Definition of "power set"

power set

noun
plural power sets
1. (set theory, of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself).
  Quotations
  Moreover, for notational convenience, we write the cardinality of a denumerable set as ℵ 0 {\displaystyle \aleph _{0}} . Cardinality of the power set of a denumerable set is written as ℵ 1 {\displaystyle \aleph _{1}} . We may thus extend this notation further by taking cardinality of the power set of the power set of a denumerable set as ℵ 2 {\displaystyle \aleph _{2}} , etc. but we do not have the need for it right now.
  2009, Arindama Singh, Elements of Computation Theory, Springer, page 16
  Theorem 4.1. A complete Boolean algebra B has a set of (complete and atomic) ca-free generators iff B is isomorphic to the power set of a power set.
  2013, A. Carsetti, Epistemic Complexity and Knowledge Construction, Springer, page 94
  Exponentiation is essentially a move to the power set—the set of all subsets of a given set. This is one of the reasons why Bertrand Russell's paradox is indeed a paradox: We cannot find a universal set because no set can contain its own power set!
  2015, Amir D. Aczel, Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, Palgrave MacMillan, page 147