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 power we exert over the future behavior of our children is enormous. Even after they have left home, even after we have left the world, there will always be part of us that will remain with them forever.”
—Neil Kurshan (20th century)
“I concluded that I was skilled, however poorly, at only one thing: marriage. And so I set about the business of selling myself and two children to some unsuspecting man who might think me a desirable second-hand mate, a man of good means and disposition willing to support another man’s children in some semblance of the style to which they were accustomed. My heart was not in the chase, but I was tired and there was no alternative. I could not afford freedom.”
—Barbara Howar (b. 1934)