power set en · NOUN
Meanings
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(of a set S) The set whose elements comprise all the subsets of S (including the empty set and S itself).
Moreover, for notational convenience, we write the cardinality of a denumerable set as #92;aleph#95;0. Cardinality of the power set of a denumerable set is written as #92;aleph#95;1. We may thus extend this notation further by taking cardinality of the power set of the power set of a denumerable set as #92;aleph#95;2, etc. but we do not have the need for it right now.
2009, Arindama Singh, Elements of Computation Theory, Springer, page 16:The power set of #92;#123;1,2#92;#125; is #92;left#92;#123;#92;empty,#92;#123;1#92;#125;,#92;#123;2#92;#125;,#92;#123;1,2#92;#125;#92;right#92;#125;.
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: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:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| powerset | alternative | lexicographic | |
| power sets | Number=Plur | lexicographic | |
| power-set | alternative | lexicographic |
Deriveds
Relateds
Translations (18)
it insieme delle parti (set of all subsets of a set) · cmn 冪集 /幂集 (set of all subsets of a set) · is veldismengi (set of all subsets of a set) · he קבוצת חוזקה \ קְבוּצַת חָזְקָה (set of all subsets of a set) · hu hatványhalmaz (set of all subsets of a set) · ko 멱집합 (set of all subsets of a set) · ja 冪集合 (set of all subsets of a set) · cs potenční množina (set of all subsets of a set) · ru булеан (set of all subsets of a set) · es conjunto de partes (set of all subsets of a set) · it insieme potenza (set of all subsets of a set) · nl machtenverzameling (set of all subsets of a set) · fr ensemble des parties (set of all subsets of a set) · sh partitivni skup (set of all subsets of a set) · sv potensmängd (set of all subsets of a set) · de Potenzmenge (set of all subsets of a set) · pl zbiór potęgowy (set of all subsets of a set) · pt conjunto de partes (set of all subsets of a set)