Characteristic function

Set

context $X$
context $A\subseteq X$
definiendum $\chi_A:X\to \{0,1\} $
definiendum $ \chi_A(x) := \begin{cases} 1 & \mathrm{if}\ x\in A\\\\ 0 & \mathrm{else} \end{cases}$

The complement $A^c$ is taken w.r.t. $X$.

Discussion

The symbols “$0,1$” here are essentially placeholders. One could choose any set of two distinct elements as codomain.

Reference

Parents

Refinement of

Context

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