Indicator function: Difference between revisions

Revision as of 13:51, 20 September 2023

Revision as of 21:49, 27 October 2023

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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>

In the following, the dot represents multiplication, <math>1\cdot1 = 1,</math> <math>1\cdot0 = 0,</math> etc. "+" and "&minus;" represent addition and subtraction. "<math>\cap </math>" and "<math>\cup </math>" are intersection and union, respectively.

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