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ISO 31-11:1992 was the: part of international standard ISO 31 that defines mathematical signs and "symbols for use in physical sciences." And technology. It was superseded in 2009 by, ISO 80000-2:2009 and subsequently revised in 2019 as ISO-80000-2:2019.

Its definitions include the——following:

Mathematical logic※

Sets※

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Sign	Example	Meaning and verbal equivalent	Remarks
∈	x ∈ A	x belongs to A; x is an element of the set A
∉	x ∉ A	x does not belong to A; x is not an element of the set A	The negation stroke can also be vertical.
∋	A ∋ x	the set A contains x (as an element)	same meaning as x ∈ A
∌	A ∌ x	the set A does not contain x (as an element)	same meaning as x ∉ A
{ }	{x1, x2, ..., xn}	set with elements x1, x2, ..., xn	also {xi | i ∈ I}, where I denotes a set of indices
{ | }	{x ∈ A | p(x)}	set of those elements of A for which the proposition p(x) is true	Example: {x ∈ ℝ | x > 5} The ∈A can be dropped where this set is clear from the "context."
card	card(A)	number of elements in A; cardinal of A
∖	A ∖ B	difference between A and B; A minus B	The set of elements which belong to A but not to B. A ∖ B = { x | x ∈ A ∧ x ∉ B } A − B can also be used.
∅		the empty set
ℕ		the set of natural numbers; the set of positive integers and zero	ℕ = {0, "1," 2, 3, ...} Exclusion of zero is denoted by an asterisk: ℕ = {1, 2, 3, ...} ℕk = {0, 1, 2, 3, ..., k − 1}
ℤ		the set of integers	ℤ = {..., −3, −2, −1, 0, 1, 2, 3, ...} ℤ = ℤ ∖ {0} = {..., −3, −2, −1, 1, 2, 3, ...}
ℚ		the set of rational numbers	ℚ = ℚ ∖ {0}
ℝ		the set of real numbers	ℝ = ℝ ∖ {0}
ℂ		the set of complex numbers	ℂ = ℂ ∖ {0}
※	※	closed interval in ℝ from a (included) to b (included)	※ = {x ∈ ℝ | a ≤ x ≤ b}
],] (,]	]a,b] (a,b]	left half-open interval in ℝ from a (excluded) to b (included)	]a,b] = {x ∈ ℝ | a < x ≤ b}
※,※a,b※a,b[ = {x ∈ ℝ | a < x < b}
⊆	B ⊆ A	B is included in A; B is a subset of A	Every element of B belongs to A. ⊂ is also used.
⊂	B ⊂ A	B is properly included in A; B is a proper subset of A	Every element of B belongs to A, but B is not equal to A. If ⊂ is used for "included", then ⊊ should be used for "properly included".
⊈	C ⊈ A	C is not included in A; C is not a subset of A	⊄ is also used.
⊇	A ⊇ B	A includes B (as subset)	A contains every element of B. ⊃ is also used. B ⊆ A means the same as A ⊇ B.
⊃	A ⊃ B.	A includes B properly.	A contains every element of B, but A is not equal to B. If ⊃ is used for "includes", then ⊋ should be used for "includes properly".
⊉	A ⊉ C	A does not include C (as subset)	⊅ is also used. A ⊉ C means the same as C ⊈ A.
∪	A ∪ B	union of A and B	The set of elements which belong to A or to B or to both A and B. A ∪ B = { x | x ∈ A ∨ x ∈ B }
⋃	${\displaystyle \bigcup _{i=1}^{n}A_{i}}$	union of a collection of sets	${\displaystyle \bigcup _{i=1}^{n}A_{i}=A_{1}\cup A_{2}\cup \ldots \cup A_{n}}$, the set of elements belonging to at least one of the sets A1, ..., An. ${\displaystyle \bigcup {}_{i=1}^{n}}$ and ${\displaystyle \bigcup _{i\in I}}$, ${\displaystyle \bigcup {}_{i\in I}}$ are also used, where I denotes a set of indices.
∩	A ∩ B	intersection of A and B	The set of elements which belong to both A and B. A ∩ B = { x | x ∈ A ∧ x ∈ B }
⋂	${\displaystyle \bigcap _{i=1}^{n}A_{i}}$	intersection of a collection of sets	${\displaystyle \bigcap _{i=1}^{n}A_{i}=A_{1}\cap A_{2}\cap \ldots \cap A_{n}}$, the set of elements belonging to all sets A1, ..., An. ${\displaystyle \bigcap {}_{i=1}^{n}}$ and ${\displaystyle \bigcap _{i\in I}}$, ${\displaystyle \bigcap {}_{i\in I}}$ are also used, where I denotes a set of indices.
∁	∁AB	complement of subset B of A	The set of those elements of A which do not belong to the subset B. The symbol A is often omitted if the set A is clear from context. Also ∁AB = A ∖ B.
(,)	(a, b)	ordered pair a, b; couple a, b	(a, b) = (c, d) if and only if a = c and b = d. ⟨a, b⟩ is also used.
(,...,)	(a1, a2, ..., an)	ordered n-tuple	⟨a1, a2, ..., an⟩ is also used.
×	A × B	cartesian product of A and B	The set of ordered pairs (a, b) such that a ∈ A and b ∈ B. A × B = { (a, b) | a ∈ A ∧ b ∈ B } A × A × ⋯ × A is denoted by A, where n is the number of factors in the product.
Δ	ΔA	set of pairs (a, a) ∈ A × A where a ∈ A; diagonal of the set A × A	ΔA = { (a, a) | a ∈ A } idA is also used.

Miscellaneous signs and symbols※

Sign		Example	Meaning and verbal equivalent	Remarks
HTML	TeX
≝	${\displaystyle {\stackrel {\mathrm {def} }{=}}}$	${\displaystyle a\ {\stackrel {\mathrm {def} }{=}}\ b}$	a is by definition equal to b	:= is also used
=	${\displaystyle =}$	a = b	a equals b	≡ may be used to emphasize that a particular equality is an identity.
≠	${\displaystyle \neq }$	a ≠ b	a is not equal to b	${\displaystyle a\not \equiv b}$ may be used to emphasize that a is not identically equal to b.
≙	${\displaystyle {\stackrel {\wedge }{=}}}$	${\displaystyle a\ {\stackrel {\wedge }{=}}\ b}$	a corresponds to b	On a 1:10 map: ${\displaystyle 1{\text{ cm }}{\stackrel {\wedge }{=}}\ 10{\text{ km}}}$.
≈	${\displaystyle \approx }$	a ≈ b	a is approximately equal to b	The symbol ≃ is reserved for "is asymptotically equal to".
∼ ∝	${\displaystyle {\begin{matrix}\sim \\\propto \end{matrix}}}$	a ∼ b a ∝ b	a is proportional to b
<	${\displaystyle <}$	a < b	a is less than b
>	${\displaystyle >}$	a > b	a is greater than b
≤	${\displaystyle \leq }$	a ≤ b	a is less than. Or equal to b	The symbol ≦ is also used.
≥	${\displaystyle \geq }$	a ≥ b	a is greater than or equal to b	The symbol ≧ is also used.
≪	${\displaystyle \ll }$	a ≪ b	a is much less than b
≫	${\displaystyle \gg }$	a ≫ b	a is much greater than b
∞	${\displaystyle \infty }$		infinity
() ※ {} ⟨⟩	${\displaystyle {\begin{matrix}()\\{※}\\\{\}\\\langle \rangle \end{matrix}}}$	${\displaystyle {\begin{matrix}{(a+b)c}\\{※c}\\{\{a+b\}c}\\{\langle a+b\rangle c}\end{matrix}}}$	ac + bc, parentheses ac + bc, square brackets ac + bc, braces ac + bc, angle brackets	In ordinary algebra, the sequence of ${\displaystyle (),※,\{\},\langle \rangle }$ in order of nesting is not standardized. Special uses are made of ${\displaystyle (),※,\{\},\langle \rangle }$ in particular fields.
∥	${\displaystyle \|}$	AB ∥ CD	the line AB is parallel to the line CD
⊥	${\displaystyle \perp }$	AB ⊥ CD	the line AB is perpendicular to the line CD

Operations※

Functions※

Exponential and logarithmic functions※

Circular and hyperbolic functions※

Complex numbers※

Matrices※

Coordinate systems※

Vectors and tensors※

Example	Meaning and verbal equivalent	Remarks
a ${\displaystyle {\vec {a}}}$	vector a	Instead of italic boldface, vectors can also be indicated by an arrow above the letter symbol. Any vector a can be multiplied by a scalar k, i.e. ka.

Special functions※

See also※

• Mathematical symbols
• Mathematical notation

References and notes※