Characteristic function

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. $X$ .

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