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Indicator function
Formulation 0
Let $X$ be a D11: Set.
The indicator function on $X$ with respect to $E \subseteq X$ is the D992: Function \begin{equation} X \to \{ 0, 1 \}, \quad x \mapsto \begin{cases} 1, \quad & x \in E \\ 0, \quad & x \in X \setminus E \end{cases} \end{equation}
Conventions
Convention 0 (Notation for indicator function) : Let $X$ be a D11: Set. We denote the D41: Indicator function on $X$ with respect to $E \subseteq X$ by $I_E$.
Subdefinitions
» D382: Heaviside function
Child definitions
» D4210: Indicator function operator
Results
» R1194: Indicator function of complement
» R3531: Pointwise product with indicator function is lower bound for unsigned basic function
» R1868: Composition of indicator function with set endomorphism
» R1193: Finite product of indicator functions equals indicator of intersection
» R4333: Binary product of indicator functions equals indicator of intersection
» R2370: Basic real arithmetic expression for cardinality of countable set
» R4565: Countable indicator partition of a euclidean real function
» R4566: Countable indicator partition of a complex function
» R4567: Countable indicator partition of a random euclidean real number
» R4568: Countable indicator partition of a random complex number
» R2966: Indicator function under scaling of the argument