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:
“As usurpation is the exercise of power, which another hath a right to, so tyranny is the exercise of power beyond right, which no body can have a right to. And this is making use of the power any one has in his hands, not for the good of those who are under it, but for his own private separate advantage.”
—John Locke (1632–1704)
“The time is out of joint. O cursèd spite
That ever I was born to set it right!”
—William Shakespeare (1564–1616)