Membership function

In mathematics, an indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. It is usually denoted by a symbol 1 or I, sometimes in boldface or blackboard boldface, with a subscript specifying the subset. In other contexts, such as computer science, this would more often be described as a boolean predicate function (to test set inclusion). The Dirichlet function is an example of an indicator function and is the indicator of the rationals. The indicator function of a subset A of a set X is a function