Indicator function: Difference between revisions

Revision as of 19:54, 28 November 2023

Revision as of 20:55, 19 January 2025

Line 41:

==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|rangecodomain]] <math>\{0,1\}</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=\equiv 1.</math> By a similar argument, if <math>A\equiv=\emptyset</math> then <math>\mathbf{1}_A=\equiv 0.</math>

If <math>A</math> and <math>B</math> are two subsets of <math>X,</math> then