## 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.