Power Set

In mathematics, the power set (or powerset) of any set S, written, P(S), ℘(S) or 2S, is the set of all subsets of S, including the empty set and S itself. 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.

Any subset of is called a family of sets over S.

Read more about Power Set:  Example, Properties, Representing Subsets As Functions, Relation To Binomial Theorem, Algorithms, Subsets of Limited Cardinality, Topologization of Power Set, Power Object

Famous quotes containing the words power and/or set:

    With all of my power of living
    I am forced to lie on the floor.
    John Ashbery (b. 1927)

    Setting limits gives your child something to define himself against. If you are able to set limits without being overly intrusive or controlling, you’ll be providing him with a firm boundary against which he can test his own ideas.
    Stanley I. Greenspan (20th century)