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:
“The farmer imagines power and place are fine things. But the President has paid dear for his White House. It has commonly cost him all his peace, and the best of his manly attributes. To preserve for a short time so conspicuous an appearance before the world, he is content to eat dust before the real masters who stand erect behind the throne.”
—Ralph Waldo Emerson (1803–1882)
“Speak of me as I am. Nothing extenuate,
Nor set down aught in malice.”
—William Shakespeare (1564–1616)