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HandWiki. Power Set. Encyclopedia. Available online: https://encyclopedia.pub/entry/32795 (accessed on 14 September 2026).
HandWiki. Power Set. Encyclopedia. Available at: https://encyclopedia.pub/entry/32795. Accessed September 14, 2026.
HandWiki. "Power Set" Encyclopedia, https://encyclopedia.pub/entry/32795 (accessed September 14, 2026).
HandWiki. (2022, November 04). Power Set. In Encyclopedia. https://encyclopedia.pub/entry/32795
HandWiki. "Power Set." Encyclopedia. Web. 04 November, 2022.
Power Set
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The content is sourced from: https://handwiki.org/wiki/Power_set

In mathematics, the power set (or powerset) of any set S is the set of all subsets of S, including the empty set and S itself, variously denoted as P(S), 𝒫(S), ℘(S) (using the "Weierstrass p"), P(S), ℙ(S), or, identifying the powerset of S with the set of all functions from S to a given set of two elements, 2S. 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 P(S) is called a family of sets over S.

axiomatic set theory power set empty set

References

  1. Puntambekar 2007, pp. 1–2
  2. Saunders Mac Lane, Ieke Moerdijk, (1992) Sheaves in Geometry and Logic Springer-Verlag. ISBN 0-387-97710-4 See page 58
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