Power set

In mathematics, the power set (or powerset) of a set S 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.
The powerset of S is variously denoted as P(S), 𝒫(S), P(S),




P



{\displaystyle \mathbb {P} }
(S), ℘(S) (using the "Weierstrass p"), or 2S. The notation 2S is used because given any set with exactly two elements, the powerset of S can be identified with the set of all functions from S into that set.Any subset of P(S) is called a family of sets over S.

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