# Difference between revisions of "Family of Sets"

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* <B>Counter-Example(s):</B> | * <B>Counter-Example(s):</B> | ||

** a [[Subset]]. | ** a [[Subset]]. | ||

− | * <B>See:</B> [[Set Theory]], [[Class (Set Theory)]]. | + | * <B>See:</B> [[Set Theory]], [[Class (Set Theory)]], [[Indexed Family]], [[Combinatorial Design]], [[Russell's Paradox]]. |

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## Latest revision as of 23:22, 10 November 2019

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.

- a Power Set
**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