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:
“Guilty. Guilty. My evil self is at that door, and I have no power to stop it.”
—Cyril Hume, and Fred McLeod Wilcox. Dr. Morbius (Walter Pidgeon)
“And therefore, as when there is a controversy in an account, the parties must by their own accord, set up for right Reason, the Reason of some Arbitrator, or Judge, to whose sentence, they will both stand, or their controversy must either come to blows, or be undecided, for want of a right Reason constituted by Nature; so is it also in all debates of what kind soever.”
—Thomas Hobbes (1579–1688)