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 superstition respecting power and office is going to the ground. The stream of human affairs flows its own way, and is very little affected by the activity of legislators. What great masses of men wish done, will be done; and they do not wish it for a freak, but because it is their state and natural end.”
—Ralph Waldo Emerson (1803–1882)
“Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.”
—Edna St. Vincent Millay (1892–1950)