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[[Image:Indicator function illustration.png|right|thumb|A three-dimensional plot of an indicator function, shown over a square two-dimensional ___domain (set {{mvar|X}}): the "raised" portion overlays those two-dimensional points which are members of the "indicated" subset ({{mvar|A}}).]]
In [[mathematics]], an '''indicator function''' or a '''characteristic function''' of a [[subset]] of a [[Set (mathematics)|set]] is a [[Function (mathematics)|function]] that maps elements of the subset to one, and all other elements of the set to zero. The indicator function of a subset
{{mvar|A}} of a set {{mvar|X}} maps {{mvar|X}} to the two-element set <math>\{ 0, 1 \}\,;</math> <math>\mathbf{1}_{A}(x)=1</math> if an element <math>x</math> in {{mvar|X}} belongs to {{mvar|A}}, and <math>\mathbf{1}_{A}(x)=0</math> if <math>x</math> does not belong to {{mvar|A}}. It may be
The [[Dirichlet function]], the indicator function of the [[rational number]]s as a subset of the [[real number]]s, is an example of an indicator function.
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