“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” (“Family of sets,” Wikipedia, retrieved 7/17/2020).
Note that the set S is a subset* of itself, so can be in F.
.
*What is the Gist of a “Subset”?
.
Disclaimer:
I am not a professional in this field, nor do I claim to know all of the jargon that is typically used in this field. I am not summarizing my sources; I simply read from a variety of websites until I feel like I understand enough about a topic to move on to what I actually wanted to learn. By definition, none of these posts address every aspect of a topic. If I am inaccurate in what I say or you know a better, simpler way to explain a concept, I would be happy to hear from you :).
