Difference between revisions of "Family of Sets"

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=== 2019 ===
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* (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Family_of_sets Retrieved:2019-11-10.
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** In [[set theory]] and related branches of [[mathematics]], a collection ''F'' of [[subset]]s of a given [[Set (mathematics)|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'''. <P> 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 [[Class (set theory)|proper class]] rather than a set.

Revision as of 23:13, 10 November 2019

A Family of Sets [math]F[/math] is a set composed of subsets from set [math]S[/math].

(* Let S = {a,b,c,1,2}, an example of a family of sets over S (in the multiset sense) is given by F = {A1, A2, A3, A4} where A1 = {a,b,c}, A2 = {1,2}, A3 = {1,2} and A4 = {a,b,1}.



References

2014

  • (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Family_of_sets Retrieved:2014-4-21.
    • 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.




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.