power set
Noun
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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).
- The power set of \{1, 2\} is \left \{\empty, \{1\}, \{2\}, \{1, 2\}\right \}.
- 2009, Arindama Singh, Elements of Computation Theory, Springer, page 16 ↗,
- Moreover, for notational convenience, we write the cardinality of a denumerable set as \aleph_0. Cardinality of the power set of a denumerable set is written as \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 \aleph_2, etc. but we do not have the need for it right now.
- 2013, A. Carsetti, Epistemic Complexity and Knowledge Construction, Springer, page 94 ↗,
- 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.
- 2015, Amir D. Aczel, Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, Palgrave MacMillan, page 147 ↗,
- 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!
- French: ensemble des parties
- German: Potenzmenge
- Italian: insieme delle parti, insieme potenza
- Portuguese: conjunto de partes
- Russian: булеан
- Spanish: conjunto de partes
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.038