===== Characteristic function =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |
| @#55CCEE: context     | @#55CCEE: $A\subseteq X$ |
| @#FFBB00: definiendum | @#FFBB00: $\chi_A:X\to \{0,1\} $ |
| @#FFBB00: definiendum | @#FFBB00: $ \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: [[http://en.wikipedia.org/wiki/Characteristic_function|Characteristic function]]
==== Parents ====
=== Refinement of ===
[[Function]]
=== Context ===
[[Subset complement]]