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set theory > characteristic function

mathematical analysis > function > characteristic function

Preferred term

characteristic function

Definition(s)

In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if $A$ is a subset of some set $X$ , then ${\\displaystyle \\mathbf {1} _{A}(x)=1}$ if ${\\displaystyle x\\in A,}$ and ${\\displaystyle \\mathbf {1} _{A}(x)=0}$ otherwise, where ${\\displaystyle \\mathbf {1} _{A}}$ is a common notation for the indicator function. Other common notations are ${\\displaystyle I_{A},}$ and ${\\displaystyle \\chi _{A}.}$
The indicator function of $A$ is the Iverson bracket of the property of belonging to $A$ ; that is,

${\\displaystyle \\mathbf {1} _{A}(x)=[x\\in A].}$

For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Indicator_function)

Broader concept(s)

Narrower concept(s)

Dirichlet function

Synonym(s)

indicator function

In other languages

fonction caractéristique

French
fonction indicatrice

URI

http://data.loterre.fr/ark:/67375/PSR-DMTN3C45-S

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