ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
▼ Deduction system
▼ Theory
▼ Zermelo-Fraenkel set theory
▼ Set
▼ Binary cartesian set product
▼ Binary relation
▼ Map
▼ Function
▼ Real collection function
▼ Euclidean real function
▼ Real function
▼ Rational function
▼ Integer function
▼ Natural number function
▼ Boolean function
▼ Indicator function
Definition D4210
Indicator function operator
Formulation 0
Let $X$ be a D11: Set such that
(i) $\mathcal{P}(X)$ is the D80: Power set of $X$
(ii) $\{ 0, 1 \}^X$ is the D4213: Set of Boolean functions from $X$ to $\{ 0, 1 \}$
The indicator function operator on $\mathcal{P}(X)$ is the D18: Map \begin{equation} \mathcal{P}(X) \to \{ 0, 1 \}^X, \quad E \mapsto I_E \end{equation}