Editing Indicator function (section)

{{Short description|Mathematical function characterizing set membership}}
{{About|the 0&ndash;1 indicator function|the 0&ndash;infinity indicator function|characteristic function (convex analysis)}}
{{More footnotes|date=December 2009}}
{{Use American English|date = March 2019}}

[[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 to zero. That is, if {{mvar|A}} is a subset of some set {{mvar|X}}, then the indicator function of {{mvar|A}} is the function <math>\mathbf{1}_A</math> defined by <math>\mathbf{1}_{A}\!(x) = 1</math> if <math>x \in A,</math> and <math>\mathbf{1}_{A}\!(x) = 0</math> otherwise. Other common notations are {{math|𝟙{{sub|''A''}}}} and <math>\chi_A.</math>{{efn|name=χαρακτήρ}}

The indicator function of {{mvar|A}} is the [[Iverson bracket]] of the property of belonging to {{mvar|A}}; that is, 

<math display="block">\mathbf{1}_{A}(x) = \left[\ x\in A\ \right].</math>

For example, the [[Dirichlet function]] is the indicator function of the [[rational number]]s as a subset of the [[real number]]s.