Английская Википедия:ISO 31-11

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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 It was superseded in 2009 by ISO 80000-2:2009 and subsequently revised in 2019 as ISO-80000-2:2019.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

Sign	Example	Name	Meaning and verbal equivalent	Remarks
∧	Шаблон:Math	conjunction sign	p and q
∨	Шаблон:Math	disjunction sign	p or q (or both)
¬	Шаблон:Math	negation sign	negation of p; not p; non p
⇒	Шаблон:Math	implication sign	if p then q; p implies q	Can also be written as q ⇐ p. Sometimes → is used.
∀	Шаблон:Math	universal quantifier	for every x belonging to A, the proposition p(x) is true	The "Шаблон:Math" can be dropped where A is clear from context.
∃	Шаблон:Math	existential quantifier	there exists an x belonging to A for which the proposition p(x) is true	The "Шаблон:Math" can be dropped where A is clear from context. Шаблон:Math is used where exactly one x exists for which p(x) is true.

Miscellaneous signs and symbols

Sign		Example	Meaning and verbal equivalent	Remarks
HTML	TeX
Шаблон:Big	<math>\stackrel{\mathrm{def}}{=}</math>	<math>a\ \stackrel\mathrm{def}{=}\ b</math>	a is by definition equal to b	:= is also used
=	<math>=</math>	Шаблон:Math	a equals b	≡ may be used to emphasize that a particular equality is an identity.
≠	<math>\ne</math>	Шаблон:Math	a is not equal to b	<math>a \not\equiv b</math> may be used to emphasize that a is not identically equal to b.
≙	<math>\stackrel{\wedge}{=}</math>	<math>a\ \stackrel{\wedge}{=}\ b</math>	a corresponds to b	On a 1:106 map: <math>1 \text{ cm }\stackrel{\wedge}{=}\ 10 \text{ km}</math>.
≈	<math>\approx</math>	Шаблон:Math	a is approximately equal to b	The symbol ≃ is reserved for "is asymptotically equal to".
∼ ∝	<math>\begin{matrix} \sim \\ \propto \end{matrix}</math>	Шаблон:Math	a is proportional to b
<	Шаблон:Tmath	Шаблон:Math	a is less than b
>	Шаблон:Tmath	Шаблон:Math	a is greater than b
≤	<math>\le</math>	Шаблон:Math	a is less than or equal to b	The symbol ≦ is also used.
≥	<math>\ge</math>	Шаблон:Math	a is greater than or equal to b	The symbol ≧ is also used.
≪	<math>\ll</math>	Шаблон:Math	a is much less than b
≫	<math>\gg</math>	Шаблон:Math	a is much greater than b
∞	<math>\infty</math>	Шаблон:Math	infinity
() [] {} Шаблон:Angbr	<math>\begin{matrix}() \\ {[]} \\ \{\} \\ \langle \rangle \end{matrix}</math>	<math>\begin{matrix} {(a+b)c} \\ {[a+b]c} \\ {\{a+b\}c} \\ {\langle a+b \rangle c} \end{matrix}</math>	ac + bc, parentheses ac + bc, square brackets ac + bc, braces ac + bc, angle brackets	In ordinary algebra, the sequence of <math>(), [], \{\}, \langle \rangle </math> in order of nesting is not standardized. Special uses are made of <math>(), [], \{\}, \langle \rangle </math> in particular fields.
∥	</math>	Шаблон:Math	the line AB is parallel to the line CD
⊥	<math>\perp</math>	Шаблон:Math	the line AB is perpendicular to the line CD

Operations

Sign	Example	Meaning and verbal equivalent	Remarks
+	a + b	a plus b
−	a − b	a minus b
±	a ± b	a plus or minus b
∓	a ∓ b	a minus or plus b	−(a ± b) = −a ∓ b

Exponential and logarithmic functions

Example	Meaning and verbal equivalent	Remarks
e	base of natural logarithms	e = 2.718 28...
ex	exponential function to the base e of x
logax	logarithm to the base a of x
lb x	binary logarithm (to the base 2) of x	lb x = log2x
ln x	natural logarithm (to the base e) of x	ln x = logex
lg x	common logarithm (to the base 10) of x	lg x = log10x

Circular and hyperbolic functions

Example	Meaning and verbal equivalent	Remarks
π	ratio of the circumference of a circle to its diameter	π ≈ Шаблон:Val

Complex numbers

Example	Meaning and verbal equivalent	Remarks
i, j	imaginary unit; iШаблон:Sup = −1	In electrotechnology, j is generally used.
Re z	real part of z	z = x + iy, where x = Re z and y = Im z
Im z	imaginary part of z
Шаблон:PipezШаблон:Pipe	absolute value of z; modulus of z	mod z is also used
arg z	argument of z; phase of z	z = reШаблон:Sup, where r = Шаблон:PipezШаблон:Pipe and φ = arg z, i.e. Re z = r cos φ and Im z = r sin φ
zШаблон:I sup	(complex) conjugate of z	sometimes a bar above z is used instead of z*
sgn z	signum z	sgn z = z / Шаблон:PipezШаблон:Pipe = exp(i arg z) for z ≠ 0, sgn 0 = 0

Matrices

Example	Meaning and verbal equivalent	Remarks
A	matrix A

Coordinate systems

Coordinates	Position vector and its differential	Name of coordinate system	Remarks
x, y, z	Шаблон:Math; Шаблон:Math	cartesian	x1, x2, x3 for the coordinates and e1, e2, e3 for the base vectors are also used. This notation easily generalizes to n-dimensional space. ex, ey, ez form an orthonormal right-handed system. For the base vectors, i, j, k are also used.
ρ, φ, z	Шаблон:Math	cylindrical	eρ(φ), eφ(φ), ez form an orthonormal right-handed system. lf z = 0, then ρ and φ are the polar coordinates.
r, θ, φ	Шаблон:Math	spherical	er(θ,φ), eθ(θ,φ),eφ(φ) form an orthonormal right-handed system.

Vectors and tensors

Example	Meaning and verbal equivalent	Remarks
Шаблон:Mvar <math>\vec a</math>	vector Шаблон:Mvar	Instead of italic boldface, vectors can also be indicated by an arrow above the letter symbol. Any vector Шаблон:Mvar can be multiplied by a scalar k, i.e. Шаблон:Mvar.

Special functions

Example	Meaning and verbal equivalent	Remarks
Шаблон:Math	cylindrical Bessel functions (of the first kind)	...

See also

• Mathematical symbols
• Mathematical notation