DIN 1302

	DIN 1302
Area	mathematics
title	General mathematical signs and terms
Brief description:	Defines signs, their way of speaking and the associated message
Latest edition	1999-12
ISO	DIN EN ISO 80000-2

The DIN standard DIN 1302 defines general mathematical symbols and terms . A representative selection of these is listed here. For the complete list and definitions, reference must be made to the original text.

Pragmatic signs

The pragmatic signs are not mathematical signs in the strict sense. Their meaning is only specified more precisely from case to case by the user and an application situation. Examples:

${\displaystyle x\approx y}$(approximately the same), (much smaller), (corresponds to), ${\displaystyle x\ll y}$ ${\displaystyle x{\mathrel {\widehat {=}}}y}$

${\displaystyle x\doteq y}$(rounded equal), (infinite),  ...   (and so on to / and so on (unlimited)), (delta ) ${\displaystyle \infty \,}$ ${\displaystyle \,\Delta x}$ ${\displaystyle x}$

General mathematical relations and links

Examples:

${\displaystyle x=y}$(equal), (unequal), (equal by definition), ${\displaystyle x\neq y}$ ${\displaystyle x\,{\stackrel {\text{def}}{=}}\,y}$

${\displaystyle x<y}$(smaller), (greater or equal), ${\displaystyle x\geq y}$

${\displaystyle x+y}$(plus; sum), (minus; difference), ${\displaystyle x-y}$

${\displaystyle x\cdot y}$or (times; product) - in DIN 1338 this is also permitted in information such as , ${\displaystyle xy}$ ${\displaystyle \,\times }$ ${\displaystyle 10{\text{ cm }}\times \,15{\text{ cm}}}$

The characters and are also used on keyboards, but they should not be used in mathematical formulas , ${\displaystyle \,\times }$ ${\displaystyle \ast }$

${\displaystyle {\frac {x}{y}}}$or (by; quotient) - in some applications it is also written, ${\displaystyle x/y}$ ${\displaystyle x:y}$

The character is also used on keyboards, but should not be used in formulas, ${\displaystyle \div }$

${\displaystyle \sum _{i=m}^{n}x_{i}}$(Sum), (product), ${\displaystyle \prod _{i=m}^{n}x_{i}}$

${\displaystyle f\sim g}$or (proportional) ${\displaystyle f\varpropto g}$

Special numbers and links

Examples:

${\displaystyle 0}$(zero; for all ), (one; for all ), (pi; circumference to diameter), (e; base of the natural logarithm), ${\displaystyle 0+x=x}$ ${\displaystyle x}$ ${\displaystyle 1}$ ${\displaystyle 1\cdot x=x}$ ${\displaystyle x}$ ${\displaystyle \pi }$ ${\displaystyle \mathrm {e} }$

${\displaystyle x^{n}}$( high ), ( -th root ; if ), ( factorial), ( over ), ${\displaystyle x}$ ${\displaystyle n}$ ${\displaystyle {\sqrt[{n}]{x}}}$ ${\displaystyle n}$ ${\displaystyle x}$ ${\displaystyle {\sqrt[{n}]{x}}\geq 0}$ ${\displaystyle x\geq 0}$ ${\displaystyle n\,!}$ ${\displaystyle n}$ ${\displaystyle {\tbinom {x}{n}}}$ ${\displaystyle x}$ ${\displaystyle n}$

${\displaystyle \operatorname {sgn} x}$(Signum ) ( amount) , (integer and fractional share ) ${\displaystyle x}$ ${\displaystyle \vert x\vert }$ ${\displaystyle x}$ ${\displaystyle {\text{int }}x}$ ${\displaystyle {\text{frac }}x}$ ${\displaystyle x}$

Complex numbers

Examples with as a complex number, as real numbers in  : ${\displaystyle z}$ ${\displaystyle x,\,y}$ ${\displaystyle z=x+\mathrm {i} \;y}$

${\displaystyle \mathrm {i} }$or in electrical engineering (imaginary unit), ${\displaystyle \mathrm {j} }$

${\displaystyle \operatorname {Re} \,z}$(Real part ; ), (imaginary part ; ), ${\displaystyle z}$ ${\displaystyle \operatorname {Re} \,z=x}$ ${\displaystyle \operatorname {Im} \,z}$ ${\displaystyle z}$ ${\displaystyle \operatorname {Im} \,z=y}$

${\displaystyle {\bar {z}}}$or ( conjugate (-complex)), (argument of ) ${\displaystyle \,z^{*}}$ ${\displaystyle z}$ ${\displaystyle \arg z}$ ${\displaystyle z}$

Sets of numbers

Examples:

${\displaystyle \mathbb {Z} }$or (set of whole numbers), or (set of complex numbers), ${\displaystyle {\mathsf {Z}}}$ ${\displaystyle \mathbb {C} }$ ${\displaystyle {\mathsf {C}}}$

${\displaystyle (a,b)}$or   (open interval),   (closed interval) ${\displaystyle ]a,b[}$ ${\displaystyle [a,b]}$

Limit values

Examples:

${\displaystyle b=\lim _{x\to a}f(x)}$(Limes for against ), ${\displaystyle x}$ ${\displaystyle a}$

${\displaystyle f\simeq g}$ (asymptotically equal)

Differentiation, integration

Examples:

${\displaystyle f'(x_{0})}$or  ( dash from or to in ), ${\displaystyle \left({\frac {\mathrm {d} f}{\mathrm {d} x}}\right)_{\!x_{0}}}$ ${\displaystyle f}$ ${\displaystyle x_{0}}$ ${\displaystyle \mathrm {d} f}$ ${\displaystyle \mathrm {d} x}$ ${\displaystyle x_{0}}$

${\displaystyle f'}$or or in certain contexts   (derivation wherever differentiable), ${\displaystyle {\frac {\mathrm {d} f}{\mathrm {d} x}}}$ ${\displaystyle {\dot {f^{\;}}}}$ ${\displaystyle \!f}$

${\displaystyle f''}$, , ..., or ;   , ... (multiple derivative) ${\displaystyle f'''}$ ${\displaystyle \!f^{(n)}}$ ${\displaystyle {\frac {\mathrm {d} ^{n}f}{\mathrm {d} x^{n}}}}$ ${\displaystyle {\ddot {f^{\;}}}}$

${\displaystyle {\frac {\partial f}{\partial x_{k}}}}$ (partial derivative)

${\displaystyle \int f(x)\,\mathrm {d} x}$, (indefinite and definite integral) ${\displaystyle \int \limits _{a}^{b}f(x)\mathrm {d} x}$

${\displaystyle F(x){\underset {x=a}{\overset {x=b}{\mid }}}}$or (at the borders) ${\displaystyle F\;{\underset {a}{\overset {b}{\mid }}}}$

Exponential and logarithmic functions

Examples with as a complex number, as real numbers: ${\displaystyle z}$ ${\displaystyle x,\,y}$

${\displaystyle \exp z}$or , (e high , exponential function), ${\displaystyle \mathrm {e} ^{z}}$ ${\displaystyle z}$

${\displaystyle \log _{y}x}$(Logarithm from to base ), (natural logarithm), (decadic logarithm), (binary logarithm), ${\displaystyle x}$ ${\displaystyle y}$ ${\displaystyle \ln x}$ ${\displaystyle \lg x}$ ${\displaystyle \operatorname {lb} x}$

is also permitted if the basis is agreed separately ${\displaystyle \log x}$

Circular and hyperbolic functions and their inversions

${\displaystyle \sin z,\cos z,\tan z,\cot z}$ (Sine, cosine, tangent, cotangent),

${\displaystyle \sinh z,\cosh z,\tanh z,\coth z}$ (Hyperbolic sinus ...),

${\displaystyle \arcsin x,\arccos x,\arctan x,\operatorname {arccot} x}$ (Arcsine ...),

${\displaystyle \operatorname {arsinh} x,\operatorname {arcosh} x,\operatorname {artanh} x,\operatorname {arcoth} x}$ (Area hyperbolic sinus ...),

also (secans, cosecans) are defined. ${\displaystyle \sec z,\csc z}$

More characters

Other mathematical symbols are specified in special standards, for example

• on vectors, matrices and tensors in DIN 1303 vectors, matrices, tensors; Signs and concepts
• on logic and set theory in DIN 5473 logic and set theory; Signs and concepts
• on Fourier, Laplace and Z transformation in DIN 5487 Fourier, Laplace and Z transformation; Signs and concepts
• for science and technology in DIN EN ISO 80000-2 sizes and units - Part 2: Mathematics

See also

• DIN 1304 symbols
• DIN 1338 Formula notation and formula set

literature

• German Institute for Standardization : DIN 1302 General mathematical symbols and terms , Beuth-Verlag, 1999.