Set function In mathematics, a set function is a function whose input is a set . The output is usually a number. Often the input is a set of real numbers , a set of points in Euclidean space , or a set of points in some measure space . Examples Examples of set functions include: The function that assigns to each set its cardinality , i.e. the number of members of the set, is a set function. The function {\displaystyle d(A)=\lim _{n\to \infty }{\frac {|A\cap \{1,\dots ,n\}|}{n}},} Definition A set is a well-defined collection of distinct objects. The objects that make up a set (also known as the elements or members of a set) can be anything: numbers, people, letters of the alphabet, other sets, and so on. Membership If B is a set and x is one of the objects of B , this is denoted x ∈ B , and is read as "x belongs to B", or "x is an element of B". If y is not a member of B then this is written as y ∉ B , and i
