Definition:Set of Sets

Definition

A set of sets is a set whose elements are themselves all sets.

Also known as

Many sources (perhaps still feeling the wrath of the cane from schoolteachers of English) feel uncomfortable about referring to a set of sets and use a synonym instead.

Thus you will find terms such as collection of sets, family of sets, assembly of sets - it goes on and on.

Beware the following

Take care when you see class of sets, because in modern set theory a class is a subtly different object from a set.

Also note that some books on, for example, topology and analysis will use the word family of sets to mean set of sets, whereas the technically accurate definition for family in recent times is a subtly different concept.

Also see

A system of sets is also defined as a set whose elements are themselves all sets, but the implication here is that the sets in question are augmented by the various operations, thus turning such sets of sets into algebraic structures.

Sources

• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 1.8$
• Ian D. Macdonald: The Theory of Groups (1968): Appendix