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==Basic properties==
The ''indicator'' or ''characteristic'' [[function (mathematics)|function]] of a subset {{mvar|A}} of some set {{mvar|X}} [[Map (mathematics)|maps]] elements of {{mvar|X}} to the [[Range of a function|range]] <math>\{
This mapping is [[surjective]] only when {{mvar|A}} is a non-empty [[proper subset]] of {{mvar|X}}. If <math>A \equiv X,</math> then <math>\mathbf{1}_A=1.</math> By a similar argument, if <math>A\equiv\emptyset</math> then <math>\mathbf{1}_A=0.</math>
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