power set

== English == === Alternative forms === power-set (attributive use) powerset === Noun === power set (plural power sets) (set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself). ==== Usage notes ==== Denoted using the notation P(S) with any one of several fonts for the letter "P" (usually uppercase). Examples include: P ( S ) {\displaystyle {\mathcal {P}}(S)} , ℘ ( S ) {\displaystyle \wp (S)} (with the Weierstrass p), P ( S ) {\displaystyle \mathbb {P} (S)} and 𝒫(S). An alternative notation is 2 S {\displaystyle 2^{S}\!\!} , derived from the consideration that a set T {\displaystyle T} in the power set is fully characterised by determining, for each element of S {\displaystyle S} , whether it is or is not in T {\displaystyle T} . ==== Derived terms ==== hyper-power set ==== Translations ==== === See also === axiom of power set === Further reading === Axiom of power set on Wikipedia.Wikipedia