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List of mathematical symbols
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List of mathematical symbols
please note:
- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
{{Expand list|date=March 2010}}This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.A mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations, a different convention may be used. For example, depending on context, the triple bar "{{math|â‰¡}}" may represent congruence or a definition. However, in mathematical logic, numerical equality is sometimes represented by "{{math|â‰¡}}" instead of "{{math|{{=}}}}", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning.Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and typeset as an image using TeX.- the content below is remote from Wikipedia
- it has been imported raw for GetWiki
Guide
This list is organized by symbol type and is intended to facilitate finding an unfamiliar symbol by its visual appearance. For a related list organized by mathematical topic, see List of mathematical symbols by subject. That list also includes LaTeX and HTML markup, and Unicode code points for each symbol (note that this article doesn't have the latter two, but they could certainly be added).There is a Wikibooks guide for using maths in LaTeX,WEB, LaTeX/Mathematics,weblink Wikibooks, 18 November 2017, and a comprehensive LaTeX symbol list. It is also possible to check to see if a Unicode code point is available as a LaTeX command, or vice versa.WEB, Cook, John, Unicode / LaTeX conversion,weblink John Cook Consulting, 18 November 2017, Also note that where there is no LaTeX command natively available for a particular symbol (although there may be options that require adding packages), the symbol could be added via other options, such as setting the document up to support Unicode,WEB, LaTeX/Special Characters,weblink Wikibooks, 18 November 2017, and entering the character in a variety of ways (e.g. copying and pasting, keyboard shortcuts, the unicode{} commandWEB, unicode - Tex Command,weblink TutorialsBay, 18 November 2017, ) as well as other optionsWEB, Unicode characters in pdflatex output using hexcode without UTF-8 input,weblink Tex Stack Exchange, 18 November 2017, and extensive additional information.WEB, fontenc vs inputenc,weblink TeX Stack Exchange, 18 November 2017, WEB, pdflatex crashes when Latex code includes unicode{f818} and unicode{f817} and how to handle it,weblink TeX Stack Exchange, 18 November 2017,- Basic symbols: Symbols widely used in mathematics, roughly through first-year calculus. More advanced meanings are included with some symbols listed here.
- Symbols based on equality "{{math|{{=}}}}": Symbols derived from or similar to the equal sign, including double-headed arrows. Not surprisingly these symbols are often associated with an equivalence relation.
- Symbols that point left or right: Symbols, such as {{math|}}, that appear to point to one side or another.
- Brackets: Symbols that are placed on either side of a variable or expression, such as {{math|{{abs|x}}}}.
- Other non-letter symbols: Symbols that do not fall in any of the other categories.
- Letter-based symbols: Many mathematical symbols are based on, or closely resemble, a letter in some alphabet. This section includes such symbols, including symbols that resemble upside-down letters. Many letters have conventional meanings in various branches of mathematics and physics. These are not listed here. The See also section, below, has several lists of such usages.
- Letter modifiers: Symbols that can be placed on or next to any letter to modify the letter's meaning.
- Symbols based on Latin letters, including those symbols that resemble or contain an {{math|X}}
- Symbols based on Hebrew or Greek letters e.g. {{math| ×‘ ,×, Î´, Î”, Ï€, Î , Ïƒ, Î£, Î¦. }} Note: symbols resembling {{math|Î›}} are grouped with "{{math|V}}" under Latin letters.
- Variations: Usage in languages written right-to-left
Basic symbols{| class"wikitable" style"margin:auto; width:100%; border:1px"
! rowspan="3" style="font-size:130%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples ! Read as
| symbol = {{math|+{edih}
| tex = +
| rowspan = 2
| name = addition
| readas = plus;add
| category = arithmetic
| explain = {{math|2 + 7}} means the sum of {{math|2}} and {{math|7}}.
| examples = {{math|2 + 7 {{=}} 9}}
}}{{row of table of mathematical symbols
| tex = +
| rowspan = 2
| name = addition
| readas = plus;add
| category = arithmetic
| explain = {{math|2 + 7}} means the sum of {{math|2}} and {{math|7}}.
| examples = {{math|2 + 7 {{=}} 9}}
| name = disjoint union
| readas = the disjoint union of ... and ...
| category = set theory
| explain = {{math|A1 + A2}} means the disjoint union of sets {{math|A1}} and {{math|A2}}.
| examples = {{math|A1 {{=}} {3, 4, 5, 6} âˆ§ A2 {{=}} {7, 8, 9, 10} â‡’A1 + A2 {{=}} {(3, 1), (4, 1), (5, 1), (6, 1), (7, 2), (8, 2), (9, 2), (10, 2)}}}
}}{hide}row of table of mathematical symbols
| readas = the disjoint union of ... and ...
| category = set theory
| explain = {{math|A1 + A2}} means the disjoint union of sets {{math|A1}} and {{math|A2}}.
| examples = {{math|A1 {{=}} {3, 4, 5, 6} âˆ§ A2 {{=}} {7, 8, 9, 10} â‡’A1 + A2 {{=}} {(3, 1), (4, 1), (5, 1), (6, 1), (7, 2), (8, 2), (9, 2), (10, 2)}}}
| symbol = {{math|âˆ’{edih}
| tex = -
| rowspan = 3
| name = subtraction
| readas = minus;take;subtract
| category = arithmetic
| explain = {{math|36 âˆ’ 11}} means the subtraction of {{math|11}} from {{math|36}}.
| examples = {{math|36 âˆ’ 11 {{=}} 25}}
}}{hide}row of table of mathematical symbols
| tex = -
| rowspan = 3
| name = subtraction
| readas = minus;take;subtract
| category = arithmetic
| explain = {{math|36 âˆ’ 11}} means the subtraction of {{math|11}} from {{math|36}}.
| examples = {{math|36 âˆ’ 11 {{=}} 25}}
| name = negative sign
| readas = negative;minus;the opposite of
| category = arithmetic
| explain = {{math|âˆ’3{edih} means the additive inverse of the number {{math|3}}.
| examples = {{math|âˆ’(âˆ’5) {{=}} 5}}
}}{hide}row of table of mathematical symbols
| readas = negative;minus;the opposite of
| category = arithmetic
| explain = {{math|âˆ’3{edih} means the additive inverse of the number {{math|3}}.
| examples = {{math|âˆ’(âˆ’5) {{=}} 5}}
| name = set-theoretic complement
| readas = minus;without
| category = set theory
| explain = {{math|A âˆ’ B{edih} means the set that contains all the elements of {{math|A}} that are not in {{math|B}}.({{math|âˆ–}} can also be used for set-theoretic complement as described below.)
| examples = {{math|{1, 2, 4} âˆ’ {1, 3, 4} {{=}} {2}}}
}}{hide}row of table of mathematical symbols
| readas = minus;without
| category = set theory
| explain = {{math|A âˆ’ B{edih} means the set that contains all the elements of {{math|A}} that are not in {{math|B}}.({{math|âˆ–}} can also be used for set-theoretic complement as described below.)
| examples = {{math|{1, 2, 4} âˆ’ {1, 3, 4} {{=}} {2}}}
| symbol = {{math|Â±{edih}
| tex = pmpm
| rowspan = 2
| name = plus-minus
| readas = plus or minus
| category = arithmetic
| explain = {{math|6 Â± 3}} means both {{math|6 + 3}} and {{math|6 âˆ’ 3}}.
| examples = The equation {{math|x {{=}} 5 Â± {{sqrt|4}}}}, has two solutions, {{math|x {{=}} 7}} and {{math|x {{=}} 3}}.
}}{hide}row of table of mathematical symbols
| tex = pmpm
| rowspan = 2
| name = plus-minus
| readas = plus or minus
| category = arithmetic
| explain = {{math|6 Â± 3}} means both {{math|6 + 3}} and {{math|6 âˆ’ 3}}.
| examples = The equation {{math|x {{=}} 5 Â± {{sqrt|4}}}}, has two solutions, {{math|x {{=}} 7}} and {{math|x {{=}} 3}}.
| name = plus-minus
| readas = plus or minus
| category = measurement
| explain = {{math|10 Â± 2{edih} or equivalently {{math|10 Â± 20%}} means the range from {{math|10 âˆ’ 2}} to {{math|10 + 2}}.
| examples = If {{math|a {{=}} 100 Â± 1 mm}}, then {{math|a â‰¥ 99 mm and a â‰¤ 101 mm}}.
}}{hide}row of table of mathematical symbols
| readas = plus or minus
| category = measurement
| explain = {{math|10 Â± 2{edih} or equivalently {{math|10 Â± 20%}} means the range from {{math|10 âˆ’ 2}} to {{math|10 + 2}}.
| examples = If {{math|a {{=}} 100 Â± 1 mm}}, then {{math|a â‰¥ 99 mm and a â‰¤ 101 mm}}.
| symbol = {{math|âˆ“{edih}
| tex = mpmp
| rowspan = 1
| name = minus-plus
| readas = minus or plus
| category = arithmetic
| explain = {{math|6 Â± (3 âˆ“ 5)}} means {{math|6 + (3 âˆ’ 5)}} and {{math|6 âˆ’ (3 + 5)}}.
| examples = {{math|cos(x Â± y) {{=}} cos(x) cos(y) âˆ“ sin(x) sin(y).}}
}}{hide}row of table of mathematical symbols
| tex = mpmp
| rowspan = 1
| name = minus-plus
| readas = minus or plus
| category = arithmetic
| explain = {{math|6 Â± (3 âˆ“ 5)}} means {{math|6 + (3 âˆ’ 5)}} and {{math|6 âˆ’ (3 + 5)}}.
| examples = {{math|cos(x Â± y) {{=}} cos(x) cos(y) âˆ“ sin(x) sin(y).}}
| symbol = {{math|Ã—{edih}{{math|â‹…}}{{math|Â·}}
| tex = timestimescdotcdot
| rowspan = 4
| name = multiplication
| readas = times;multiplied by
| category = arithmetic
| explain = {{math|3 Ã— 4}} or {{math|3 â‹… 4}} means the multiplication of {{math|3}} by {{math|4}}.
| examples = {{math|7 â‹… 8 {{=}} 56}}
}}{hide}row of table of mathematical symbols
| tex = timestimescdotcdot
| rowspan = 4
| name = multiplication
| readas = times;multiplied by
| category = arithmetic
| explain = {{math|3 Ã— 4}} or {{math|3 â‹… 4}} means the multiplication of {{math|3}} by {{math|4}}.
| examples = {{math|7 â‹… 8 {{=}} 56}}
| name = dot product scalar product
| readas = dot
| category = linear algebra vector algebra
| explain = {{math|u â‹… v{edih} means the dot product of vectors {{math|u}} and {{math|v}}
| examples = {{math|(1, 2, 5) â‹… (3, 4, âˆ’1) {{=}} 6}}
}}{hide}row of table of mathematical symbols
| readas = dot
| category = linear algebra vector algebra
| explain = {{math|u â‹… v{edih} means the dot product of vectors {{math|u}} and {{math|v}}
| examples = {{math|(1, 2, 5) â‹… (3, 4, âˆ’1) {{=}} 6}}
| name = cross product vector product
| readas = cross
| category = linear algebra vector algebra
| explain = {{math|u Ã— v{edih} means the cross product of vectors {{math|u}} and {{math|v}}
| examples = {{math|(1, 2, 5) Ã— (3, 4, âˆ’1) {{=}} {{aligned table|cols=3|col1width=20px|col2width=20px|col3width=20px
|style=display: inline-table; vertical-align: middle; text-align: center; padding: 0px; margin: 0px; border-left: 1px solid black; border-right: 1px solid black
|{{math|i}} | {{math|j}} | {{math|k}}
|1 | 2 | 5
|3 | 4 | âˆ’1
}}{{=}} (âˆ’22, 16, âˆ’2)}}
}}{hide}row of table of mathematical symbols
| readas = cross
| category = linear algebra vector algebra
| explain = {{math|u Ã— v{edih} means the cross product of vectors {{math|u}} and {{math|v}}
| examples = {{math|(1, 2, 5) Ã— (3, 4, âˆ’1) {{=}} {{aligned table|cols=3|col1width=20px|col2width=20px|col3width=20px
|style=display: inline-table; vertical-align: middle; text-align: center; padding: 0px; margin: 0px; border-left: 1px solid black; border-right: 1px solid black
|{{math|i}} | {{math|j}} | {{math|k}}
|1 | 2 | 5
|3 | 4 | âˆ’1
}}{{=}} (âˆ’22, 16, âˆ’2)}}
| name = placeholder
| readas = (silent)
| category = functional analysis
| explain = A {{math|Â·{edih} means a placeholder for an argument of a function. Indicates the functional nature of an expression without assigning a specific symbol for an argument.
| examples = {{math|{{abs|}}}}
}}{hide}row of table of mathematical symbols
| readas = (silent)
| category = functional analysis
| explain = A {{math|Â·{edih} means a placeholder for an argument of a function. Indicates the functional nature of an expression without assigning a specific symbol for an argument.
| examples = {{math|{{abs|}}}}
| symbol = {{math|Ã·{edih}{{math|â„}}
| tex = divdiv/
| rowspan = 3
| name = division (Obelus)
| readas = divided by;over
| category = arithmetic
| explain = {{math|6 Ã· 3}} or {{math|6 â„ 3}} means the division of {{math|6}} by {{math|3}}.
| examples = {{math|2 Ã· 4 {{=}} 0.5}}{{math|12 â„ 4 {{=}} 3}}
}}{hide}row of table of mathematical symbols
| tex = divdiv/
| rowspan = 3
| name = division (Obelus)
| readas = divided by;over
| category = arithmetic
| explain = {{math|6 Ã· 3}} or {{math|6 â„ 3}} means the division of {{math|6}} by {{math|3}}.
| examples = {{math|2 Ã· 4 {{=}} 0.5}}{{math|12 â„ 4 {{=}} 3}}
| name = quotient group
| readas = mod
| category = group theory
| explain = {{math|G / H{edih} means the quotient of group {{math|G}} modulo its subgroup {{math|H}}.
| examples = {{math|{0, a, 2a, b, b + a, b + 2a} / {0, b} {{=}} {{0, b}, {a, b + a}, {2a, b + 2a}}}}
}}{hide}row of table of mathematical symbols
| readas = mod
| category = group theory
| explain = {{math|G / H{edih} means the quotient of group {{math|G}} modulo its subgroup {{math|H}}.
| examples = {{math|{0, a, 2a, b, b + a, b + 2a} / {0, b} {{=}} {{0, b}, {a, b + a}, {2a, b + 2a}}}}
| name = quotient set
| readas = mod
| category = set theory
| explain = {{math|A/~{edih} means the set of all {{math|~}} equivalence classes in {{math|A}}.
| examples = If we define {{math|~}} by {{math|x ~ y â‡” x âˆ’ y âˆˆ â„¤}}, then {{math|â„/~ {{=}} {x + n : n âˆˆ â„¤, x âˆˆ [0,1)}}}.
}}{hide}row of table of mathematical symbols
| readas = mod
| category = set theory
| explain = {{math|A/~{edih} means the set of all {{math|~}} equivalence classes in {{math|A}}.
| examples = If we define {{math|~}} by {{math|x ~ y â‡” x âˆ’ y âˆˆ â„¤}}, then {{math|â„/~ {{=}} {x + n : n âˆˆ â„¤, x âˆˆ [0,1)}}}.
| symbol = {{math|âˆš{edih}
| tex = surdsurdsqrt{x}sqrt{x}
| rowspan = 2
| name = square root (radical symbol)
| readas = the (principal) square root of
| category = real numbers
| explain = {{math|{{sqrt|x}}}} means the nonnegative number whose square is{{nbsp}}{{math|x}}.
| examples = {{math|{{sqrt|4}} {{=}} 2}}
}}{hide}row of table of mathematical symbols
| tex = surdsurdsqrt{x}sqrt{x}
| rowspan = 2
| name = square root (radical symbol)
| readas = the (principal) square root of
| category = real numbers
| explain = {{math|{{sqrt|x}}}} means the nonnegative number whose square is{{nbsp}}{{math|x}}.
| examples = {{math|{{sqrt|4}} {{=}} 2}}
| name = complex square root
| readas = the (complex) square root of
| category = complex numbers
| explain = If {{math|z {{={edih} r exp(iÏ†)}} is represented in polar coordinates with {{math|âˆ’Ï€ < Ï† â‰¤ Ï€}}, then {{math|{{sqrt|z}} {{=}} {{sqrt|r}} exp(iÏ†/2)}}.
| examples = {{math|{{sqrt|âˆ’1}} {{=}} i}}
}}{hide}row of table of mathematical symbols
| readas = the (complex) square root of
| category = complex numbers
| explain = If {{math|z {{={edih} r exp(iÏ†)}} is represented in polar coordinates with {{math|âˆ’Ï€ < Ï† â‰¤ Ï€}}, then {{math|{{sqrt|z}} {{=}} {{sqrt|r}} exp(iÏ†/2)}}.
| examples = {{math|{{sqrt|âˆ’1}} {{=}} i}}
| symbol = {{math|âˆ‘{edih}
| tex = sumsum
| rowspan = 1
| name = summation
| readas = sum over ... from ... to ... of
| category = calculus
| explain = sum_{k=1}^{n}{a_k} means a_1 + a_2 + cdots + a_n.
| examples = sum_{k=1}^{4}{k^2} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30
}}{hide}row of table of mathematical symbols
| tex = sumsum
| rowspan = 1
| name = summation
| readas = sum over ... from ... to ... of
| category = calculus
| explain = sum_{k=1}^{n}{a_k} means a_1 + a_2 + cdots + a_n.
| examples = sum_{k=1}^{4}{k^2} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30
| symbol = {{math|{{intmath{edih}}}
| tex = intint
| rowspan = 3
| name = indefinite integral or antiderivative
| readas = indefinite integral of- OR -the antiderivative of
| category = calculus
| tex = intint
| rowspan = 3
| name = indefinite integral or antiderivative
| readas = indefinite integral of- OR -the antiderivative of
| category = calculus
| explain = {{math|{{intmath}} f(x) dx}} means a function whose derivative is {{mvar|f}}.
| examples = int x^2 dx = frac{x^3}3 +C
}}{{row of table of mathematical symbols
| examples = int x^2 dx = frac{x^3}3 +C
| name = definite integral
| readas = integral from ... to ... of ... with respect to
| category = calculus
| explain = {{math|{{intmath||a|b}} f(x) dx}} means the signed area between the {{mvar|x}}-axis and the graph of the function {{mvar|f}} between {{math|x {{=}} a}} and {{math|x {{=}} b}}.
| examples = {{math|{{intmath||a|b}} x2 dx {{=}} {{sfrac|b3 âˆ’ a3|3}}}}
}}{{row of table of mathematical symbols
| readas = integral from ... to ... of ... with respect to
| category = calculus
| explain = {{math|{{intmath||a|b}} f(x) dx}} means the signed area between the {{mvar|x}}-axis and the graph of the function {{mvar|f}} between {{math|x {{=}} a}} and {{math|x {{=}} b}}.
| examples = {{math|{{intmath||a|b}} x2 dx {{=}} {{sfrac|b3 âˆ’ a3|3}}}}
| name = line integral
| readas = line/ path/ curve/ integral of ... along ...
| category = calculus
| explain = {{math|{{intmath||C}} f ds}} means the integral of {{mvar|f}} along the curve {{mvar|C}}, {{math|{{intmath||a|b}} f(r(t)) {{abs|r'(t)}} dt}}, where {{math|r}} is a parametrization of {{mvar|C}}. (If the curve is closed, the symbol {{math|{{intmath|oint}}}} may be used instead, as described below.)
| examples =
}}{hide}row of table of mathematical symbols
| readas = line/ path/ curve/ integral of ... along ...
| category = calculus
| explain = {{math|{{intmath||C}} f ds}} means the integral of {{mvar|f}} along the curve {{mvar|C}}, {{math|{{intmath||a|b}} f(r(t)) {{abs|r'(t)}} dt}}, where {{math|r}} is a parametrization of {{mvar|C}}. (If the curve is closed, the symbol {{math|{{intmath|oint}}}} may be used instead, as described below.)
| examples =
| symbol = {{math|{{intmath|oint{edih}}}
| tex = ointoint
| rowspan = 1
| name = Contour integral;closed line integral
| readas = contour integral of
| category = calculus
| explain = Similar to the integral, but used to denote a single integration over a closed curve or loop. It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface. Instances where the latter requires simultaneous double integration, the symbol {{math|{{intmath|oiint}}}} would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol {{math|{{intmath|oiiint}}}}.
The contour integral can also frequently be found with a subscript capital letter C, {{math|{{intmath|oint}}'C}}, denoting that a closed loop integral is, in fact, around a contour {{mvar|C}}, or sometimes dually appropriately, a circle {{mvar|C}}. In representations of Gauss's Law, a subscript capital S, {{math|{{intmath|oint}}'S}}, is used to denote that the integration is over a closed surface.
| tex = ointoint
| rowspan = 1
| name = Contour integral;closed line integral
| readas = contour integral of
| category = calculus
| explain = Similar to the integral, but used to denote a single integration over a closed curve or loop. It is sometimes used in physics texts involving equations regarding Gauss's Law, and while these formulas involve a closed surface integral, the representations describe only the first integration of the volume over the enclosing surface. Instances where the latter requires simultaneous double integration, the symbol {{math|{{intmath|oiint}}}} would be more appropriate. A third related symbol is the closed volume integral, denoted by the symbol {{math|{{intmath|oiiint}}}}.
| examples = If {{mvar|C}} is a Jordan curve about 0, then {{math|{{intmath|oint}}C {{sfrac|1|z}} dz {{=}} 2Ï€i}}.
}}{hide}row of table of mathematical symbols
| symbol = {{math|â€¦â‹¯â‹®â‹°â‹±{edih}
| tex = ldotsldotscdotscdotsvdotsvdotsddotsddots
| rowspan = 1
| name = ellipsis
| readas = and so forth
| category = everywhere
| explain = Indicates omitted values from a pattern.
| examples = 1/2 + 1/4 + 1/8 + 1/16 + â‹¯ = 1
}}{hide}row of table of mathematical symbols
| tex = ldotsldotscdotscdotsvdotsvdotsddotsddots
| rowspan = 1
| name = ellipsis
| readas = and so forth
| category = everywhere
| explain = Indicates omitted values from a pattern.
| examples = 1/2 + 1/4 + 1/8 + 1/16 + â‹¯ = 1
| symbol = {{math|âˆ´{edih}
| tex = thereforetherefore
| rowspan = 1
| name = therefore
| readas = therefore;so;hence
| category = everywhere
| explain = Sometimes used in proofs before logical consequences.
| examples = All humans are mortal. Socrates is a human. âˆ´ Socrates is mortal.
}}{hide}row of table of mathematical symbols
| tex = thereforetherefore
| rowspan = 1
| name = therefore
| readas = therefore;so;hence
| category = everywhere
| explain = Sometimes used in proofs before logical consequences.
| examples = All humans are mortal. Socrates is a human. âˆ´ Socrates is mortal.
| symbol = {{math|âˆµ{edih}
| tex = becausebecause
| rowspan = 1
| name = (wikt:because|because)
| readas = because;since
| category = everywhere
| explain = Sometimes used in proofs before reasoning.
| examples = 11 is prime âˆµ it has no positive integer factors other than itself and one.
}}{hide}row of table of mathematical symbols
| tex = becausebecause
| rowspan = 1
| name = (wikt:because|because)
| readas = because;since
| category = everywhere
| explain = Sometimes used in proofs before reasoning.
| examples = 11 is prime âˆµ it has no positive integer factors other than itself and one.
| name = factorial
| symbol = {{math|!{edih}
| tex = !
| rowspan = 2
| readas = factorial
| category = combinatorics
| explain = n! means the product 1 times 2 times cdots times n.
| examples = 4! = 1times2times3times4 = 24
}}{{row of table of mathematical symbols
| symbol = {{math|!{edih}
| tex = !
| rowspan = 2
| readas = factorial
| category = combinatorics
| explain = n! means the product 1 times 2 times cdots times n.
| examples = 4! = 1times2times3times4 = 24
| name = logical negation
| readas = not
| category = propositional logic
| explain = The statement !A is true if and only if A is false.A slash placed through another operator is the same as "!" placed in front.(The symbol ! is primarily from computer science. It is avoided in mathematical texts, where the notation Â¬A is preferred.)
| examples = !(!A) â‡” A x â‰ y â‡” !(x = y)
}}{hide}row of table of mathematical symbols
| readas = not
| category = propositional logic
| explain = The statement !A is true if and only if A is false.A slash placed through another operator is the same as "!" placed in front.(The symbol ! is primarily from computer science. It is avoided in mathematical texts, where the notation Â¬A is preferred.)
| examples = !(!A) â‡” A x â‰ y â‡” !(x = y)
| symbol = {{math|Â¬{edih}{{math|Ëœ}}
| tex = negnegsim
| rowspan = 1
| name = logical negation
| readas = not
| category = propositional logic
| explain = The statement Â¬A is true if and only if A is false.A slash placed through another operator is the same as "Â¬" placed in front.(The symbol ~ has many other uses, so Â¬ or the slash notation is preferred. Computer scientists will often use ! but this is avoided in mathematical texts.)
| examples = Â¬(Â¬A) â‡” A x â‰ y â‡” Â¬(x = y)
}}{hide}row of table of mathematical symbols
| tex = negnegsim
| rowspan = 1
| name = logical negation
| readas = not
| category = propositional logic
| explain = The statement Â¬A is true if and only if A is false.A slash placed through another operator is the same as "Â¬" placed in front.(The symbol ~ has many other uses, so Â¬ or the slash notation is preferred. Computer scientists will often use ! but this is avoided in mathematical texts.)
| examples = Â¬(Â¬A) â‡” A x â‰ y â‡” Â¬(x = y)
| symbol = {{math|âˆ{edih}
| tex = proptopropto
| rowspan = 1
| name = proportionality
| readas = is proportional to;varies as
| category = everywhere
| explain = y âˆ x means that y = kx for some constant k.
| examples = if y = 2x, then y âˆ x.
}}{hide}row of table of mathematical symbols
| tex = proptopropto
| rowspan = 1
| name = proportionality
| readas = is proportional to;varies as
| category = everywhere
| explain = y âˆ x means that y = kx for some constant k.
| examples = if y = 2x, then y âˆ x.
| symbol = {{math|âˆž{edih}
| tex = inftyinfty
| rowspan = 1
| name = infinity
| readas = infinity
| category = numbers
| explain = âˆž is an element of the extended number line that is greater than all real numbers; it often occurs in limits.
| examples = lim_{xto 0} frac{1}{|x|} = infty
}}{hide}row of table of mathematical symbols
| tex = inftyinfty
| rowspan = 1
| name = infinity
| readas = infinity
| category = numbers
| explain = âˆž is an element of the extended number line that is greater than all real numbers; it often occurs in limits.
| examples = lim_{xto 0} frac{1}{|x|} = infty
| symbol = {{math|â– â–¡âˆŽâ–®â€£{edih}
| tex = blacksquareblacksquareBoxBoxblacktrianglerightblacktriangleright
| rowspan = 1
| name = end of proof
| readas = QED;tombstone;Halmos finality symbol
| category = everywhere
| explain = Used to mark the end of a proof.(May also be written Q.E.D.)| examples =
}}| tex = blacksquareblacksquareBoxBoxblacktrianglerightblacktriangleright
| rowspan = 1
| name = end of proof
| readas = QED;tombstone;Halmos finality symbol
| category = everywhere
| explain = Used to mark the end of a proof.(May also be written Q.E.D.)| examples =
Symbols based on equality{| class"wikitable" style"margin:auto; width:100%; border:1px"
! rowspan="3" style="font-size:130%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples! Read as
| symbol = {{math|{{={edih}}}
| tex = =
| rowspan = 1
| name = equality
| readas = is equal to;equals
| category = everywhere
| explain = x = y means x and y represent the same thing or value.|examples = 2 = 21 + 1 = 236 - 5 = 31
}}{hide}row of table of mathematical symbols
| tex = =
| rowspan = 1
| name = equality
| readas = is equal to;equals
| category = everywhere
| explain = x = y means x and y represent the same thing or value.|examples = 2 = 21 + 1 = 236 - 5 = 31
| symbol = {{math|â‰ {edih}
| tex = nene
| rowspan = 1
| name = inequality
| readas = is not equal to;does not equal
| category = everywhere
| explain = x ne y means that x and y do not represent the same thing or value.(The forms !=, /= or are generally used in programming languages where ease of typing and use of ASCII text is preferred.)
| examples = 2 + 2 ne 536 - 5 ne 30
}}{hide}row of table of mathematical symbols
| tex = nene
| rowspan = 1
| name = inequality
| readas = is not equal to;does not equal
| category = everywhere
| explain = x ne y means that x and y do not represent the same thing or value.(The forms !=, /= or are generally used in programming languages where ease of typing and use of ASCII text is preferred.)
| examples = 2 + 2 ne 536 - 5 ne 30
| symbol = {{math|â‰ˆ{edih}
| tex = approxapprox
| rowspan = 2
| name = approximately equal
| readas = is approximately equal to
| category = everywhere
| explain = x â‰ˆ y means x is approximately equal to y.This may also be written â‰ƒ, â‰…, ~, â™Ž (Libra Symbol), or â‰’.
| examples = Ï€ â‰ˆ 3.14159
}}{{row of table of mathematical symbols
| tex = approxapprox
| rowspan = 2
| name = approximately equal
| readas = is approximately equal to
| category = everywhere
| explain = x â‰ˆ y means x is approximately equal to y.This may also be written â‰ƒ, â‰…, ~, â™Ž (Libra Symbol), or â‰’.
| examples = Ï€ â‰ˆ 3.14159
| name = isomorphism
| readas = is isomorphic to
| category = group theory
| explain = G â‰ˆ H means that group G is isomorphic (structurally identical) to group H.(â‰… can also be used for isomorphic, as described below.)
| examples = Q8 / C2 â‰ˆ V
}}{hide}row of table of mathematical symbols
| readas = is isomorphic to
| category = group theory
| explain = G â‰ˆ H means that group G is isomorphic (structurally identical) to group H.(â‰… can also be used for isomorphic, as described below.)
| examples = Q8 / C2 â‰ˆ V
| symbol = {{math|~{edih}
| tex = sim sim
| rowspan = 6
| name = probability distribution
| readas = has distribution
| category = statistics
| explain = X ~ D, means the random variable X has the probability distribution D.
| examples = X ~ N(0,1), the standard normal distribution
}}{hide}row of table of mathematical symbols
| tex = sim sim
| rowspan = 6
| name = probability distribution
| readas = has distribution
| category = statistics
| explain = X ~ D, means the random variable X has the probability distribution D.
| examples = X ~ N(0,1), the standard normal distribution
| name = row equivalence
| readas = is row equivalent to
| category = matrix theory
| explain = A ~ B means that B can be generated by using a series of elementary row operations on A
| examples = begin{bmatrix}
1&2
2&4
end{bmatrix} sim begin{bmatrix}
| readas = is row equivalent to
| category = matrix theory
| explain = A ~ B means that B can be generated by using a series of elementary row operations on A
| examples = begin{bmatrix}
1&2
2&4
1&2
0&0
end{bmatrix{edih}}{{row of table of mathematical symbols
0&0
| name = same order of magnitude
| readas = roughly similar;poorly approximates;is on the order of
| category = approximation theory
| explain = m ~ n means the quantities m and n have the same order of magnitude, or general size. (Note that ~ is used for an approximation that is poor, otherwise use â‰ˆ .)
| examples = 2 ~ 58 Ã— 9 ~ 100but Ï€2 â‰ˆ 10
}}{{row of table of mathematical symbols
| readas = roughly similar;poorly approximates;is on the order of
| category = approximation theory
| explain = m ~ n means the quantities m and n have the same order of magnitude, or general size. (Note that ~ is used for an approximation that is poor, otherwise use â‰ˆ .)
| examples = 2 ~ 58 Ã— 9 ~ 100but Ï€2 â‰ˆ 10
| name = similarity
| readas = is similar toWEB,weblink Math is Fun website,
| category = geometry
| explain = â–³ABC ~ â–³DEF means triangle ABC is similar to (has the same shape) triangle DEF.
| examples =
}}{{row of table of mathematical symbols
| readas = is similar toWEB,weblink Math is Fun website,
| category = geometry
| explain = â–³ABC ~ â–³DEF means triangle ABC is similar to (has the same shape) triangle DEF.
| examples =
| name = asymptotically equivalent
| readas = is asymptotically equivalent to
| category = asymptotic analysis
| explain = f ~ g means lim_{ntoinfty} frac{f(n)}{g(n)} = 1.
| examples = x ~ x+1}}
{{row of table of mathematical symbols
| readas = is asymptotically equivalent to
| category = asymptotic analysis
| explain = f ~ g means lim_{ntoinfty} frac{f(n)}{g(n)} = 1.
| examples = x ~ x+1}}
| name = equivalence relation
| readas = are in the same equivalence class
| category = everywhere
| explain = a ~ b means b in [a] (and equivalently a in [b]).
| examples = 1 ~ 5 mod 4}}
{{anchor|readas is defined as}}{hide}row of table of mathematical symbols
| readas = are in the same equivalence class
| category = everywhere
| explain = a ~ b means b in [a] (and equivalently a in [b]).
| examples = 1 ~ 5 mod 4}}
| symbol = {{math|{{={edih}:}}{{math|:{{=}}}}{{math|â‰¡}}{{math|:â‡”}}{{math|â‰œ}}{{math|â‰}}{{math|â‰}}
| tex = =: := equiv equiv:Leftrightarrow :Leftrightarrow triangleq triangleqoverset{underset{mathrm{def}}{}}{=} overset{underset{mathrm{def}}{}}{=}doteq doteq
| rowspan = 1
| name = definition
| readas = is defined as;is equal by definition to
| category = everywhere
| explain = x := y, y =: x or x â‰¡ y means x is defined to be another name for y, under certain assumptions taken in context.(Some writers use â‰¡ to mean congruence).P â‡” Q means P is defined to be logically equivalent to Q.
| examples = cosh x := frac{e^x + e^{-x}}{2}[a,b]:= acdot b - b cdot a
}}{hide}row of table of mathematical symbols
| tex = =: := equiv equiv:Leftrightarrow :Leftrightarrow triangleq triangleqoverset{underset{mathrm{def}}{}}{=} overset{underset{mathrm{def}}{}}{=}doteq doteq
| rowspan = 1
| name = definition
| readas = is defined as;is equal by definition to
| category = everywhere
| explain = x := y, y =: x or x â‰¡ y means x is defined to be another name for y, under certain assumptions taken in context.(Some writers use â‰¡ to mean congruence).P â‡” Q means P is defined to be logically equivalent to Q.
| examples = cosh x := frac{e^x + e^{-x}}{2}[a,b]:= acdot b - b cdot a
| symbol = {{math|â‰…{edih}
| tex = cong cong
| rowspan = 2
| name = congruence
| readas = is congruent to
| category = geometry
| explain = â–³ABC â‰… â–³DEF means triangle ABC is congruent to (has the same measurements as) triangle DEF.
| examples =
}}{{row of table of mathematical symbols
| tex = cong cong
| rowspan = 2
| name = congruence
| readas = is congruent to
| category = geometry
| explain = â–³ABC â‰… â–³DEF means triangle ABC is congruent to (has the same measurements as) triangle DEF.
| examples =
| name = isomorphic
| readas = is isomorphic to
| category = abstract algebra
| explain = G â‰… H means that group G is isomorphic (structurally identical) to group H.(â‰ˆ can also be used for isomorphic, as described above.)
| examples = V â‰… C2 Ã— C2
}}{hide}row of table of mathematical symbols
| readas = is isomorphic to
| category = abstract algebra
| explain = G â‰… H means that group G is isomorphic (structurally identical) to group H.(â‰ˆ can also be used for isomorphic, as described above.)
| examples = V â‰… C2 Ã— C2
| symbol = {{math|â‰¡{edih}
| tex = equiv equiv
| rowspan = 1
| name = congruence relation
| readas = ... is congruent to ... modulo ...
| category = modular arithmetic
| explain = a â‰¡ b (mod n) means a âˆ’ b is divisible by n
| examples = 5 â‰¡ 2 (mod 3)
}}{hide}row of table of mathematical symbols
| tex = equiv equiv
| rowspan = 1
| name = congruence relation
| readas = ... is congruent to ... modulo ...
| category = modular arithmetic
| explain = a â‰¡ b (mod n) means a âˆ’ b is divisible by n
| examples = 5 â‰¡ 2 (mod 3)
| symbol = {{math|â‡”{edih}{{math|â†”}}
| tex = Leftrightarrow Leftrightarrow iffiffleftrightarrow leftrightarrow
| rowspan = 1
| name = material equivalence
| readas = if and only if;iff
| category = propositional logic
| explain = A â‡” B means A is true if B is true and A is false if B is false.
| examples = x + 5 = y + 2 â‡” x + 3 = y
}}{hide}row of table of mathematical symbols
| tex = Leftrightarrow Leftrightarrow iffiffleftrightarrow leftrightarrow
| rowspan = 1
| name = material equivalence
| readas = if and only if;iff
| category = propositional logic
| explain = A â‡” B means A is true if B is true and A is false if B is false.
| examples = x + 5 = y + 2 â‡” x + 3 = y
| symbol = {{math|:{{={edih}}}{{math|{{=}}:}}
| tex = :==:
| rowspan = 1
| name = Assignment
| readas = is defined to be
| category = everywhere
| explain = A := b means A is defined to have the value b.
| examples = Let a := 3, then... f(x) := x + 3
}}| tex = :==:
| rowspan = 1
| name = Assignment
| readas = is defined to be
| category = everywhere
| explain = A := b means A is defined to have the value b.
| examples = Let a := 3, then... f(x) := x + 3
Symbols that point left or right{| class"wikitable" style"margin:auto; width:100%; border:1px"
! rowspan="3" style="font-size:130%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples! Read as
| symbol = {{math|{edih}
| tex =
| rowspan = 2
| name = strict inequality
| readas = is less than,is greater than
| category = order theory
| explain = x < y means {{mvar|x}} is less than {{mvar|y}}.x > y means {{mvar|x}} is greater than {{mvar|y}}.
| examples = 3 < 4 5 > 4
}}{hide}row of table of mathematical symbols
| tex =
| rowspan = 2
| name = strict inequality
| readas = is less than,is greater than
| category = order theory
| explain = x < y means {{mvar|x}} is less than {{mvar|y}}.x > y means {{mvar|x}} is greater than {{mvar|y}}.
| examples = 3 < 4 5 > 4
| name = proper subgroup
| readas = is a proper subgroup of
| category = group theory
| explain = H < G means {{mvar|H{edih} is a proper subgroup of {{mvar|G}}.
| examples = 5mathrm{Z} < mathrm{Z} mathrm{A}_3 < mathrm{S}_3
}}{hide}row of table of mathematical symbols
| readas = is a proper subgroup of
| category = group theory
| explain = H < G means {{mvar|H{edih} is a proper subgroup of {{mvar|G}}.
| examples = 5mathrm{Z} < mathrm{Z} mathrm{A}_3 < mathrm{S}_3
| symbol = {{math|â‰ª{edih}{{math|â‰«}}
| tex = ll gg llgg
| rowspan = 3
| name = significant (strict) inequality
| readas = is much less than,is much greater than
| category = order theory
| explain = {{math|x â‰ª y}} means x is much less than y.{{math|x â‰« y}} means x is much greater than y.
| examples = {{math|0.003 â‰ª 1000000}}
}}{hide}row of table of mathematical symbols
| tex = ll gg llgg
| rowspan = 3
| name = significant (strict) inequality
| readas = is much less than,is much greater than
| category = order theory
| explain = {{math|x â‰ª y}} means x is much less than y.{{math|x â‰« y}} means x is much greater than y.
| examples = {{math|0.003 â‰ª 1000000}}
| name = asymptotic comparison
| readas = is of smaller order than,is of greater order than
| category = analytic number theory
| explain = {{math|f â‰ª g{edih} means the growth of f is asymptotically bounded by g.(This is I. M. Vinogradov's notation. Another notation is the Big O notation, which looks like {{math|1=f = O(g)}}.)
| examples = {{math|x â‰ª ex}}
}}{{row of table of mathematical symbols
| readas = is of smaller order than,is of greater order than
| category = analytic number theory
| explain = {{math|f â‰ª g{edih} means the growth of f is asymptotically bounded by g.(This is I. M. Vinogradov's notation. Another notation is the Big O notation, which looks like {{math|1=f = O(g)}}.)
| examples = {{math|x â‰ª ex}}
| name = absolute continuity
| readas = is absolutely continuous with respect to
| category = measure theory
| explain = mullnu means that mu is absolutely continuous with respect to nu, i.e., whenever nu(A)=0, we have mu(A)=0.
| examples = If c is the counting measure on [0,1] and mu is the Lebesgue measure, then mull c.
}}{hide}row of table of mathematical symbols
| readas = is absolutely continuous with respect to
| category = measure theory
| explain = mullnu means that mu is absolutely continuous with respect to nu, i.e., whenever nu(A)=0, we have mu(A)=0.
| examples = If c is the counting measure on [0,1] and mu is the Lebesgue measure, then mull c.
| symbol = {{math|â‰¤{edih}{{math|â‰¥}}
| tex = le gelege
| rowspan = 3
| name = inequality
| readas = is less than or equal to,is greater than or equal to
| category = order theory
| explain = {{math|x â‰¤ y}} means x is less than or equal to y.{{math|x â‰¥ y}} means x is greater than or equal to y.(The forms = are generally used in programming languages, where ease of typing and use of ASCII text is preferred.)({{math|â‰¦}} and {{math|â‰§}} are also used by some writers to mean the same thing as {{math|â‰¤}} and {{math|â‰¥}}, but this usage seems to be less common.)
| examples = {{math|3 â‰¤ 4}} and {{math|5 â‰¤ 5}}{{math|5 â‰¥ 4}} and {{math|5 â‰¥ 5}}
}}{hide}row of table of mathematical symbols
| tex = le gelege
| rowspan = 3
| name = inequality
| readas = is less than or equal to,is greater than or equal to
| category = order theory
| explain = {{math|x â‰¤ y}} means x is less than or equal to y.{{math|x â‰¥ y}} means x is greater than or equal to y.(The forms = are generally used in programming languages, where ease of typing and use of ASCII text is preferred.)({{math|â‰¦}} and {{math|â‰§}} are also used by some writers to mean the same thing as {{math|â‰¤}} and {{math|â‰¥}}, but this usage seems to be less common.)
| examples = {{math|3 â‰¤ 4}} and {{math|5 â‰¤ 5}}{{math|5 â‰¥ 4}} and {{math|5 â‰¥ 5}}
| name = subgroup
| readas = is a subgroup of
| category = group theory
| explain = {{math|H â‰¤ G{edih} means H is a subgroup of G.
| examples = {{math|Z â‰¤ Z}}{{math|A3 â‰¤ S3}}
}}{hide}row of table of mathematical symbols
| readas = is a subgroup of
| category = group theory
| explain = {{math|H â‰¤ G{edih} means H is a subgroup of G.
| examples = {{math|Z â‰¤ Z}}{{math|A3 â‰¤ S3}}
| name = reduction
| readas = is reducible to
| category = computational complexity theory
| explain = {{math|A â‰¤ B{edih} means the problem A can be reduced to the problem B. Subscripts can be added to the â‰¤ to indicate what kind of reduction.
| examples = If
| readas = is reducible to
| category = computational complexity theory
| explain = {{math|A â‰¤ B{edih} means the problem A can be reduced to the problem B. Subscripts can be added to the â‰¤ to indicate what kind of reduction.
| examples = If
exists f in F mbox{ . } forall x in mathbb{N} mbox{ . } x in A Leftrightarrow f(x) in B
then
A leq_{F} B
}}{hide}row of table of mathematical symbols
| symbol = {{math|â‰¦{edih}{{math|â‰§}}
| tex = leqq geqq leqqgeqq
| rowspan = 2
| name = congruence relation
| readas = ... is less than ... is greater than ...
| category =modular arithmetic
| explain =
| examples = {{math|10a â‰¡ 5 (mod 5) for 1 â‰¦ a â‰¦ 10}}
}}{{row of table of mathematical symbols
| tex = leqq geqq leqqgeqq
| rowspan = 2
| name = congruence relation
| readas = ... is less than ... is greater than ...
| category =modular arithmetic
| explain =
| examples = {{math|10a â‰¡ 5 (mod 5) for 1 â‰¦ a â‰¦ 10}}
| name = vector inequality
| readas = ... is less than or equal... is greater than or equal...
| category = order theory
| explain = {{math|x â‰¦ y}} means that each component of vector x is less than or equal to each corresponding component of vector y.{{math|x â‰§ y}} means that each component of vector x is greater than or equal to each corresponding component of vector y.It is important to note that {{math|x â‰¦ y}} remains true if every element is equal. However, if the operator is changed, {{math|x â‰¤ y}} is true if and only if {{math|x â‰ y}} is also true.
| examples =
}}{hide}row of table of mathematical symbols
| readas = ... is less than or equal... is greater than or equal...
| category = order theory
| explain = {{math|x â‰¦ y}} means that each component of vector x is less than or equal to each corresponding component of vector y.{{math|x â‰§ y}} means that each component of vector x is greater than or equal to each corresponding component of vector y.It is important to note that {{math|x â‰¦ y}} remains true if every element is equal. However, if the operator is changed, {{math|x â‰¤ y}} is true if and only if {{math|x â‰ y}} is also true.
| examples =
| symbol = {{math|â‰º{edih}{{math|â‰»}}
| tex = prec succ precsucc
| rowspan = 2
| name = Karp reduction
| readas = is Karp reducible to;is polynomial-time many-one reducible to
| category = computational complexity theory
| explain = {{math|L1 â‰º L2}} means that the problem L1 is Karp reducible to L2.{{Citation|last=RÃ³nyai|first=Lajos|title=Algoritmusok(Algorithms)|year=1998|publisher=TYPOTEX|isbn=963-9132-16-0}}
| examples = If {{math|L1 â‰º L2 and L2 âˆˆ P}}, then {{math|L1 âˆˆ P}}.
}}{hide}row of table of mathematical symbols
| tex = prec succ precsucc
| rowspan = 2
| name = Karp reduction
| readas = is Karp reducible to;is polynomial-time many-one reducible to
| category = computational complexity theory
| explain = {{math|L1 â‰º L2}} means that the problem L1 is Karp reducible to L2.{{Citation|last=RÃ³nyai|first=Lajos|title=Algoritmusok(Algorithms)|year=1998|publisher=TYPOTEX|isbn=963-9132-16-0}}
| examples = If {{math|L1 â‰º L2 and L2 âˆˆ P}}, then {{math|L1 âˆˆ P}}.
| name = Nondominated order
| readas = is nondominated by
| category = Multi-objective optimization
| explain = {{math|P â‰º Q{edih} means that the element P is nondominated by element Q.JOURNAL, 10.1109/4235.996017, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6, 2, 182, 2002, Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.,
| examples = If {{math|P1 â‰º Q2}} then forall_i P_i leq Q_i and exists P_i < Q_i
}}{hide}row of table of mathematical symbols
| readas = is nondominated by
| category = Multi-objective optimization
| explain = {{math|P â‰º Q{edih} means that the element P is nondominated by element Q.JOURNAL, 10.1109/4235.996017, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transactions on Evolutionary Computation, 6, 2, 182, 2002, Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.,
| examples = If {{math|P1 â‰º Q2}} then forall_i P_i leq Q_i and exists P_i < Q_i
| symbol = {{math|â—…{edih}{{math|â–»}}◅▻
| tex = triangleleft triangleright trianglelefttriangleright
| rowspan = 3
| name = normal subgroup
| readas = is a normal subgroup of
| category = group theory
| explain = {{math|N â—… G}} means that N is a normal subgroup of group G.
| examples = {{math|Z(G) â—… G}}
}}{hide}row of table of mathematical symbols
| tex = triangleleft triangleright trianglelefttriangleright
| rowspan = 3
| name = normal subgroup
| readas = is a normal subgroup of
| category = group theory
| explain = {{math|N â—… G}} means that N is a normal subgroup of group G.
| examples = {{math|Z(G) â—… G}}
| name = ideal
| readas = is an ideal of
| category = ring theory
| explain = {{math|I â—… R{edih} means that I is an ideal of ring R.
| examples = {{math|(2) â—… Z}}
}}{hide}row of table of mathematical symbols
| readas = is an ideal of
| category = ring theory
| explain = {{math|I â—… R{edih} means that I is an ideal of ring R.
| examples = {{math|(2) â—… Z}}
| name = antijoin
| readas = the antijoin of
| category = relational algebra
| explain = {{math|R â–» S{edih} means the antijoin of the relations R and S, the tuples in R for which there is not a tuple in S that is equal on their common attribute names.
| examples = R triangleright S = R - R ltimes S
}}{hide}row of table of mathematical symbols
| readas = the antijoin of
| category = relational algebra
| explain = {{math|R â–» S{edih} means the antijoin of the relations R and S, the tuples in R for which there is not a tuple in S that is equal on their common attribute names.
| examples = R triangleright S = R - R ltimes S
| symbol = {{math|â‡’{edih}{{math|â†’}}{{math|âŠƒ}}
| tex = Rightarrow rightarrow supset Rightarrowrightarrowsupset
| rowspan = 1
| name = material implication
| readas = implies;if ... then
| category = propositional logic, Heyting algebra
| explain = A â‡’ B means if A is true then B is also true; if A is false then nothing is said about B.(â†’ may mean the same as â‡’, or it may have the meaning for functions given below.)(âŠƒ may mean the same as â‡’, or it may have the meaning for superset given below.)
| examples = {{math|1=x = 6 â‡’ x2 âˆ’ 5 = 36 âˆ’ 5 = 31}} is true, but {{math|1=x2 âˆ’ 5 = 36 âˆ’5 = 31 â‡’ x = 6}} is in general false (since x could be âˆ’6).
}}{hide}row of table of mathematical symbols
| tex = Rightarrow rightarrow supset Rightarrowrightarrowsupset
| rowspan = 1
| name = material implication
| readas = implies;if ... then
| category = propositional logic, Heyting algebra
| explain = A â‡’ B means if A is true then B is also true; if A is false then nothing is said about B.(â†’ may mean the same as â‡’, or it may have the meaning for functions given below.)(âŠƒ may mean the same as â‡’, or it may have the meaning for superset given below.)
| examples = {{math|1=x = 6 â‡’ x2 âˆ’ 5 = 36 âˆ’ 5 = 31}} is true, but {{math|1=x2 âˆ’ 5 = 36 âˆ’5 = 31 â‡’ x = 6}} is in general false (since x could be âˆ’6).
| symbol = {{math|âŠ†{edih}{{math|âŠ‚}}
| tex = subseteq subset subseteqsubset
| rowspan = 1
| name = subset
| readas = is a subset of
| category = set theory
| explain = (subset) {{math|A âŠ† B}} means every element of A is also an element of B.{{Citation | last1=Goldrei | first1=Derek | title=Classic Set Theory | page=4 | year=1996 | publisher=Chapman and Hall | isbn=0-412-60610-0 | location=London }}(proper subset) {{math|A âŠ‚ B}} means {{math|A âŠ† B}} but {{math|A â‰ B}}. (Some writers use the symbol âŠ‚ as if it were the same as âŠ†.)
| examples = {{math|(A âˆ© B) âŠ† Aâ„• âŠ‚ â„šâ„š âŠ‚ â„}}
}}{hide}row of table of mathematical symbols
| tex = subseteq subset subseteqsubset
| rowspan = 1
| name = subset
| readas = is a subset of
| category = set theory
| explain = (subset) {{math|A âŠ† B}} means every element of A is also an element of B.{{Citation | last1=Goldrei | first1=Derek | title=Classic Set Theory | page=4 | year=1996 | publisher=Chapman and Hall | isbn=0-412-60610-0 | location=London }}(proper subset) {{math|A âŠ‚ B}} means {{math|A âŠ† B}} but {{math|A â‰ B}}. (Some writers use the symbol âŠ‚ as if it were the same as âŠ†.)
| examples = {{math|(A âˆ© B) âŠ† Aâ„• âŠ‚ â„šâ„š âŠ‚ â„}}
| symbol = {{math|âŠ‡{edih}{{math|âŠƒ}}
| tex = supseteq supset supseteqsupset
| rowspan = 1
| name = superset
| readas = is a superset of
| category = set theory
| explain = {{math|A âŠ‡ B}} means every element of B is also an element of A.{{math|A âŠƒ B}} means {{math|A âŠ‡ B}} but {{math|A â‰ B}}. (Some writers use the symbol âŠƒ as if it were the same as âŠ‡.)
| examples = {{math|(A âˆª B) âŠ‡ Bâ„ âŠƒ â„š}}
}}{hide}row of table of mathematical symbols
| tex = supseteq supset supseteqsupset
| rowspan = 1
| name = superset
| readas = is a superset of
| category = set theory
| explain = {{math|A âŠ‡ B}} means every element of B is also an element of A.{{math|A âŠƒ B}} means {{math|A âŠ‡ B}} but {{math|A â‰ B}}. (Some writers use the symbol âŠƒ as if it were the same as âŠ‡.)
| examples = {{math|(A âˆª B) âŠ‡ Bâ„ âŠƒ â„š}}
| symbol = Subset
| tex = Subset
| rowspan = 1
| name = compact embedding
| readas = is compactly contained in
| category = set theory
| explain = {{math|A â‹ B{edih} means the closure of B is a compact subset of A.
| examples = mathbb{Q}cap (0,1) Subset [0, 5]
}}{hide}row of table of mathematical symbols
| tex = Subset
| rowspan = 1
| name = compact embedding
| readas = is compactly contained in
| category = set theory
| explain = {{math|A â‹ B{edih} means the closure of B is a compact subset of A.
| examples = mathbb{Q}cap (0,1) Subset [0, 5]
| symbol = {{math|â†’{edih}
| tex = to to
| rowspan = 1
| name = function arrow
| readas = from ... to
| category = set theory, type theory
| explain = {{math|f: X â†’ Y}} means the function f maps the set X into the set Y.
| examples = Let f: â„¤ â†’ â„• âˆª {0} be defined by {{math|1=f(x) := x2}}.
}}{hide}row of table of mathematical symbols
| tex = to to
| rowspan = 1
| name = function arrow
| readas = from ... to
| category = set theory, type theory
| explain = {{math|f: X â†’ Y}} means the function f maps the set X into the set Y.
| examples = Let f: â„¤ â†’ â„• âˆª {0} be defined by {{math|1=f(x) := x2}}.
| symbol = {{math|â†¦{edih}
| tex = mapsto mapsto
| rowspan = 1
| name = function arrow
| readas = maps to
| category = set theory
| explain = {{math|f: a â†¦ b}} means the function f maps the element a to the element b.
| examples = Let {{math|f: x â†¦ x + 1}} (the successor function).
}}{hide}row of table of mathematical symbols
| tex = mapsto mapsto
| rowspan = 1
| name = function arrow
| readas = maps to
| category = set theory
| explain = {{math|f: a â†¦ b}} means the function f maps the element a to the element b.
| examples = Let {{math|f: x â†¦ x + 1}} (the successor function).
| symbol = {{math|â†{edih}
| tex = leftarrowleftarrow
| rowspan = 1
| name = Converse implication
| readas = .. if ..
| category = logic
| explain = {{math|a â† b}} means that for the propositions a and b, if b implies a, then a is the converse implication of b.a to the element b. This reads as "a if b", or "not b without a". It is not to be confused with the assignment operator in computer science.
| examples =
}}{hide}row of table of mathematical symbols
| tex = leftarrowleftarrow
| rowspan = 1
| name = Converse implication
| readas = .. if ..
| category = logic
| explain = {{math|a â† b}} means that for the propositions a and b, if b implies a, then a is the converse implication of b.a to the element b. This reads as "a if b", or "not b without a". It is not to be confused with the assignment operator in computer science.
| examples =
| symbol = {{math|<:{edih}{{math|<Â·}}
| tex =
| tex = # !,sharp
| rowspan = 3
| name = cardinality
| readas = cardinality of;size of;order of
| category = set theory
| explain = #X means the cardinality of the set X.(|...| may be used instead as described above.)
| examples = #{4, 6, 8} = 3
}}{{row of table of mathematical symbols
| tex =
| tex = # !,sharp
| rowspan = 3
| name = cardinality
| readas = cardinality of;size of;order of
| category = set theory
| explain = #X means the cardinality of the set X.(|...| may be used instead as described above.)
| examples = #{4, 6, 8} = 3
| name = connected sum
| readas = connected sum of;knot sum of;knot composition of
| category = topology, knot theory
| explain = A#B is the connected sum of the manifolds A and B. If A and B are knots, then this denotes the knot sum, which has a slightly stronger condition.
| examples = A#S'm is homeomorphic to A, for any manifold A, and the sphere S'm.
}}{{row of table of mathematical symbols
| readas = connected sum of;knot sum of;knot composition of
| category = topology, knot theory
| explain = A#B is the connected sum of the manifolds A and B. If A and B are knots, then this denotes the knot sum, which has a slightly stronger condition.
| examples = A#S'm is homeomorphic to A, for any manifold A, and the sphere S'm.
| name = primorial
| readas = primorial
| category = number theory
| explain = n# is product of all prime numbers less than or equal to n.
| examples = 12# = 2 Ã— 3 Ã— 5 Ã— 7 Ã— 11 = 2310
}}{hide}row of table of mathematical symbols
| readas = primorial
| category = number theory
| explain = n# is product of all prime numbers less than or equal to n.
| examples = 12# = 2 Ã— 3 Ã— 5 Ã— 7 Ã— 11 = 2310
| symbol = {{math|(colon (punctuation)|:){edih}
| tex = : !,
| rowspan = 5
| name = such that
| readas = such that;so that
| category = everywhere
| explain = : means "such that", and is used in proofs and the set-builder notation (described below).
| examples = âˆƒ n âˆˆ â„•: n is even.
}}{{row of table of mathematical symbols
| tex = : !,
| rowspan = 5
| name = such that
| readas = such that;so that
| category = everywhere
| explain = : means "such that", and is used in proofs and the set-builder notation (described below).
| examples = âˆƒ n âˆˆ â„•: n is even.
| name = field extension
| readas = extends;over
| category = field theory
| explain = K : F means the field K extends the field F.This may also be written as K â‰¥ F.
| examples = â„ : â„š
}}{{row of table of mathematical symbols
| readas = extends;over
| category = field theory
| explain = K : F means the field K extends the field F.This may also be written as K â‰¥ F.
| examples = â„ : â„š
| name = inner product of matrices
| readas = inner product of
| category = linear algebra
| explain = A : B means the Frobenius inner product of the matrices A and B.The general inner product is denoted by âŸ¨u, vâŸ©, âŸ¨u | vâŸ© or (u | v), as described below. For spatial vectors, the dot product notation, xÂ·y is common. See also braâ€“ket notation.
| examples = A:B = sum_{i,j} A_{ij}B_{ij}
}}{hide}row of table of mathematical symbols
| readas = inner product of
| category = linear algebra
| explain = A : B means the Frobenius inner product of the matrices A and B.The general inner product is denoted by âŸ¨u, vâŸ©, âŸ¨u | vâŸ© or (u | v), as described below. For spatial vectors, the dot product notation, xÂ·y is common. See also braâ€“ket notation.
| examples = A:B = sum_{i,j} A_{ij}B_{ij}
| name = index of a subgroup
| readas = index of subgroup
| category = group theory
| explain = The index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G
| examples = |G:H| = frac{|G|}{|H|}
{edih}{hide}row of table of mathematical symbols
| readas = index of subgroup
| category = group theory
| explain = The index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G
| examples = |G:H| = frac{|G|}{|H|}
| name = division
| readas = divided byover
| category = everywhere
| explain = A : B means the division of A with B (dividing A by B)
| examples =10 : 2 = 5
{edih}{hide}row of table of mathematical symbols
| readas = divided byover
| category = everywhere
| explain = A : B means the division of A with B (dividing A by B)
| examples =10 : 2 = 5
| symbol = {{math|â‹®{edih}
| tex = vdots !,vdots !,
| rowspan = 1
| name = vertical ellipsis
| readas = vertical ellipsis
| category = everywhere
| explain = Denotes that certain constants and terms are missing out (e.g. for clarity) and that only the important terms are being listed.
| examples = P(r,t) = chi vdots E(r,t_1)E(r,t_2)E(r,t_3)
}}{hide}row of table of mathematical symbols
| tex = vdots !,vdots !,
| rowspan = 1
| name = vertical ellipsis
| readas = vertical ellipsis
| category = everywhere
| explain = Denotes that certain constants and terms are missing out (e.g. for clarity) and that only the important terms are being listed.
| examples = P(r,t) = chi vdots E(r,t_1)E(r,t_2)E(r,t_3)
| symbol = {{math|â‰€{edih}
| tex = wr !,wr !,
| rowspan = 1
| name = wreath product
| readas = wreath product of ... by ...
| category = group theory
| explain = A â‰€ H means the wreath product of the group A by the group H.This may also be written A wr H.
| examples = mathrm{S}_n wr mathrm{Z}_2 is isomorphic to the automorphism group of the complete bipartite graph on (n,n) vertices.
}}{hide}row of table of mathematical symbols
| tex = wr !,wr !,
| rowspan = 1
| name = wreath product
| readas = wreath product of ... by ...
| category = group theory
| explain = A â‰€ H means the wreath product of the group A by the group H.This may also be written A wr H.
| examples = mathrm{S}_n wr mathrm{Z}_2 is isomorphic to the automorphism group of the complete bipartite graph on (n,n) vertices.
| symbol = {{math|â†¯{edih}{{math|â¨³}}{{math|â‡’â‡}}
| tex = blitzalightning: requires usepackage{stmaryd}.WEB, Math symbols defined by LaTeX package Â«stmaryrdÂ»,weblink 16 November 2017,
smashtimes requires usepackage{unicode-math} and setmathfont{XITS Math} or another Open Type Math Font.WEB, Answer to Is there a â€œcontradictionâ€ symbol in some font, somewhere?,weblink TeX Stack Exchange, 16 November 2017, RightarrowLeftarrowRightarrowLeftarrowbotbotnleftrightarrownleftrightarrowtextreferencemarkContradiction!WEB, The Comprehensive LATEX Symbol List,weblink 16 November 2017, 15, Because of the lack of notational consensus, it is probably better to spell out â€œContradiction!â€ than to use a symbol for this purpose., | tex = blitzalightning: requires usepackage{stmaryd}.WEB, Math symbols defined by LaTeX package Â«stmaryrdÂ»,weblink 16 November 2017,
| rowspan = 1
| name = downwards zigzag arrow
| readas = contradiction; this contradicts that
| category = everywhere
| explain = Denotes that contradictory statements have been inferred. For clarity, the exact point of contradiction can be appended.
| examples = x + 4 = x âˆ’ 3 â€»Statement: Every finite, non-empty, ordered set has a largest element. Otherwise, let's assume that X is a finite, non-empty, ordered set with no largest element. Then, for some x_1 in X, there exists an x_2 in X with x_1 < x_2, but then there's also an x_3 in X with x_2 < x_3, and so on. Thus, x_1, x_2, x_3, ... are distinct elements in X. â†¯ X is finite.
}}{hide}row of table of mathematical symbols
| name = downwards zigzag arrow
| readas = contradiction; this contradicts that
| category = everywhere
| explain = Denotes that contradictory statements have been inferred. For clarity, the exact point of contradiction can be appended.
| examples = x + 4 = x âˆ’ 3 â€»Statement: Every finite, non-empty, ordered set has a largest element. Otherwise, let's assume that X is a finite, non-empty, ordered set with no largest element. Then, for some x_1 in X, there exists an x_2 in X with x_1 < x_2, but then there's also an x_3 in X with x_2 < x_3, and so on. Thus, x_1, x_2, x_3, ... are distinct elements in X. â†¯ X is finite.
| symbol = {{math|âŠ•{edih}{{math|âŠ»}}
| tex = oplus !,oplus !,veebar !,veebar !,
| rowspan = 2
| name = exclusive or
| readas = xor
| category = propositional logic, Boolean algebra
| explain = The statement A âŠ• B is true when either A or B, but not both, are true. A âŠ» B means the same.
| examples = (Â¬A) âŠ• A is always true, A âŠ• A is always false.
}}{{row of table of mathematical symbols
| tex = oplus !,oplus !,veebar !,veebar !,
| rowspan = 2
| name = exclusive or
| readas = xor
| category = propositional logic, Boolean algebra
| explain = The statement A âŠ• B is true when either A or B, but not both, are true. A âŠ» B means the same.
| examples = (Â¬A) âŠ• A is always true, A âŠ• A is always false.
| name = direct sum
| readas = direct sum of
| category = abstract algebra
| explain = The direct sum is a special way of combining several objects into one general object.(The bun symbol âŠ•, or the coproduct symbol âˆ, is used; âŠ» is only for logic.)
| examples = Most commonly, for vector spaces U, V, and W, the following consequence is used:U = V âŠ• W â‡” (U = V + W) âˆ§ (V âˆ© W = {0})
}}{{row of table of mathematical symbols
| readas = direct sum of
| category = abstract algebra
| explain = The direct sum is a special way of combining several objects into one general object.(The bun symbol âŠ•, or the coproduct symbol âˆ, is used; âŠ» is only for logic.)
| examples = Most commonly, for vector spaces U, V, and W, the following consequence is used:U = V âŠ• W â‡” (U = V + W) âˆ§ (V âˆ© W = {0})
| symbol = {~wedge!!!!!!bigcirc~}
| tex = {~wedge!!!!!!bigcirc~}{~wedge!!!!!!bigcirc~}
| rowspan = 1
| name = Kulkarniâ€“Nomizu product
| readas = Kulkarniâ€“Nomizu product
| category = tensor algebra
| explain = Derived from the tensor product of two symmetric type (0,2) tensors; it has the algebraic symmetries of the Riemann tensor. f=g{,wedge!!!!!!bigcirc,}h has components f_{alphabetagammadelta}=g_{alphagamma}h_{betadelta}+g_{betadelta}h_{alphagamma}-g_{alphadelta}h_{betagamma}-g_{betagamma}h_{alphadelta}.
| examples =
}}{hide}row of table of mathematical symbols
| tex = {~wedge!!!!!!bigcirc~}{~wedge!!!!!!bigcirc~}
| rowspan = 1
| name = Kulkarniâ€“Nomizu product
| readas = Kulkarniâ€“Nomizu product
| category = tensor algebra
| explain = Derived from the tensor product of two symmetric type (0,2) tensors; it has the algebraic symmetries of the Riemann tensor. f=g{,wedge!!!!!!bigcirc,}h has components f_{alphabetagammadelta}=g_{alphagamma}h_{betadelta}+g_{betadelta}h_{alphagamma}-g_{alphadelta}h_{betagamma}-g_{betagamma}h_{alphadelta}.
| examples =
| symbol = {{math|â–¡{edih}
| tex = Box !,Box !
| rowspan = 1
| name = D'Alembertian;wave operator
| readas = non-Euclidean Laplacian
| category = vector calculus
| explain = It is the generalisation of the Laplace operator in the sense that it is the differential operator which is invariant under the isometry group of the underlying space and it reduces to the Laplace operator if restricted to time independent functions.
| examples = square = frac{1}{c^2}{partial^2 over partial t^2 } - {partial^2 over partial x^2 } - {partial^2 over partial y^2 } - {partial^2 over partial z^2 }
}}| tex = Box !,Box !
| rowspan = 1
| name = D'Alembertian;wave operator
| readas = non-Euclidean Laplacian
| category = vector calculus
| explain = It is the generalisation of the Laplace operator in the sense that it is the differential operator which is invariant under the isometry group of the underlying space and it reduces to the Laplace operator if restricted to time independent functions.
| examples = square = frac{1}{c^2}{partial^2 over partial t^2 } - {partial^2 over partial x^2 } - {partial^2 over partial y^2 } - {partial^2 over partial z^2 }
Letter-based symbols
Includes upside-down letters.Letter modifiers
Also called diacritics.{| class="wikitable" style="margin:auto; width:100%; border:1px"! rowspan="3" style="font-size:100%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples! Read as
| symbol = {{math|{{overline|a{edih}}}
| tex = bar{a}bar{a}
| rowspan = 5
| name = mean
| readas = overbar;... bar
| category = statistics
| explain = bar{x} (often read as "x bar") is the mean (average value of x_i).
| examples = x = {1,2,3,4,5}; bar{x} = 3.
}}{{row of table of mathematical symbols
| tex = bar{a}bar{a}
| rowspan = 5
| name = mean
| readas = overbar;... bar
| category = statistics
| explain = bar{x} (often read as "x bar") is the mean (average value of x_i).
| examples = x = {1,2,3,4,5}; bar{x} = 3.
| name = finite sequence, tuple
| readas = finite sequence, tuple
| category = model theory
| explain = overline{a} means the finite sequence/tuple (a_1,a_2, ... ,a_n)..
| examples = overline{a}:=(a_1,a_2, ... ,a_n).
}}{{row of table of mathematical symbols
| readas = finite sequence, tuple
| category = model theory
| explain = overline{a} means the finite sequence/tuple (a_1,a_2, ... ,a_n)..
| examples = overline{a}:=(a_1,a_2, ... ,a_n).
| name = algebraic closure
| readas = algebraic closure of
| category = field theory
| explain = overline{F} is the algebraic closure of the field F.
| examples = The field of algebraic numbers is sometimes denoted as overline{mathbb{Q}} because it is the algebraic closure of the rational numbers {mathbb{Q}}.
}}{{row of table of mathematical symbols
| readas = algebraic closure of
| category = field theory
| explain = overline{F} is the algebraic closure of the field F.
| examples = The field of algebraic numbers is sometimes denoted as overline{mathbb{Q}} because it is the algebraic closure of the rational numbers {mathbb{Q}}.
| name = complex conjugate
| readas = conjugate
| category = complex numbers
| explain = overline{z} means the complex conjugate of z.(zâˆ— can also be used for the conjugate of z, as described above.)
| examples = overline{3+4i} = 3-4i.
}}{{row of table of mathematical symbols
| readas = conjugate
| category = complex numbers
| explain = overline{z} means the complex conjugate of z.(zâˆ— can also be used for the conjugate of z, as described above.)
| examples = overline{3+4i} = 3-4i.
| name = topological closure
| readas = (topological) closure of
| category = topology
| explain = overline{S} is the topological closure of the set S.This may also be denoted as cl(S) or Cl(S).
| examples = In the space of the real numbers, overline{mathbb{Q}} = mathbb{R} (the rational numbers are dense in the real numbers).
}}{hide}row of table of mathematical symbols
| readas = (topological) closure of
| category = topology
| explain = overline{S} is the topological closure of the set S.This may also be denoted as cl(S) or Cl(S).
| examples = In the space of the real numbers, overline{mathbb{Q}} = mathbb{R} (the rational numbers are dense in the real numbers).
| symbol = overset{rightharpoonup}{a}
| tex = overset{rightharpoonup}{a}overset{rightharpoonup}{a}
| rowspan = 1
| name = vector
| readas = harpoon
| category = linear algebra
| explain =
| examples =
{edih}{hide}row of table of mathematical symbols
| tex = overset{rightharpoonup}{a}overset{rightharpoonup}{a}
| rowspan = 1
| name = vector
| readas = harpoon
| category = linear algebra
| explain =
| examples =
| symbol = {{math|Ã¢{edih}
| tex = hat ahat a
| rowspan = 2
| name = unit vector
| readas = hat
| category = geometry
| explain = mathbf{hat a} (pronounced "a hat") is the normalized version of vector mathbf a, having length 1.
| examples =
}}{{row of table of mathematical symbols
| tex = hat ahat a
| rowspan = 2
| name = unit vector
| readas = hat
| category = geometry
| explain = mathbf{hat a} (pronounced "a hat") is the normalized version of vector mathbf a, having length 1.
| examples =
| name = estimator
| readas = estimator for
| category = statistics
| explain = hat theta is the estimator or the estimate for the parameter theta.
| examples = The estimator mathbf{hat mu} = frac {sum_i x_i} {n} produces a sample estimate mathbf{hat mu} (mathbf x) for the mean mu.
}}{hide}row of table of mathematical symbols
| readas = estimator for
| category = statistics
| explain = hat theta is the estimator or the estimate for the parameter theta.
| examples = The estimator mathbf{hat mu} = frac {sum_i x_i} {n} produces a sample estimate mathbf{hat mu} (mathbf x) for the mean mu.
| symbol = {{math|Ê¹{edih}
| tex = ''
| rowspan = 1
| name = derivative
| readas = ... prime;derivative of
| category = calculus
| explain = f Ê¹(x) means the derivative of the function f at the point x, i.e., the slope of the tangent to f at x.(The single-quote character ' is sometimes used instead, especially in ASCII text.)
| examples =If f(x) := x2, then f Ê¹(x) = 2x.
}}{hide}row of table of mathematical symbols
| tex = ''
| rowspan = 1
| name = derivative
| readas = ... prime;derivative of
| category = calculus
| explain = f Ê¹(x) means the derivative of the function f at the point x, i.e., the slope of the tangent to f at x.(The single-quote character ' is sometimes used instead, especially in ASCII text.)
| examples =If f(x) := x2, then f Ê¹(x) = 2x.
| symbol = {{math|â€¢{edih}
| tex = dot{,}dot{,}
| rowspan = 1
| name = derivative
| readas = ... dot;time derivative of
| category = calculus
| explain = dot{x} means the derivative of x with respect to time. That is dot{x}(t)=frac{partial}{partial t}x(t).
| examples = If x(t) := t2, then dot{x}(t)=2t.
}}| tex = dot{,}dot{,}
| rowspan = 1
| name = derivative
| readas = ... dot;time derivative of
| category = calculus
| explain = dot{x} means the derivative of x with respect to time. That is dot{x}(t)=frac{partial}{partial t}x(t).
| examples = If x(t) := t2, then dot{x}(t)=2t.
Symbols based on Latin letters{| class"wikitable" style"margin:auto; width:100%; border:1px"
! rowspan="3" style="font-size:130%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples! Read as
| symbol = {{math|âˆ€{edih}
| tex = forallforall
| rowspan = 1
| name = universal quantification
| readas = for all;for any;for each;for every
| category = predicate logic
| explain = {{math|1=âˆ€ x, P(x)}} means P(x) is true for all x.
| examples = {{math|1=âˆ€ n âˆˆ â„•,}} {{math|1=n2 â‰¥ n}}.
}}{hide}row of table of mathematical symbols
| tex = forallforall
| rowspan = 1
| name = universal quantification
| readas = for all;for any;for each;for every
| category = predicate logic
| explain = {{math|1=âˆ€ x, P(x)}} means P(x) is true for all x.
| examples = {{math|1=âˆ€ n âˆˆ â„•,}} {{math|1=n2 â‰¥ n}}.
| symbol = {{math|ð”¹{edih}{{math|B}}
| tex = mathbb{B}mathbb{B} mathbf{B}mathbf{B}
| rowspan = 1
| name = boolean domain
| readas = B;the (set of) boolean values;the (set of) truth values;
| category = set theory, boolean algebra
| explain = ð”¹ means either {0, 1}, {false, true}, {F, T}, or left { bot,top right }.
| examples = {{math|(Â¬False) âˆˆ ð”¹}}
}}{hide}row of table of mathematical symbols
| tex = mathbb{B}mathbb{B} mathbf{B}mathbf{B}
| rowspan = 1
| name = boolean domain
| readas = B;the (set of) boolean values;the (set of) truth values;
| category = set theory, boolean algebra
| explain = ð”¹ means either {0, 1}, {false, true}, {F, T}, or left { bot,top right }.
| examples = {{math|(Â¬False) âˆˆ ð”¹}}
| symbol = {{math|â„‚{edih}{{math|C}}
| tex = mathbb{C}mathbb{C} mathbf{C}mathbf{C}
| rowspan = 1
| name = complex numbers
| readas = C;the (set of) complex numbers
| category = numbers
| explain = â„‚ means {{math|1={{mset|a + b i : a,b âˆˆ â„}}}}.
| examples = {{math|1=i = {{sqrt|âˆ’1}} âˆˆ â„‚}}
}}{hide}row of table of mathematical symbols
| tex = mathbb{C}mathbb{C} mathbf{C}mathbf{C}
| rowspan = 1
| name = complex numbers
| readas = C;the (set of) complex numbers
| category = numbers
| explain = â„‚ means {{math|1={{mset|a + b i : a,b âˆˆ â„}}}}.
| examples = {{math|1=i = {{sqrt|âˆ’1}} âˆˆ â„‚}}
| symbol = {{math|ð” {edih}
| tex = mathfrak cmathfrak c
| rowspan = 1
| name = cardinality of the continuum
| readas = cardinality of the continuum;c;cardinality of the real numbers
| category = set theory
| explain = The cardinality of mathbb R is denoted by |mathbb R| or by the symbol mathfrak c (a lowercase Fraktur letter C).
| examples = mathfrak c = {beth}_{1}
}}{hide}row of table of mathematical symbols
| tex = mathfrak cmathfrak c
| rowspan = 1
| name = cardinality of the continuum
| readas = cardinality of the continuum;c;cardinality of the real numbers
| category = set theory
| explain = The cardinality of mathbb R is denoted by |mathbb R| or by the symbol mathfrak c (a lowercase Fraktur letter C).
| examples = mathfrak c = {beth}_{1}
| symbol = {{math|âˆ‚{edih}
| tex = partialpartial
| rowspan = 3
| name = partial derivative
| readas = partial;d
| category = calculus
| explain = âˆ‚f/âˆ‚x'i means the partial derivative of f with respect to x'i, where f is a function on (x1, ..., xn).
| examples = If f(x,y) := x2y, then âˆ‚f/âˆ‚x = 2xy,
}}{hide}row of table of mathematical symbols
| tex = partialpartial
| rowspan = 3
| name = partial derivative
| readas = partial;d
| category = calculus
| explain = âˆ‚f/âˆ‚x'i means the partial derivative of f with respect to x'i, where f is a function on (x1, ..., xn).
| examples = If f(x,y) := x2y, then âˆ‚f/âˆ‚x = 2xy,
| name = boundary
| readas = boundary of
| category = topology
| explain = âˆ‚M means the boundary of M
| examples = âˆ‚{x : ||x|| â‰¤ 2} = {x : ||x|| = 2}
{edih}{{row of table of mathematical symbols
| readas = boundary of
| category = topology
| explain = âˆ‚M means the boundary of M
| examples = âˆ‚{x : ||x|| â‰¤ 2} = {x : ||x|| = 2}
| name = degree of a polynomial
| readas = degree of
| category = algebra
| explain = âˆ‚f means the degree of the polynomial f. (This may also be written deg f.)
| examples = âˆ‚(x2 âˆ’ 1) = 2
}}{hide}row of table of mathematical symbols
| readas = degree of
| category = algebra
| explain = âˆ‚f means the degree of the polynomial f. (This may also be written deg f.)
| examples = âˆ‚(x2 âˆ’ 1) = 2
| symbol = {{math|ð”¼{edih}{{math|E}}
| tex = mathbb Emathbb Emathrm{E}mathrm{E}
| rowspan = 1
| name = expected value
| readas = expected value
| category = probability theory
| explain = the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained
| examples = mathbb{E}[X] = frac{x_1p_1 + x_2p_2 + dotsb + x_kp_k}{p_1 + p_2 + dotsb + p_k}
}}{hide}row of table of mathematical symbols
| tex = mathbb Emathbb Emathrm{E}mathrm{E}
| rowspan = 1
| name = expected value
| readas = expected value
| category = probability theory
| explain = the value of a random variable one would "expect" to find if one could repeat the random variable process an infinite number of times and take the average of the values obtained
| examples = mathbb{E}[X] = frac{x_1p_1 + x_2p_2 + dotsb + x_kp_k}{p_1 + p_2 + dotsb + p_k}
| symbol = {{math|âˆƒ{edih}
| tex = existsexists
| rowspan = 1
| name = existential quantification
| readas = there exists;there is;there are
| category = predicate logic
| explain = âˆƒ x: P(x) means there is at least one x such that P(x) is true.
| examples = âˆƒ n âˆˆ â„•: n is even.
}}{hide}row of table of mathematical symbols
| tex = existsexists
| rowspan = 1
| name = existential quantification
| readas = there exists;there is;there are
| category = predicate logic
| explain = âˆƒ x: P(x) means there is at least one x such that P(x) is true.
| examples = âˆƒ n âˆˆ â„•: n is even.
| symbol = {{math|âˆƒ!{edih}
| tex = exists!exists!
| rowspan = 1
| name = uniqueness quantification
| readas = there exists exactly one
| category = predicate logic
| explain = âˆƒ! x: P(x) means there is exactly one x such that P(x) is true.
| examples = âˆƒ! n âˆˆ â„•: n + 5 = 2n.
}}{hide}row of table of mathematical symbols
| tex = exists!exists!
| rowspan = 1
| name = uniqueness quantification
| readas = there exists exactly one
| category = predicate logic
| explain = âˆƒ! x: P(x) means there is exactly one x such that P(x) is true.
| examples = âˆƒ! n âˆˆ â„•: n + 5 = 2n.
| symbol = {{math|âˆˆ{edih}{{math|âˆ‰}}
| tex = inin notinnotin
| rowspan = 1
| name = set membership
| readas = is an element of;is not an element of
| category = everywhere, set theory
| explain = a âˆˆ S means a is an element of the set S; a âˆ‰ S means a is not an element of S.
| examples = (1/2)âˆ’1 âˆˆ â„•2âˆ’1 âˆ‰ â„•
}}{hide}row of table of mathematical symbols
| tex = inin notinnotin
| rowspan = 1
| name = set membership
| readas = is an element of;is not an element of
| category = everywhere, set theory
| explain = a âˆˆ S means a is an element of the set S; a âˆ‰ S means a is not an element of S.
| examples = (1/2)âˆ’1 âˆˆ â„•2âˆ’1 âˆ‰ â„•
| symbol = {{math|âˆŒ{edih}
| tex = notninotni
| rowspan = 1
| name = set membership
| readas = does not contain as an element
| category = set theory
| explain = S âˆŒ e means the same thing as e âˆ‰ S, where S is a set and e is not an element of S.
| examples =
}}{hide}row of table of mathematical symbols
| tex = notninotni
| rowspan = 1
| name = set membership
| readas = does not contain as an element
| category = set theory
| explain = S âˆŒ e means the same thing as e âˆ‰ S, where S is a set and e is not an element of S.
| examples =
| symbol = {{math|âˆ‹{edih}
| tex = nini
| rowspan = 2
| name = such that symbol
| readas = such that
| category = mathematical logic
| explain = often abbreviated as "s.t."; : and | are also used to abbreviate "such that". The use of âˆ‹ goes back to early mathematical logic and its usage in this sense is declining. The symbol backepsilon ("back epsilon") is sometimes specifically used for "such that" to avoid confusion with set membership.
| examples = Choose x âˆ‹ 2|x and 3|x. (Here | is used in the sense of "divides".)
}}{{row of table of mathematical symbols
| tex = nini
| rowspan = 2
| name = such that symbol
| readas = such that
| category = mathematical logic
| explain = often abbreviated as "s.t."; : and | are also used to abbreviate "such that". The use of âˆ‹ goes back to early mathematical logic and its usage in this sense is declining. The symbol backepsilon ("back epsilon") is sometimes specifically used for "such that" to avoid confusion with set membership.
| examples = Choose x âˆ‹ 2|x and 3|x. (Here | is used in the sense of "divides".)
| name = set membership
| readas = contains as an element
| category = set theory
| explain = S âˆ‹ e means the same thing as e âˆˆ S, where S is a set and e is an element of S.
| examples =
}}{hide}row of table of mathematical symbols
| readas = contains as an element
| category = set theory
| explain = S âˆ‹ e means the same thing as e âˆˆ S, where S is a set and e is an element of S.
| examples =
| symbol = {{math|ð”½{edih}
| tex = mathbb{F}mathbb{F}
| rowspan = 1
| name = Galois field
| readas = Galois field, or finite field
| category = Field (mathematics) theory
| explain = mathbb{F}_{p^n}, for any prime p and integer n, is the unique finite field with order p^n, often written mathrm{GF}(p^n), and sometimes also known as mathbf{Z}/pmathbf{Z}, mathbb{Z}/pmathbb{Z}, or mathbb{Z}_p, although this last notation is ambiguous.
| examples = left(mathbb{F}_{2^{255}-19}right)^2 is mathrm{GF}(2^{255}-19)^2, the finite field in whose quadratic extension the popuar elliptic curve Curve25519 is computed.
}}{hide}row of table of mathematical symbols
| tex = mathbb{F}mathbb{F}
| rowspan = 1
| name = Galois field
| readas = Galois field, or finite field
| category = Field (mathematics) theory
| explain = mathbb{F}_{p^n}, for any prime p and integer n, is the unique finite field with order p^n, often written mathrm{GF}(p^n), and sometimes also known as mathbf{Z}/pmathbf{Z}, mathbb{Z}/pmathbb{Z}, or mathbb{Z}_p, although this last notation is ambiguous.
| examples = left(mathbb{F}_{2^{255}-19}right)^2 is mathrm{GF}(2^{255}-19)^2, the finite field in whose quadratic extension the popuar elliptic curve Curve25519 is computed.
| symbol = {{math|â„{edih}{{math|H}}
| tex = mathbb{H}mathbb{H} mathbf{H}mathbf{H}
| rowspan = 1
| name = quaternions or Hamiltonian quaternions
| readas = H;the (set of) quaternions
| category = numbers
| explain = â„ means {a + b i + c j + d k : a,b,c,d âˆˆ â„}.
| examples =
}}{hide}row of table of mathematical symbols
| tex = mathbb{H}mathbb{H} mathbf{H}mathbf{H}
| rowspan = 1
| name = quaternions or Hamiltonian quaternions
| readas = H;the (set of) quaternions
| category = numbers
| explain = â„ means {a + b i + c j + d k : a,b,c,d âˆˆ â„}.
| examples =
| symbol = {{math|ð•€{edih}{{math|I}}
| tex = mathbb{I}mathbb{I} mathbf{I}mathbf{I}
| rowspan = 1
| name = Indicator function
| readas = the indicator of
| category = Boolean algebra
| explain = The indicator function of a subset A of a set X is a function mathbf{1}_A colon X to { 0,1 } defined as :mathbf{1}_A(x) :=
begin{cases}1 &text{if } x in A, end{cases}
| tex = mathbb{I}mathbb{I} mathbf{I}mathbf{I}
| rowspan = 1
| name = Indicator function
| readas = the indicator of
| category = Boolean algebra
| explain = The indicator function of a subset A of a set X is a function mathbf{1}_A colon X to { 0,1 } defined as :mathbf{1}_A(x) :=
| examples =
}}{hide}row of table of mathematical symbols
| symbol = {{math|â„•{edih}{{math|N}}
| tex = mathbb{N}mathbb{N} mathbf{N}mathbf{N}
| rowspan = 1
| name = natural numbers
| readas = the (set of) natural numbers
| category = numbers
| explain = N means either { 0, 1, 2, 3, ...} or { 1, 2, 3, ...}. The choice depends on the area of mathematics being studied; e.g. number theorists prefer the latter; analysts, set theorists and computer scientists prefer the former. To avoid confusion, always check an author's definition of N.Set theorists often use the notation Ï‰ (for least infinite ordinal) to denote the set of natural numbers (including zero), along with the standard ordering relation â‰¤.
| examples = â„• = {|a| : a âˆˆ â„¤} or â„• = {|a| > 0: a âˆˆ â„¤}
}}{hide}row of table of mathematical symbols
| tex = mathbb{N}mathbb{N} mathbf{N}mathbf{N}
| rowspan = 1
| name = natural numbers
| readas = the (set of) natural numbers
| category = numbers
| explain = N means either { 0, 1, 2, 3, ...} or { 1, 2, 3, ...}. The choice depends on the area of mathematics being studied; e.g. number theorists prefer the latter; analysts, set theorists and computer scientists prefer the former. To avoid confusion, always check an author's definition of N.Set theorists often use the notation Ï‰ (for least infinite ordinal) to denote the set of natural numbers (including zero), along with the standard ordering relation â‰¤.
| examples = â„• = {|a| : a âˆˆ â„¤} or â„• = {|a| > 0: a âˆˆ â„¤}
| symbol = {{math|â—‹{edih}
| tex = circcirc
| rowspan = 1
| name = Hadamard product
| readas = entrywise product
| category = linear algebra
| explain = For two matrices (or vectors) of the same dimensions A, B in {mathbb R}^{m times n} the Hadamard product is a matrix of the same dimensions A circ B in {mathbb R}^{m times n} with elements given by (A circ B)_{i,j} = (A)_{i,j} cdot (B)_{i,j}.
| examples = begin{bmatrix}
1&2
2&4
end{bmatrix} circ begin{bmatrix}
| tex = circcirc
| rowspan = 1
| name = Hadamard product
| readas = entrywise product
| category = linear algebra
| explain = For two matrices (or vectors) of the same dimensions A, B in {mathbb R}^{m times n} the Hadamard product is a matrix of the same dimensions A circ B in {mathbb R}^{m times n} with elements given by (A circ B)_{i,j} = (A)_{i,j} cdot (B)_{i,j}.
| examples = begin{bmatrix}
1&2
2&4
1&2
0&0
end{bmatrix} = begin{bmatrix}
0&0
1&4
0&0
end{bmatrix}}}{hide}row of table of mathematical symbols
0&0
| symbol = {{math|âˆ˜{edih}
| tex = circcirc
| rowspan = 1
| name = function composition
| readas = composed with
| category = set theory
| explain = f âˆ˜ g is the function such that (f âˆ˜ g)(x) = f(g(x)).{{Citation | last1=Goldrei | first1=Derek | title=Classic Set Theory | page=5 | year=1996 | publisher=Chapman and Hall | isbn=0-412-60610-0 | location=London }}
| examples = if f(x) := 2x, and g(x) := x + 3, then (f âˆ˜ g)(x) = 2(x + 3).
}}{hide}row of table of mathematical symbols
| tex = circcirc
| rowspan = 1
| name = function composition
| readas = composed with
| category = set theory
| explain = f âˆ˜ g is the function such that (f âˆ˜ g)(x) = f(g(x)).{{Citation | last1=Goldrei | first1=Derek | title=Classic Set Theory | page=5 | year=1996 | publisher=Chapman and Hall | isbn=0-412-60610-0 | location=London }}
| examples = if f(x) := 2x, and g(x) := x + 3, then (f âˆ˜ g)(x) = 2(x + 3).
| symbol = {{math|O{edih}
| tex = OO
| rowspan = 1
| name = Big O notation
| readas = big-oh of
| category = Computational complexity theory
| explain = The Big O notation describes the limiting behavior of a function, when the argument tends towards a particular value or infinity.
| examples = If f(x) = 6x4 âˆ’ 2x3 + 5 and g(x) = x4, then f(x)=O(g(x))mbox{ as }xtoinfty,
}}{hide}row of table of mathematical symbols
| tex = OO
| rowspan = 1
| name = Big O notation
| readas = big-oh of
| category = Computational complexity theory
| explain = The Big O notation describes the limiting behavior of a function, when the argument tends towards a particular value or infinity.
| examples = If f(x) = 6x4 âˆ’ 2x3 + 5 and g(x) = x4, then f(x)=O(g(x))mbox{ as }xtoinfty,
| symbol = {{math|âˆ…{edih}{{math| { } }}
| tex = emptyemptyset varnothingvarnothing {}{}
| rowspan = 1
| name = empty set
| readas = the empty set
null set
| category = set theory
| explain = âˆ… means the set with no elements. { } means the same.
| examples = {{math|1={{mset|n âˆˆ â„• : 1 < n2 < 4}} = âˆ…}}
}}{hide}row of table of mathematical symbols
| tex = emptyemptyset varnothingvarnothing {}{}
| rowspan = 1
| name = empty set
| readas = the empty set
null set
| category = set theory
| explain = âˆ… means the set with no elements. { } means the same.
| examples = {{math|1={{mset|n âˆˆ â„• : 1 < n2 < 4}} = âˆ…}}
| symbol = {{math|â„™{edih}{{math|P}}
| tex = mathbb{P}mathbb{P} mathbf{P}mathbf{P}
| rowspan = 4
| name = set of primes
| readas = P;the set of prime numbers
| category = arithmetic
| explain = â„™ is often used to denote the set of prime numbers.
| examples = 2in mathbb{P}, 3in mathbb{P}, 8notin mathbb{P}
}}{{row of table of mathematical symbols
| tex = mathbb{P}mathbb{P} mathbf{P}mathbf{P}
| rowspan = 4
| name = set of primes
| readas = P;the set of prime numbers
| category = arithmetic
| explain = â„™ is often used to denote the set of prime numbers.
| examples = 2in mathbb{P}, 3in mathbb{P}, 8notin mathbb{P}
| name = projective space
| readas = P;the projective space;the projective line;the projective plane
| category = topology
| explain = â„™ means a space with a point at infinity.
| examples = mathbb{P}^1,mathbb{P}^2
}}{{row of table of mathematical symbols
| readas = P;the projective space;the projective line;the projective plane
| category = topology
| explain = â„™ means a space with a point at infinity.
| examples = mathbb{P}^1,mathbb{P}^2
| name = probability
| readas = the probability of
| category = probability theory
| explain = â„™(X) means the probability of the event X occurring.This may also be written as P(X), Pr(X), P[X] or Pr[X].
| examples = If a fair coin is flipped, â„™(Heads) = â„™(Tails) = 0.5.
}}{{row of table of mathematical symbols
| readas = the probability of
| category = probability theory
| explain = â„™(X) means the probability of the event X occurring.This may also be written as P(X), Pr(X), P[X] or Pr[X].
| examples = If a fair coin is flipped, â„™(Heads) = â„™(Tails) = 0.5.
| name = Power set
| readas = the Power set of
| category = Powerset
| explain = Given a set S, the power set of S is the set of all subsets of the set S. The power set of S0 is
denoted by P(S).
| readas = the Power set of
| category = Powerset
| explain = Given a set S, the power set of S is the set of all subsets of the set S. The power set of S0 is
| examples =The power set P({0, 1, 2}) is the set of all subsets of {0, 1, 2}. Hence,
P({0, 1, 2}) = {âˆ…, {0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {0, 1, 2} }.}}{hide}row of table of mathematical symbols
| symbol = {{math|â„š{edih}{{math|Q}}
| tex = mathbb{Q}mathbb{Q} mathbf{Q}mathbf{Q}
| rowspan = 1
| name = rational numbers
| readas = Q;the (set of) rational numbers;the rationals
| category = numbers
| explain = â„š means {p/q : p âˆˆ â„¤, q âˆˆ â„•}.
| examples = 3.14000... âˆˆ â„šÏ€ âˆ‰ â„š
}}{hide}row of table of mathematical symbols
| tex = mathbb{Q}mathbb{Q} mathbf{Q}mathbf{Q}
| rowspan = 1
| name = rational numbers
| readas = Q;the (set of) rational numbers;the rationals
| category = numbers
| explain = â„š means {p/q : p âˆˆ â„¤, q âˆˆ â„•}.
| examples = 3.14000... âˆˆ â„šÏ€ âˆ‰ â„š
| symbol = {{math|â„{edih}{{math|R}}
| tex = mathbb{R}mathbb{R} mathbf{R}mathbf{R}
| rowspan = 1
| name = real numbers
| readas = R;the (set of) real numbers;the reals
| category = numbers
| explain = â„ means the set of real numbers.
| tex = mathbb{R}mathbb{R} mathbf{R}mathbf{R}
| rowspan = 1
| name = real numbers
| readas = R;the (set of) real numbers;the reals
| category = numbers
| explain = â„ means the set of real numbers.
| examples = Ï€ âˆˆ â„âˆš(âˆ’1) âˆ‰ â„
}}{hide}row of table of mathematical symbols
| symbol = {{math|â€ {edih}
| tex = {}^dagger{}^dagger
| rowspan = 1
| name = conjugate transpose
| readas = conjugate transpose;adjoint;Hermitian adjoint/conjugate/transpose/dagger
| category = matrix operations
| explain = Aâ€ means the transpose of the complex conjugate of A.{{citation | title=Quantum Computation and Quantum Information | last1=Nielsen | first1=Michael A | author1-link=Michael Nielsen | last2=Chuang | first2=Isaac L | year=2000 | publisher=Cambridge University Press | location=New York | isbn=0-521-63503-9 | oclc= 43641333 | pages=69â€“70 }}This may also be written Aâˆ—T, ATâˆ—, Aâˆ—, {{overline|A}}T or {{overline|AT}}.
| examples = If A = (a'ij) then Aâ€ = ({{overline|a'ji}}).
}}{hide}row of table of mathematical symbols
| tex = {}^dagger{}^dagger
| rowspan = 1
| name = conjugate transpose
| readas = conjugate transpose;adjoint;Hermitian adjoint/conjugate/transpose/dagger
| category = matrix operations
| explain = Aâ€ means the transpose of the complex conjugate of A.{{citation | title=Quantum Computation and Quantum Information | last1=Nielsen | first1=Michael A | author1-link=Michael Nielsen | last2=Chuang | first2=Isaac L | year=2000 | publisher=Cambridge University Press | location=New York | isbn=0-521-63503-9 | oclc= 43641333 | pages=69â€“70 }}This may also be written Aâˆ—T, ATâˆ—, Aâˆ—, {{overline|A}}T or {{overline|AT}}.
| examples = If A = (a'ij) then Aâ€ = ({{overline|a'ji}}).
| symbol = {{math|T{edih}
| tex = {}^{mathsf{T}}{}^{mathsf{T}}
| rowspan = 1
| name = transpose
| readas = transpose
| category = matrix operations
| explain = AT means A, but with its rows swapped for columns. This may also be written Aâ€², At or Atr.
| examples = If A = (a'ij) then AT = (a'ji).
}}{hide}row of table of mathematical symbols
| tex = {}^{mathsf{T}}{}^{mathsf{T}}
| rowspan = 1
| name = transpose
| readas = transpose
| category = matrix operations
| explain = AT means A, but with its rows swapped for columns. This may also be written Aâ€², At or Atr.
| examples = If A = (a'ij) then AT = (a'ji).
| symbol = {{math|âŠ¤{edih}
| tex = toptop
| rowspan = 2
| name = top element
| readas = the top element
| category = lattice theory
| explain = âŠ¤ means the largest element of a lattice.
| examples = âˆ€x : x âˆ¨ âŠ¤ = âŠ¤
}}{{row of table of mathematical symbols
| tex = toptop
| rowspan = 2
| name = top element
| readas = the top element
| category = lattice theory
| explain = âŠ¤ means the largest element of a lattice.
| examples = âˆ€x : x âˆ¨ âŠ¤ = âŠ¤
| name = top type
| readas = the top type; top
| category = type theory
| explain = âŠ¤ means the top or universal type; every type in the type system of interest is a subtype of top.
| examples = âˆ€ types T, T
{hide}row of table of mathematical symbols
| readas = the top type; top
| category = type theory
| explain = âŠ¤ means the top or universal type; every type in the type system of interest is a subtype of top.
| examples = âˆ€ types T, T
| symbol = {{math|âˆ¨{edih}
| tex = lorlor
| rowspan = 1
| name = logical disjunction or join in a lattice
| readas = or;max;join
| category = propositional logic, lattice theory
| explain = The statement A âˆ¨ B is true if A or B (or both) are true; if both are false, the statement is false. For functions A(x) and B(x), A(x) âˆ¨ B(x) is used to mean max(A(x), B(x)).
| examples = n â‰¥ 4 âˆ¨ n â‰¤ 2 â‡” n â‰ 3 when n is a natural number.
}}{hide}row of table of mathematical symbols
| tex = lorlor
| rowspan = 1
| name = logical disjunction or join in a lattice
| readas = or;max;join
| category = propositional logic, lattice theory
| explain = The statement A âˆ¨ B is true if A or B (or both) are true; if both are false, the statement is false. For functions A(x) and B(x), A(x) âˆ¨ B(x) is used to mean max(A(x), B(x)).
| examples = n â‰¥ 4 âˆ¨ n â‰¤ 2 â‡” n â‰ 3 when n is a natural number.
| symbol = {{math|âˆ§{edih}
| tex = landland
| rowspan = 2
| name = logical conjunction or meet in a lattice
| readas = and;min;meet
| category = propositional logic, lattice theory
| explain = The statement A âˆ§ B is true if A and B are both true; else it is false. For functions A(x) and B(x), A(x) âˆ§ B(x) is used to mean min(A(x), B(x)).
| examples = n < 4 âˆ§ n > 2 â‡” n = 3 when n is a natural number.
}}{{row of table of mathematical symbols
| tex = landland
| rowspan = 2
| name = logical conjunction or meet in a lattice
| readas = and;min;meet
| category = propositional logic, lattice theory
| explain = The statement A âˆ§ B is true if A and B are both true; else it is false. For functions A(x) and B(x), A(x) âˆ§ B(x) is used to mean min(A(x), B(x)).
| examples = n < 4 âˆ§ n > 2 â‡” n = 3 when n is a natural number.
| name = wedge product
| readas = wedge product;exterior product
| category = exterior algebra
| explain = u âˆ§ v means the wedge product of any multivectors u and v. In three-dimensional Euclidean space the wedge product and the cross product of two vectors are each other's Hodge dual.
| examples = u wedge v = *(u times v) text{ if } u, v in mathbb{R}^3
}}{hide}row of table of mathematical symbols
| readas = wedge product;exterior product
| category = exterior algebra
| explain = u âˆ§ v means the wedge product of any multivectors u and v. In three-dimensional Euclidean space the wedge product and the cross product of two vectors are each other's Hodge dual.
| examples = u wedge v = *(u times v) text{ if } u, v in mathbb{R}^3
| symbol = {{math|Ã—{edih}
| tex = timestimes
| rowspan = 4
| name = multiplication
| readas = times;multiplied by
| category = arithmetic
| explain = 3 Ã— 4 means the multiplication of 3 by 4.(The symbol * is generally used in programming languages, where ease of typing and use of ASCII text is preferred.)
| examples = 7 Ã— 8 = 56
}}{{row of table of mathematical symbols
| tex = timestimes
| rowspan = 4
| name = multiplication
| readas = times;multiplied by
| category = arithmetic
| explain = 3 Ã— 4 means the multiplication of 3 by 4.(The symbol * is generally used in programming languages, where ease of typing and use of ASCII text is preferred.)
| examples = 7 Ã— 8 = 56
| name = Cartesian product
| readas = the Cartesian product of ... and ...;the direct product of ... and ...
| category = set theory
| explain = X Ã— Y means the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y.
| examples = {1,2} Ã— {3,4} = {(1,3),(1,4),(2,3),(2,4)}
}}{hide}row of table of mathematical symbols
| readas = the Cartesian product of ... and ...;the direct product of ... and ...
| category = set theory
| explain = X Ã— Y means the set of all ordered pairs with the first element of each pair selected from X and the second element selected from Y.
| examples = {1,2} Ã— {3,4} = {(1,3),(1,4),(2,3),(2,4)}
| name = cross product
| readas = cross
| category = linear algebra
| explain = u Ã— v means the cross product of vectors u and v
| examples = (1,2,5) Ã— (3,4,âˆ’1) = (âˆ’22, 16, âˆ’ 2)
{edih}{{row of table of mathematical symbols
| readas = cross
| category = linear algebra
| explain = u Ã— v means the cross product of vectors u and v
| examples = (1,2,5) Ã— (3,4,âˆ’1) = (âˆ’22, 16, âˆ’ 2)
| name = group of units
| readas = the group of units of
| category = ring theory
| explain = RÃ— consists of the set of units of the ring R, along with the operation of multiplication.This may also be written Râˆ— as described below, or U(R).
| examples = begin{align} (mathbb{Z} / 5mathbb{Z})^times & = { [1], [2], [3], [4] } & cong mathrm{C}_4 end{align}
}}{hide}row of table of mathematical symbols
| readas = the group of units of
| category = ring theory
| explain = RÃ— consists of the set of units of the ring R, along with the operation of multiplication.This may also be written Râˆ— as described below, or U(R).
| examples = begin{align} (mathbb{Z} / 5mathbb{Z})^times & = { [1], [2], [3], [4] } & cong mathrm{C}_4 end{align}
| symbol = {{math|âŠ—{edih}
| tex = otimesotimes
| rowspan = 1
| name = tensor product, tensor product of modules
| readas = tensor product of
| category = linear algebra
| explain = V otimes U means the tensor product of V and U.{{citation | title=Quantum Computation and Quantum Information | last1=Nielsen | first1=Michael A | author1-link=Michael Nielsen | last2=Chuang | first2=Isaac L | year=2000 | publisher = Cambridge University Press | location=New York | isbn=0-521-63503-9 | oclc= 43641333 | pages=71â€“72 }} V otimes_R U means the tensor product of modules V and U over the ring R.
| examples = {1, 2, 3, 4} âŠ— {1, 1, 2} = {{1, 1, 2}, {2, 2, 4}, {3, 3, 6}, {4, 4, 8}}
}}{hide}row of table of mathematical symbols
| tex = otimesotimes
| rowspan = 1
| name = tensor product, tensor product of modules
| readas = tensor product of
| category = linear algebra
| explain = V otimes U means the tensor product of V and U.{{citation | title=Quantum Computation and Quantum Information | last1=Nielsen | first1=Michael A | author1-link=Michael Nielsen | last2=Chuang | first2=Isaac L | year=2000 | publisher = Cambridge University Press | location=New York | isbn=0-521-63503-9 | oclc= 43641333 | pages=71â€“72 }} V otimes_R U means the tensor product of modules V and U over the ring R.
| examples = {1, 2, 3, 4} âŠ— {1, 1, 2} = {{1, 1, 2}, {2, 2, 4}, {3, 3, 6}, {4, 4, 8}}
| symbol = {{math|â‹‰{edih}{{math|â‹Š}}
| tex = ltimesltimesrtimesrtimes
| rowspan = 2
| name = semidirect product
| readas = the semidirect product of
| category = group theory
| explain = N â‹ŠÏ† H is the semidirect product of N (a normal subgroup) and H (a subgroup), with respect to Ï†. Also, if G = N â‹ŠÏ† H, then G is said to split over N.(â‹Š may also be written the other way round, as â‹‰, or as Ã—.)
| examples = D_{2n} cong mathrm{C}_n rtimes mathrm{C}_2
}}{{row of table of mathematical symbols
| tex = ltimesltimesrtimesrtimes
| rowspan = 2
| name = semidirect product
| readas = the semidirect product of
| category = group theory
| explain = N â‹ŠÏ† H is the semidirect product of N (a normal subgroup) and H (a subgroup), with respect to Ï†. Also, if G = N â‹ŠÏ† H, then G is said to split over N.(â‹Š may also be written the other way round, as â‹‰, or as Ã—.)
| examples = D_{2n} cong mathrm{C}_n rtimes mathrm{C}_2
| name = semijoin
| readas = the semijoin of
| category = relational algebra
| explain = R â‹‰ S is the semijoin of the relations R and S, the set of all tuples in R for which there is a tuple in S that is equal on their common attribute names.
| examples = R ltimes S = Pia1,..,an(R bowtie S)
}}{hide}row of table of mathematical symbols
| readas = the semijoin of
| category = relational algebra
| explain = R â‹‰ S is the semijoin of the relations R and S, the set of all tuples in R for which there is a tuple in S that is equal on their common attribute names.
| examples = R ltimes S = Pia1,..,an(R bowtie S)
| symbol = {{math|â‹ˆ{edih}
| tex = bowtiebowtie
| rowspan = 1
| name = natural join
| readas = the natural join of
| category = relational algebra
| explain = R â‹ˆ S is the natural join of the relations R and S, the set of all combinations of tuples in R and S that are equal on their common attribute names.
| examples =
}}{hide}row of table of mathematical symbols
| tex = bowtiebowtie
| rowspan = 1
| name = natural join
| readas = the natural join of
| category = relational algebra
| explain = R â‹ˆ S is the natural join of the relations R and S, the set of all combinations of tuples in R and S that are equal on their common attribute names.
| examples =
| symbol = {{math|â„¤{edih}{{math|Z}}
| tex = mathbb{Z}mathbb{Z}mathbf{Z}mathbf{Z}
| rowspan = 1
| name = integers
| readas = the (set of) integers
| category = numbers
| explain = â„¤ means {..., âˆ’3, âˆ’2, âˆ’1, 0, 1, 2, 3, ...}.
â„¤+ or â„¤> means {1, 2, 3, ...} .â„¤â‰¥ means {0, 1, 2, 3, ...} .â„¤* is used by some authors to mean {0, 1, 2, 3, ...}Z^* from Wolfram MathWorldand others to mean {... -2, -1, 1, 2, 3, ... }LK Turner, FJ BUdden, D Knighton, "Advanced Mathematics", Book 2, Longman 1975. .
| tex = mathbb{Z}mathbb{Z}mathbf{Z}mathbf{Z}
| rowspan = 1
| name = integers
| readas = the (set of) integers
| category = numbers
| explain = â„¤ means {..., âˆ’3, âˆ’2, âˆ’1, 0, 1, 2, 3, ...}.
| examples = â„¤ = {p, âˆ’p : p âˆˆ â„• âˆª {0}}
}}{hide}row of table of mathematical symbols
| symbol = {{math|â„¤n{edih}{{math|â„¤p}}{{math|Zn}}{{math|Zp}}
| tex =mathbb{Z}_nmathbb{Z}_nmathbb{Z}_pmathbb{Z}_pmathbf{Z}_nmathbf{Z}_nmathbf{Z}_p
| rowspan = 2
| name = integers mod n
| readas = the (set of) integers modulo n
| category = numbers
| explain = â„¤n means {[0], [1], [2], ...[nâˆ’1]} with addition and multiplication modulo n.Note that any letter may be used instead of n, such as p. To avoid confusion with p-adic numbers, use â„¤/pâ„¤ or â„¤/(p) instead.
| examples = â„¤3 = {[0], [1], [2]}
}}{{row of table of mathematical symbols
| tex =mathbb{Z}_nmathbb{Z}_nmathbb{Z}_pmathbb{Z}_pmathbf{Z}_nmathbf{Z}_nmathbf{Z}_p
| rowspan = 2
| name = integers mod n
| readas = the (set of) integers modulo n
| category = numbers
| explain = â„¤n means {[0], [1], [2], ...[nâˆ’1]} with addition and multiplication modulo n.Note that any letter may be used instead of n, such as p. To avoid confusion with p-adic numbers, use â„¤/pâ„¤ or â„¤/(p) instead.
| examples = â„¤3 = {[0], [1], [2]}
| name = p-adic integers
| readas = the (set of) p-adic integers
| category = numbers
| explain = Note that any letter may be used instead of p, such as n or l.
| examples =
}}| readas = the (set of) p-adic integers
| category = numbers
| explain = Note that any letter may be used instead of p, such as n or l.
| examples =
Symbols based on Hebrew or Greek letters{| class"wikitable" style"margin:auto; width:100%; border:1px"
! rowspan="3" style="font-size:130%;" | Symbolin HTML! rowspan="3" style="font-size:130%;" | Symbolin TeX! style="text-align:left;" | Name! rowspan="3" style="font-size:130%;" | Explanation! rowspan="3" style="font-size:130%;" | Examples! Read as
| symbol = {{math|â„µ{edih}
| tex = alephaleph
| rowspan = 1
| name = aleph number
| readas = aleph
| category = set theory
| explain = â„µÎ± represents an infinite cardinality (specifically, the Î±-th one, where Î± is an ordinal).
| examples = |â„•| = â„µ0, which is called aleph-null.
}}{hide}row of table of mathematical symbols
| tex = alephaleph
| rowspan = 1
| name = aleph number
| readas = aleph
| category = set theory
| explain = â„µÎ± represents an infinite cardinality (specifically, the Î±-th one, where Î± is an ordinal).
| examples = |â„•| = â„µ0, which is called aleph-null.
| symbol = {{math|â„¶{edih}
| tex = bethbeth
| rowspan = 1
| name = beth number
| readas = beth
| category = set theory
| explain = â„¶Î± represents an infinite cardinality (similar to â„µ, but â„¶ does not necessarily index all of the numbers indexed by â„µ. ).
| examples = beth_1 = |P(mathbb{N})| = 2^{aleph_0}.
}}{hide}row of table of mathematical symbols
| tex = bethbeth
| rowspan = 1
| name = beth number
| readas = beth
| category = set theory
| explain = â„¶Î± represents an infinite cardinality (similar to â„µ, but â„¶ does not necessarily index all of the numbers indexed by â„µ. ).
| examples = beth_1 = |P(mathbb{N})| = 2^{aleph_0}.
| symbol = {{math|Î´{edih}
| tex = deltadelta
| rowspan = 3
| name = Dirac delta function
| readas = Dirac delta of
| category = hyperfunction
| explain = delta(x) = begin{cases} infty, & x = 0 0, & x ne 0 end{cases}
| examples = Î´(x)
}}{hide}row of table of mathematical symbols
| tex = deltadelta
| rowspan = 3
| name = Dirac delta function
| readas = Dirac delta of
| category = hyperfunction
| explain = delta(x) = begin{cases} infty, & x = 0 0, & x ne 0 end{cases}
| examples = Î´(x)
| name = Kronecker delta
| readas = Kronecker delta of
| category = hyperfunction
| explain = delta_{ij} = begin{cases} 1, & i = j 0, & i ne j end{cases}
| examples = Î´ij
{edih}{{row of table of mathematical symbols
| readas = Kronecker delta of
| category = hyperfunction
| explain = delta_{ij} = begin{cases} 1, & i = j 0, & i ne j end{cases}
| examples = Î´ij
| name = Functional derivative
| readas = Functional derivative of
| category = Differential operators
| explain =
begin{align}leftlangle frac{delta F[varphi(x)]}{deltavarphi(x)}, f(x) rightrangle&= int frac{delta F[varphi(x)]}{deltavarphi(x')} f(x')dx' &= lim_{varepsilonto 0}frac{F[varphi(x)+varepsilon f(x)]-F[varphi(x)]}{varepsilon} &= left.frac{d}{depsilon}F[varphi+epsilon f]right|_{epsilon=0}.end{align}
| readas = Functional derivative of
| category = Differential operators
| explain =
| examples =
frac{delta V(r)}{delta rho(r')} = frac{1}{4piepsilon_0|r-r'|}}}{hide}row of table of mathematical symbols
| symbol = {{math|âˆ†{edih}{{math|âŠ–}}{{math|âŠ•}}
| tex = vartrianglevartriangle ominusominus oplusoplus
| rowspan = 1
| name = symmetric difference
| readas = symmetric difference
| category = set theory
| explain = A âˆ† B (or A âŠ– B) means the set of elements in exactly one of A or B.(Not to be confused with delta, Î”, described below.)
| examples = {1,5,6,8} âˆ† {2,5,8} = {1,2,6}{3,4,5,6} âŠ– {1,2,5,6} = {1,2,3,4}
}}{hide}row of table of mathematical symbols
| tex = vartrianglevartriangle ominusominus oplusoplus
| rowspan = 1
| name = symmetric difference
| readas = symmetric difference
| category = set theory
| explain = A âˆ† B (or A âŠ– B) means the set of elements in exactly one of A or B.(Not to be confused with delta, Î”, described below.)
| examples = {1,5,6,8} âˆ† {2,5,8} = {1,2,6}{3,4,5,6} âŠ– {1,2,5,6} = {1,2,3,4}
| symbol = {{math|Î”{edih}
| tex = DeltaDelta
| rowspan = 2
| name = delta
| readas = delta;change in
| category = calculus
| explain = Î”x means a (non-infinitesimal) change in x.(If the change becomes infinitesimal, Î´ and even d are used instead. Not to be confused with the symmetric difference, written âˆ†, above.)
| examples = tfrac{Delta y}{Delta x} is the gradient of a straight line.
}}{hide}row of table of mathematical symbols
| tex = DeltaDelta
| rowspan = 2
| name = delta
| readas = delta;change in
| category = calculus
| explain = Î”x means a (non-infinitesimal) change in x.(If the change becomes infinitesimal, Î´ and even d are used instead. Not to be confused with the symmetric difference, written âˆ†, above.)
| examples = tfrac{Delta y}{Delta x} is the gradient of a straight line.
| name = Laplacian
| readas = Laplace operator
| category = vector calculus
| explain = The Laplace operator is a second order differential operator in n-dimensional Euclidean space
| examples = If Æ’ is a twice-differentiable real-valued function, then the Laplacian of Æ’ is defined by Delta f = nabla^2 f = nabla cdot nabla f
{edih}{hide}row of table of mathematical symbols
| readas = Laplace operator
| category = vector calculus
| explain = The Laplace operator is a second order differential operator in n-dimensional Euclidean space
| examples = If Æ’ is a twice-differentiable real-valued function, then the Laplacian of Æ’ is defined by Delta f = nabla^2 f = nabla cdot nabla f
| symbol = {{math|âˆ‡{edih}
| tex = nablanabla
| rowspan = 3
| name = gradient
| readas = del;nabla;gradient of
| category = vector calculus
| explain = âˆ‡f (x1, ..., xn) is the vector of partial derivatives (âˆ‚f / âˆ‚x1, ..., âˆ‚f / âˆ‚xn).
| examples = If f (x,y,z) := 3xy + zÂ², then âˆ‡f = (3y, 3x, 2z)
}}{{row of table of mathematical symbols
| tex = nablanabla
| rowspan = 3
| name = gradient
| readas = del;nabla;gradient of
| category = vector calculus
| explain = âˆ‡f (x1, ..., xn) is the vector of partial derivatives (âˆ‚f / âˆ‚x1, ..., âˆ‚f / âˆ‚xn).
| examples = If f (x,y,z) := 3xy + zÂ², then âˆ‡f = (3y, 3x, 2z)
| name = divergence
| readas = del dot;divergence of
| category = vector calculus
| explain = nabla cdot vec v = {partial v_x over partial x} + {partial v_y over partial y} + {partial v_z over partial z}
| examples = If vec v := 3xymathbf{i}+y^2 zmathbf{j}+5mathbf{k} , then nabla cdot vec v = 3y + 2yz .
}}{{row of table of mathematical symbols
| readas = del dot;divergence of
| category = vector calculus
| explain = nabla cdot vec v = {partial v_x over partial x} + {partial v_y over partial y} + {partial v_z over partial z}
| examples = If vec v := 3xymathbf{i}+y^2 zmathbf{j}+5mathbf{k} , then nabla cdot vec v = 3y + 2yz .
| name = curl
| readas = curl of
| category = vector calculus
| explain = nabla times vec v = left( {partial v_z over partial y} - {partial v_y over partial z} right) mathbf{i} + left( {partial v_x over partial z} - {partial v_z over partial x} right) mathbf{j} + left( {partial v_y over partial x} - {partial v_x over partial y} right) mathbf{k}
| examples = If vec v := 3xymathbf{i}+y^2 zmathbf{j}+5mathbf{k} , then nablatimesvec v = -y^2mathbf{i} - 3xmathbf{k} .
}}{hide}row of table of mathematical symbols
| readas = curl of
| category = vector calculus
| explain = nabla times vec v = left( {partial v_z over partial y} - {partial v_y over partial z} right) mathbf{i} + left( {partial v_x over partial z} - {partial v_z over partial x} right) mathbf{j} + left( {partial v_y over partial x} - {partial v_x over partial y} right) mathbf{k}
| examples = If vec v := 3xymathbf{i}+y^2 zmathbf{j}+5mathbf{k} , then nablatimesvec v = -y^2mathbf{i} - 3xmathbf{k} .
| symbol = {{math|Ï€{edih}
| tex = pipi
| rowspan = 3
| name = Pi
| readas = pi;3.1415926...;â‰ˆ355Ã·113
| category = mathematical constant
| explain = Used in various formulas involving circles; {{pi}} is equivalent to the amount of area a circle would take up in a square of equal width with an area of 4 square units, roughly 3.14159. It is also the ratio of the circumference to the diameter of a circle.
| examples = A = Ï€R2 = 314.16 â†’ R = 10
}}{{row of table of mathematical symbols
| tex = pipi
| rowspan = 3
| name = Pi
| readas = pi;3.1415926...;â‰ˆ355Ã·113
| category = mathematical constant
| explain = Used in various formulas involving circles; {{pi}} is equivalent to the amount of area a circle would take up in a square of equal width with an area of 4 square units, roughly 3.14159. It is also the ratio of the circumference to the diameter of a circle.
| examples = A = Ï€R2 = 314.16 â†’ R = 10
| name = projection
| readas = Projection of
| category = relational algebra
| explain = pi_{a_1, ldots,a_n}( R ) restricts R to the {a_1,ldots,a_n} attribute set.
| examples = pi_{text{Age,Weight}}(text{Person})
}}{{row of table of mathematical symbols
| readas = Projection of
| category = relational algebra
| explain = pi_{a_1, ldots,a_n}( R ) restricts R to the {a_1,ldots,a_n} attribute set.
| examples = pi_{text{Age,Weight}}(text{Person})
| name = Homotopy group
| readas = the nth Homotopy group of
| category = Homotopy theory
| explain = pi_n( X ) consists of homotopy equivalence classes of base point preserving maps from an n-dimensional sphere (with base point) into the pointed space X.
| examples = pi_i(S^4)= pi_i(S^7)oplus pi_{i-1}(S^3)
}}{hide}row of table of mathematical symbols
| readas = the nth Homotopy group of
| category = Homotopy theory
| explain = pi_n( X ) consists of homotopy equivalence classes of base point preserving maps from an n-dimensional sphere (with base point) into the pointed space X.
| examples = pi_i(S^4)= pi_i(S^7)oplus pi_{i-1}(S^3)
| symbol = {{math|âˆ{edih}
| tex = prodprod
| rowspan = 2
| name = product
| readas = product over ... from ... to ... of
| category = arithmetic
| explain = prod_{k=1}^na_k means a_1 a_2 dots a_n.
| examples = prod_{k=1}^4(k+2) = (1+2)(2+2)(3+2)(4+2) = 3 times 4 times 5 times 6 = 360
}}{{row of table of mathematical symbols
| tex = prodprod
| rowspan = 2
| name = product
| readas = product over ... from ... to ... of
| category = arithmetic
| explain = prod_{k=1}^na_k means a_1 a_2 dots a_n.
| examples = prod_{k=1}^4(k+2) = (1+2)(2+2)(3+2)(4+2) = 3 times 4 times 5 times 6 = 360
| name = Cartesian product
| readas = the Cartesian product of;the direct product of
| category = set theory
| explain = prod_{i=0}^{n}{Y_i} means the set of all (n+1)-tuples
| readas = the Cartesian product of;the direct product of
| category = set theory
| explain = prod_{i=0}^{n}{Y_i} means the set of all (n+1)-tuples
(y0, ..., yn).
| examples = prod_{n=1}^{3}{mathbb{R}} = mathbb{R}timesmathbb{R}timesmathbb{R} = mathbb{R}^3
}}{hide}row of table of mathematical symbols
| symbol = {{math|âˆ{edih}
| tex = coprodcoprod
| rowspan = 1
| name = coproduct
| readas = coproduct over ... from ... to ... of
| category = category theory
| explain = A general construction which subsumes the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism.
| examples =
}}{hide}row of table of mathematical symbols
| tex = coprodcoprod
| rowspan = 1
| name = coproduct
| readas = coproduct over ... from ... to ... of
| category = category theory
| explain = A general construction which subsumes the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism.
| examples =
| symbol = {{math|Ïƒ{edih}
| tex = sigma sigma
| rowspan = 1
| name = selection
| readas = Selection of
| category = relational algebra
| explain = The selection sigma_{a theta b}( R ) selects all those tuples in R for which theta holds between the a and the b attribute. The selection sigma_{a theta v}( R ) selects all those tuples in R for which theta holds between the a attribute and the value v.
| examples = sigma_{mathrm{Age} ge 34}(mathrm{Person}) sigma_{mathrm{Age} = mathrm{Weight}}(mathrm{Person})
}}{hide}row of table of mathematical symbols
| tex = sigma sigma
| rowspan = 1
| name = selection
| readas = Selection of
| category = relational algebra
| explain = The selection sigma_{a theta b}( R ) selects all those tuples in R for which theta holds between the a and the b attribute. The selection sigma_{a theta v}( R ) selects all those tuples in R for which theta holds between the a attribute and the value v.
| examples = sigma_{mathrm{Age} ge 34}(mathrm{Person}) sigma_{mathrm{Age} = mathrm{Weight}}(mathrm{Person})
| symbol = {{math|âˆ‘{edih}
| tex = sumsum
| rowspan = 1
| name = summation
| readas = sum over ... from ... to ... of
| category = arithmetic
| explain = sum_{k=1}^{n}{a_k} means a_1 + a_2 + cdots + a_n.
| examples = sum_{k=1}^{4}{k^2} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30
}}| tex = sumsum
| rowspan = 1
| name = summation
| readas = sum over ... from ... to ... of
| category = arithmetic
| explain = sum_{k=1}^{n}{a_k} means a_1 + a_2 + cdots + a_n.
| examples = sum_{k=1}^{4}{k^2} = 1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30
Variations
In mathematics written in Persian or Arabic, some symbols may be reversed to make right-to-left writing and reading easier.M. Benatia, A. Lazrik, and K. Sami, "Arabic mathematical symbols in Unicode", 27th Internationalization and Unicode Conference, 2005.See also
- Greek letters used in mathematics, science, and engineering
- List of letters used in mathematics and science
- List of common physics notations
- Diacritic
- ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)
- Latin letters used in mathematics
- List of mathematical abbreviations
- List of mathematical symbols by subject
- Mathematical Alphanumeric Symbols (Unicode block)
- Mathematical constants and functions
- Mathematical notation
- Mathematical operators and symbols in Unicode
- Notation in probability and statistics
- Physical constants
- Table of logic symbols
- Table of mathematical symbols by introduction date
- Typographical conventions in mathematical formulae
- APL syntax and symbols
References
External links
- Jeff Miller: Earliest Uses of Various Mathematical Symbols
- Numericana: Scientific Symbols and Icons
- GIF and PNG Images for Math Symbols
- weblink" title="web.archive.org/web/20070117015443weblink">Mathematical Symbols in Unicode
- Using Greek and special characters from Symbol font in HTML
- DeTeXify handwritten symbol recognition â€” doodle a symbol in the box, and the program will tell you what its name is
- Handbook for Spoken Mathematics â€” pronunciation guide to many commonly used symbols
- Index of Unicode symbols
- Range 2100â€“214F: Unicode Letterlike Symbols
- Range 2190â€“21FF: Unicode Arrows
- Range 2200â€“22FF: Unicode Mathematical Operators
- Range 27C0â€“27EF: Unicode Miscellaneous Mathematical Symbolsâ€“A
- Range 2980â€“29FF: Unicode Miscellaneous Mathematical Symbolsâ€“B
- Range 2A00â€“2AFF: Unicode Supplementary Mathematical Operators
- Short list of commonly used LaTeX symbols and weblink" title="web.archive.org/web/20090323063515weblink">Comprehensive LaTeX Symbol List
- MathML Characters - sorts out Unicode, HTML and MathML/TeX names on one page
- Unicode values and MathML names
- Unicode values and Postscript names from the source code for Ghostscript
- content above as imported from Wikipedia
- "List of mathematical symbols" does not exist on GetWiki (yet)
- time: 6:52pm EST - Thu, Jan 17 2019
- "List of mathematical symbols" does not exist on GetWiki (yet)
- time: 6:52pm EST - Thu, Jan 17 2019
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