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Reference.org
Power set
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the power set (or powerset) of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> S is the set of all <a href="/facts/Subset/SJGERmbA">subsets</a> of S, including the <a href="/facts/Empty_set/ffEk3eA6">empty set</a> and S itself. In <a href="/facts/Axiomatic_set_theory/1ptfsvUP">axiomatic set theory</a> (as developed, for example, in the <a href="/facts/ZFC/UYIsPbXw">ZFC</a> axioms), the existence of the power set of any set is <a href="/facts/Postulated/mLjP14Mc">postulated</a> by the <a href="/facts/Axiom_of_power_set/Fmmj03nn">axiom of power set</a>. The powerset of S is variously denoted as P(<i>S</i>), 𝒫(<i>S</i>), <i>P</i>(<i>S</i>), P ( S ) {\displaystyle \mathbb {P} (S)} , or 2<i>S</i>. Any subset of P(<i>S</i>) is called a <i><a href="/facts/Family_of_sets/WbYof7lP">family of sets</a></i> over S. </p>