Family of Sets
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A Family of Sets is a set composed of subsets from a set.
- AKA: Set of Sets, Set Set.
- Context:
- It can be represented by a Family of Sets Data Structure.
- …
- Example(s):
- a Power Set P(S) is a family of sets over S.
- a k-subsets S(k) of a set S form a family of sets.
- The class Ord of all ordinal numbers is a large family of sets; that is, it is not itself a set but instead a proper class.
- a Sperner Set Family,
- a Helly Set Family.
- …
- Counter-Example(s):
- a Subset.
- See: Set Theory, Class (Set Theory), Indexed Family, Combinatorial Design, Russell's Paradox.
References
2019
- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Family_of_sets Retrieved:2019-11-10.
- In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.
The term "collection" is used here because, in some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class rather than a set.
- In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.