# Difference between revisions of "Family of Sets"

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+ | * (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 [[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].

**Context:**- It can be represented by a Family of Sets Data Structure.

**Example(s):**

(* Let *S* = {a,b,c,1,2}, an example of a family of sets over *S* (in the multiset sense) is given by *F* = {A_{1}, A_{2}, A_{3}, A_{4}} where A_{1} = {a,b,c}, A_{2} = {1,2}, A_{3} = {1,2} and A_{4} = {a,b,1}.

- 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.

- The class Ord of all ordinal numbers is a
**See:**Set Theory, Subset, Class (Set Theory).

## 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.

- In set theory and related branches of mathematics, a collection

### 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