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:
“Anyone who is kind to man knows the fragmentariness of most men, and wants to arrange a society of power in which men fall naturally into a collective wholeness, since they cannot have an individual wholeness. In this collective wholeness they will be fulfilled. But if they make efforts at individual fulfilment, they must fail for they are by nature fragmentary.”
—D.H. (David Herbert)
“The whole object of travel is not to set foot on foreign land; it is at last to set foot on one’s own country as a foreign land.”
—Gilbert Keith Chesterton (1874–1936)