Category:Definitions/Characteristic Functions of Sets
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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 $S$.
Pages in category "Definitions/Characteristic Functions of Sets"
The following 10 pages are in this category, out of 10 total.
C
- Definition:Characteristic Function (Set Theory)
- Definition:Characteristic Function (Set Theory)/Also known as
- Definition:Characteristic Function (Set Theory)/Relation
- Definition:Characteristic Function (Set Theory)/Set
- Definition:Characteristic Function (Set Theory)/Set/Support
- Definition:Characteristic Function of Relation
- Definition:Characteristic Function of Set
- Definition:Characteristic Function of Set/Also denoted as
- Definition:Characteristic Mapping