Table of mathematical symbols by introduction date について

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Table of mathematical symbols by introduction date ：ウィキペディア英語版

Table of mathematical symbols by introduction date

The following table lists many specialized symbols commonly used in mathematics, ordered by their introduction date.

||set brackets
| rowspan=3| means the set consisting of ''a'', ''b'', and ''c''.
| rowspan=3|ℕ =
|-
|align=center|the set of …
|-
|align=right|set theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

\Delta

||symmetric difference
| rowspan=3|

A\Delta B

means the set of elements in exactly one of ''A'' or ''B''.
| rowspan=3|

\Delta

=
|-
|align=center|symmetric difference
|-
|align=right|set theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

∖

||set-theoretic complement
| rowspan=3|''A'' ∖ ''B'' means the set that contains all those elements of ''A'' that are not in ''B''.
| rowspan=3| ∖ =
|-
|align=center|minus; without
|-
|align=right|set theory
|-
| rowspan=6 bgcolor=#d0f0d0 align=center|

( )

||function application
| rowspan=3|''f''(''x'') means the value of the function ''f'' at the element ''x''.
| rowspan=3|If ''f''(''x'') := ''x''², then ''f''(3) = 3² = 9.
|-
|align=center|of
|-
|align=right|set theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

||function composition
| rowspan=3|''f''o''g'' is the function, such that (''f''o''g'')(''x'') = ''f''(''g''(''x'')).
| rowspan=3|if ''f''(''x'') := 2''x'', and ''g''(''x'') := ''x'' + 3, then (''f''o''g'')(''x'') = 2(''x'' + 3).
|-
|align=center|composed with
|-
|align=right|set theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

''π''

||pi
| rowspan=3|''π'' is the ratio of a circle's circumference to its diameter. Its value is 3.14159265... .
| rowspan=3|''A'' = ''π'' ''r''² is the area of a circle with radius ''r''
''π'' radians = 180°
''π'' ≈ 22 / 7
|-
|align=center|pi
|-
|align=right|Euclidean geometry
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

||…||

||norm
| rowspan=3| || ''x'' || is the norm of the element ''x'' of a normed vector space.
| rowspan=3| || ''x'' + ''y'' || ≤ || ''x'' || + || ''y'' ||
|-
|align=center|norm of
length of
|-
|align=right| linear algebra
|-
||Cartesian product
| rowspan=3|

\prod_^

means the set of all (n+1)-tuples
::(''y''₀, …, ''y''_''n'').
| rowspan=3|

\prod_^\times\mathbb\times\mathbb = \mathbb^3

∐

||coproduct
| rowspan=3|
| rowspan=3|
|-
|align=center|coproduct over … from … to … of
|-
|align=right|category theory
|-
|boundary
| rowspan=3| ∂''M'' means the boundary of ''M''
| rowspan=3| ∂ =
|-
|align=center|boundary of
|-
|align=right|topology
|-
| rowspan=6 bgcolor=#d0f0d0 align=center|

⊥

||perpendicular
| rowspan=3|''x'' ⊥ ''y'' means ''x'' is perpendicular to ''y''; or more generally ''x'' is orthogonal to ''y''.
| rowspan=3|If ''l'' ⊥ ''m'' and ''m'' ⊥ ''n'' then ''l'' || ''n''.
|-
|align=center|is perpendicular to
|-
|align=right|geometry
|-
||bottom element
| rowspan=3|''x'' = ⊥ means ''x'' is the smallest element.
| rowspan=3|∀''x'' : ''x'' ∧ ⊥ = ⊥
|-
|align=center|the bottom element
|-
|align=right|lattice theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

||parallel
| rowspan=3|''x'' || ''y'' means ''x'' is parallel to ''y''.
| rowspan=3|If ''l'' || ''m'' and ''m'' ⊥ ''n'' then ''l'' ⊥ ''n''.
|-
|align=center|is parallel to
|-
|align=right|geometry
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

⊧

||entailment
| rowspan=3| ''A'' ⊧ ''B'' means the sentence ''A'' entails the sentence ''B'', that is every model in which ''A'' is true, ''B'' is also true.
| rowspan=3| ''A'' ⊧ ''A'' ∨ ¬''A''
|-
|align=center|entails
|-
|align=right| model theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

⊢

||inference
| rowspan=3|''x'' ⊢ ''y'' means ''y'' is derived from ''x''.
| rowspan=3| ''A'' → ''B'' ⊢ ¬''B'' → ¬''A''
|-
|align=center|infers or is derived from
|-
|align=right|propositional logic, predicate logic
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

◅

||normal subgroup
| rowspan=3| ''N'' ◅ ''G'' means that ''N'' is a normal subgroup of group ''G''.
| rowspan=3| ''Z''(''G'') ◅ ''G''
|-
|align=center|is a normal subgroup of
|-
|align=right|group theory
|-
| rowspan=6 bgcolor=#d0f0d0 align=center|

||quotient group
| rowspan=3| ''G''/''H'' means the quotient of group ''G'' modulo its subgroup ''H''.
| rowspan=3| / =
|-
|align=center| mod
|-
|align=right| group theory
|-
|quotient set
| rowspan=3| ''A''/~ means the set of all ~ equivalence classes in ''A''.
|-
|align=center|
|-
|align=right| set theory
|-
| rowspan=6 bgcolor=#d0f0d0 align=center|

≈

||isomorphism
| rowspan=3| ''G'' ≈ ''H'' means that group ''G'' is isomorphic to group ''H''
| rowspan=3| ''Q'' / ≈ ''V'',
where ''Q'' is the quaternion group and ''V'' is the Klein four-group.
|-
|align=center | is isomorphic to
|-
|align=right| group theory
|-
|approximately equal
| rowspan=3|''x'' ≈ ''y'' means ''x'' is approximately equal to ''y''
| rowspan=3|π ≈ 3.14159
|-
|align=center|is approximately equal to
|-
|align=right|everywhere
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

||same order of magnitude
| rowspan=3| ''m'' ~ ''n'', means the quantities ''m'' and ''n'' have the general size.
(''Note that'' ~ ''is used for an approximation that is poor, otherwise use '' ≈ .)
| rowspan=3|2 ~ 5
8 × 9 ~ 100
but π² ≈ 10
|-
|align=right|roughly similar
poorly approximates
|-
|align=right|Approximation theory
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

〈,〉

( | )

·

:

||inner product
| rowspan=3|〈''x'',''y''〉 means the inner product of ''x'' and ''y'' as defined in an inner product space.

For spatial vectors, the dot product notation, ''x''·''y'' is common.

For matricies, the colon notation may be used.
| rowspan=3|The standard inner product between two vectors ''x'' = (2, 3) and ''y'' = (−1, 5) is:
〈x, y〉 = 2×−1 + 3×5 = 13

A:B = \sum_ A_B_

⊗

||tensor product
| rowspan=3| ''V'' ⊗ ''U'' means the tensor product of ''V'' and ''U''.
| rowspan=3| ⊗ =

|-
|align=center| tensor product of
|-
|align=right| linear algebra
|-
| rowspan=3 bgcolor=#d0f0d0 align=center|

||convolution
| rowspan=3| ''f''
* ''g'' means the convolution of ''f'' and ''g''.
| rowspan=3|

(f  * g )(t) = \int f(\tau) g(t - \tau)\, d\tau

|-
|align=center| convolution
|-
|align=right|
-->
|}
==See also==

* History of mathematical notation
* History of the Hindu-Arabic numeral system
* Table of mathematical symbols

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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