {\ sim}}}$ ${\ displaystyle X \; {\ stackrel {a} {\ sim}} \; F}$ the random variable approximately follows the distribution${\ displaystyle X}$${\ displaystyle F}$ \approx &asymp; U+2248
${\ displaystyle {\ stackrel {H_ {0}} {\ sim}}}$ ${\ displaystyle X \; {\ stackrel {H_ {0}} {\ sim}} \; F}$ the random variable follows the distribution under the null hypothesis${\ displaystyle X}$${\ displaystyle F}$ \sim &sim; U+223C
${\ displaystyle \ perp \! \! \! \ perp}$ ${\ displaystyle X \ perp \! \! \! \ perp Y}$ the random variables and are stochastically independent ${\ displaystyle X}$${\ displaystyle Y}$ Stochastically independent random variables - - -

Note: there are some notation variants for the operators; instead of round brackets, square brackets are often used.

### statistics

symbol use interpretation items Latex HTML Unicode
${\ displaystyle {\ tilde {~}}}$ ${\ displaystyle {\ tilde {x}}}$ Median of the values ${\ displaystyle x_ {1}, \ ldots, x_ {n}}$ Median \tilde U+0303
${\ displaystyle {\ bar {~}}}$ ${\ displaystyle {\ bar {X}}}$ Sample mean of the random variable ${\ displaystyle X_ {1}, \ ldots, X_ {n}}$ Average \bar U+0305
${\ displaystyle {\ bar {~}}}$ ${\ displaystyle {\ bar {x}}}$ Mean of the values ${\ displaystyle x_ {1}, \ ldots, x_ {n}}$ Average \bar U+0305
${\ displaystyle \ langle ~~ \ rangle}$ ${\ displaystyle \ langle f \ rangle}$ Mean of all values ​​of a function (in physics) ${\ displaystyle f}$ \langle \rangle &lang; &rang; U+27E8/9
${\ displaystyle {\ hat {~}}}$ ${\ displaystyle {\ hat {p}}}$ Estimated value for the parameter ${\ displaystyle p}$ Estimator \hat U+0302

## logic

### Definition sign

symbol use interpretation items Latex HTML Unicode
${\ displaystyle:}$ ${\ displaystyle A: = B}$ ${\ displaystyle A}$is set equal by definition${\ displaystyle B}$ definition : U+003A
${\ displaystyle A: \ Leftrightarrow B}$ ${\ displaystyle A}$is set equivalent to by definition${\ displaystyle B}$

### Junctures

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ land}$ ${\ displaystyle A \ land B}$ Statement and statement${\ displaystyle A}$${\ displaystyle B}$ Conjunction (logic) \land &and; U+2227
${\ displaystyle \ lor}$ ${\ displaystyle A \ lor B}$ Statement or statement (or both) ${\ displaystyle A}$${\ displaystyle B}$ Disjunction \lor &or; U+2228
${\ displaystyle \ Leftrightarrow}$ ${\ displaystyle A \ Leftrightarrow B}$ Statement follows from statement and vice versa ${\ displaystyle A}$${\ displaystyle B}$ Logical equivalence \Leftrightarrow &hArr; U+21D4
${\ displaystyle \ leftrightarrow}$ ${\ displaystyle A \ leftrightarrow B}$ \leftrightarrow &harr; U+2194
${\ displaystyle \ Rightarrow}$ ${\ displaystyle A \ Rightarrow B}$ statement follows statement${\ displaystyle A}$${\ displaystyle B}$ implication \Rightarrow &rArr; U+21D2
${\ displaystyle \ rightarrow}$ ${\ displaystyle A \ rightarrow B}$ \rightarrow &rarr; U+2192
${\ displaystyle \ nsim}$ ${\ displaystyle A \ nsim B}$ either statement or statement${\ displaystyle A}$${\ displaystyle B}$ Contravalence / antivalence \nsim &nsim; U+2241
${\ displaystyle \ oplus}$ ${\ displaystyle A \ oplus B}$ \oplus &oplus; U+2295
${\ displaystyle \ veebar}$ ${\ displaystyle A \, \ veebar \, B}$ \veebar U+22BB
${\ displaystyle {\ dot {\ lor}}}$ ${\ displaystyle A \, {\ dot {\ lor}} \, B}$ \dot\lor U+2A52
${\ displaystyle \ nleftrightarrow}$ ${\ displaystyle A \ nleftrightarrow B}$ \nleftrightarrow U+21AE
${\ displaystyle \ nLeftrightarrow}$ ${\ displaystyle A \ nLeftrightarrow B}$ \nLeftrightarrow U+21CE
${\ displaystyle \ lnot}$ ${\ displaystyle \ lnot A}$ not statement ${\ displaystyle A}$ negation \lnot &not; U+00AC
${\ displaystyle {\ overline {~~}}}$ ${\ displaystyle {\ overline {A}}}$ \bar U+0305

### Quantifiers

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ forall}$ ${\ displaystyle \ forall \, x}$ for all elements ${\ displaystyle x}$ Universal quantifier \forall &forall; U+2200
${\ displaystyle \ bigwedge}$ ${\ displaystyle \ bigwedge _ {x}}$ \bigwedge U+22C0
${\ displaystyle \ exists}$ ${\ displaystyle \ exists \, x}$ there is at least one element ${\ displaystyle x}$ Existential quantifier \exists &exist; U+2203
${\ displaystyle \ bigvee}$ ${\ displaystyle \ bigvee _ {x}}$ \bigvee U+22C1
${\ displaystyle \ exists!}$ ${\ displaystyle \ exists! \, x}$ there is exactly one element ${\ displaystyle x}$ Number quantifier \exists! &exist; U+2203
${\ displaystyle \ bigvee ^ {\ centerdot}}$ ${\ displaystyle \ bigvee _ {x} ^ {\ centerdot}}$ \dot\bigvee U+2A52
${\ displaystyle \ nexists}$ ${\ displaystyle \ nexists \, x}$ there is no element ${\ displaystyle x}$ Existential quantifier \nexists U+2204

### Deduction sign

symbol use interpretation items Latex HTML Unicode
${\ displaystyle \ vdash}$ ${\ displaystyle A \ vdash B}$ Statement is syntactically from statement derivable ${\ displaystyle B}$${\ displaystyle A}$ Derivability relation \vdash U+22A2
${\ displaystyle \ models}$ ${\ displaystyle A \ models B}$ Statement follows semantically from statement${\ displaystyle B}$${\ displaystyle A}$ conclusion \models, \vDash &DoubleRightTee; U+22A8
${\ displaystyle \ models A}$ The statement is generally valid ${\ displaystyle A}$ Tautology (logic)
${\ displaystyle \ top}$ ${\ displaystyle A \ top}$ \top &perp; U+22A4
${\ displaystyle \ bot}$ ${\ displaystyle A \ bot}$ Statement is contradicting itself ${\ displaystyle A}$ Contradiction \bot U+22A5
${\ displaystyle \ therefore}$ ${\ displaystyle A \ therefore B}$ Statement is true, therefore statement is also true ${\ displaystyle A}$${\ displaystyle B}$ Derivation (logic) \therefore U+2234
${\ displaystyle \ because}$ ${\ displaystyle A \ because B}$ Statement is true, because statement is also true ${\ displaystyle A}$${\ displaystyle B}$ \because U+2235
Contradiction Proof of contradiction \lightning U+21AF
${\ displaystyle \ blacksquare}$ End of proof quod erat demonstrandum \blacksquare U+220E
${\ displaystyle \ Box}$ \Box U+25A1