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:
“Mothers who have little sense of their own minds and voices are unable to imagine such capacities in their children. Not being fully aware of the power of words for communicating meaning, they expect their children to know what is on their minds without the benefit of words. These parents do not tell their children what they mean by “good” much less why. Nor do they ask the children to explain themselves.”
—Mary Field Belenky (20th century)
“She’s just a child,
but I’m the one who’s fainthearted.
She’s the woman,
but I’m the coward.
She bears that high, swollen set of breasts,
but I’m the one who’s burdened.
The heavy hips are hers,
but I’m unable to move.
It’s a wonder
how clumsy I’ve become
because of flaws
that shelter themselves
in another.”
—Amaru (c. seventh century A.D.)