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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, one has 1 A = 1 {\displaystyle \mathbf {1} _{A}=1} if x ∈ A , {\displaystyle x\in A,} and 1 A = 0 {\displaystyle \mathbf {1} _{A}=0} otherwise, where 1 A {\displaystyle \mathbf {1} _{A}} is a common notation for the indicator function. Other common notations are I A , {\displaystyle I_{A},} and χ A . {\displaystyle \chi _{A}.}
The indicator function of A is the Iverson bracket of the property of belonging to A; that is,