Category:Characteristic Functions of Sets
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This category contains results about Characteristic Functions of Sets.
Definitions specific to this category can be found in Definitions/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 $S$.
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