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Characteristic function
Definition
| $X$ |
| $A\subseteq X$ |
| $\chi_A:X\to \{0,1\} $ |
| $ \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
Wikipedia: Characteristic function
Parents
Refinement of
Requirements
