Category:Definitions/Characteristic Functions of Sets

This category contains definitions related to Characteristic Functions of Sets.
Related results can be found in Category:Characteristic Functions of Sets.

Let $E \subseteq S$.

The characteristic function of $E$ is the function $\chi_E: S \to \set {0, 1}$ defined as:

$\map {\chi_E} x = \begin {cases}

1 & : x \in E \\ 0 & : x \notin E \end {cases}$

That is:

$\map {\chi_E} x = \begin {cases}

1 & : x \in E \\ 0 & : x \in \relcomp S E \end {cases}$ where $\relcomp S E$ denotes the complement of $E$ relative to $S$.