Talk:Family of sets

This is functionally incomprehensible to anyone without a grounding in number theory. Can some attempt be made to explain this in non-jargon terms? 99.111.150.112 (talk) 07:03, 7 December 2019 (UTC)

It's set theory, not number theory. And it's perhaps a little cryptic in its current form, but Ptolemy I Soter#Euclid also comes to mind as relevant. —David Eppstein (talk) 07:19, 7 December 2019 (UTC)

In the mathematics literature (see e.g. Herstein), far more often the term family is a synonym for function, so a family of sets is a set-valued function. Boute (talk) 10:05, 12 February 2021 (UTC)

I think there is a mistake in the table: a Dynkin system is not closed under intersection, is it? 62.240.134.129 (talk) 09:06, 2 October 2021 (UTC)

I edited the corresponding page (Template:Families of sets), so the table should be correct now. Jakeskat (talk) 18:29, 30 June 2022 (UTC)

"If every point of a cover lies in exactly one member, the cover is a partition of a set". Counterexample:

A = {1, 4, 7}

F = {{1,2,3}, {4,5,6}, {7,8,9}}

Here, all the points in family of sets F lie in exactly one member of a family. Moreover, F is a cover of A. But F is not a partition of A, as the union of a partition must be the same as the initial set A. Killigann (talk) 13:32, 17 October 2024 (UTC)

I have clarified that

If every point of a cover lies in exactly one member of ${\displaystyle X}$, the cover is a partition of ${\displaystyle X.}$

That is, "points" refers to members of ${\displaystyle X}$—not the family.—Anita5192 (talk) 14:11, 17 October 2024 (UTC)