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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, then if and otherwise, where is a common notation for the indicator function. Other common notations are and
The indicator function of A is the Iverson bracket of the property of belonging to A; that is,
For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers.