Indicator Functions
Indicator functions are functions defined on a set; it maps a subset to 1 and everything else to 0.
Contents
Description
For a set A, an indicator function is 1B : A -> {0,1} where for every x ∈ A, f(x) = 1 if x ∈ B, else 0.
As a concrete example, the Dirichlet function indicates the subset of real numbers that are rational numbers. It is notated as 1Q to mean that 1Q(x) = 1 if x ∈ Q, else 0.
Another common notation used for the set of real numbers is 1(a,b)(x), as in a function that maps x to 1 if a ≤ x ≤ b, else 0.