power set
Sign in to saveset (in mathematics) containing all subsets of a given set
AI overview
A power set is a collection that contains every possible subset you can make from a given set, including the empty set and the set itself. It matters because it's a fundamental concept in mathematics that helps us understand how sets relate to each other and is used in logic, probability, and computer science.
AI-generated from the Wikipedia summary — may contain errors.
Key facts
- Type
- Set operation
- Field
- Set theory
- Statement
- The power set is the set that contains all subsets of a given set.
- Symbolic statement
- x ∈ P ( S ) ⟺ x ⊆ S
via Wikipedia infobox
Article
In mathematics, the power set (or powerset) of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory (as developed, for example, in the ZFC axioms), the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), 𝒫(S), P(S),
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