# power set

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power set
The power set of a set S is the set of all subsets of S. See also Cantor's theorem.

Philosophy dictionary. . 2011.

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• Power set — In mathematics, given a set S , the power set (or powerset) of S , written mathcal{P}(S), P ( S ), or 2 S , is the set of all subsets of S . In axiomatic set theory (as developed e.g. in the ZFC axioms), the existence of the power set of any set… …   Wikipedia

• power set — Math. the collection of all subsets of a given set. [1950 55] * * * power set noun (mathematics) A set comprising all the subsets of a given set • • • Main Entry: ↑power …   Useful english dictionary

• power set — noun The set of all subsets of a set. Notation for a set S: or 2 The power set of 1, 2 is Ø, , , 1, nbsp;2 …   Wiktionary

• power set — Math. the collection of all subsets of a given set. [1950 55] * * * …   Universalium

• Axiom of power set — In mathematics, the axiom of power set is one of the Zermelo Fraenkel axioms of axiomatic set theory.In the formal language of the Zermelo Fraenkel axioms, the axiom reads::forall A , exists P , forall B , [B in P iff forall C , (C in B… …   Wikipedia

• Set tools — are a forging tools that are meant to be struck by a hammer, either sledge or power. Set tools are usually made with a handle to keep the smith a safe distance from the action. Set tools for the anvil, where they are struck with a sledgehammer,… …   Wikipedia

• Set (mathematics) — This article gives an introduction to what mathematicians call intuitive or naive set theory; for a more detailed account see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory. The intersection of two sets is… …   Wikipedia

• Power graph analysis — In computational biology, power graph analysis is a method for the analysis andrepresentation of complex networks. Power graph analysis is the computation, analysis and visual representation of a power graph from a graphs (networks).Power graph… …   Wikipedia

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• Set theory — This article is about the branch of mathematics. For musical set theory, see Set theory (music). A Venn diagram illustrating the intersection of two sets. Set theory is the branch of mathematics that studies sets, which are collections of objects …   Wikipedia

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