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:
“What is good?—Everything that heightens the feeling of power, the will to power, power itself in man.”
—Friedrich Nietzsche (1844–1900)
“True love does not quarrel for slight reasons, such mistakes as mutual acquaintances can explain away, but, alas, however slight the apparent cause, only for adequate and fatal and everlasting reasons, which can never be set aside.”
—Henry David Thoreau (1817–1862)