<P> In mathematics, the power set (or powerset) of any set S is the set of all subsets of S, including the empty set and S itself, variously denoted as P (S), P (S), ℘ (S) (using the "Weierstrass p"), P (S), P (S), or, identifying the powerset of S with the set of all functions from S to a given set of two elements, 2 . In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set . </P> <P> Any subset of P (S) is called a family of sets over S . </P>

The set of all possible subsets of a set is called