# characteristic function

**characteristic function** of a subset *S* of a universal set *U*. A function that indicates whether or not an element is a member of the subset *S*. It is the function *f* : *U* → {0,1}

defined as follows: *f*(*x*) = 1 if *x* ∈ *S* *f*(*x*) = 0 if *x* ∉ *S*

The codomain might also be given as {true,false} or {1,2}.

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