Talk:Equipotent sets

"Equipotence is an equivalence relation on a family of sets" — As for me, a "family" means, a mapping from an "index" set (to something). Here I'd say, on the class of all sets. But maybe dialects differ. Boris Tsirelson (talk) 20:30, 10 January 2015 (CET)

Really, I see that the terminology is unstable. In "Centred family of sets" I see indexed family; but in "Upper bound of a family of topologies" I see that "family" is just another name for a set. Boris Tsirelson (talk) 20:38, 10 January 2015 (CET)

I deliberately used "family" to avoid the word "class" here, because of logical difficulties. An equivalence relation is defined as a subset of a certain set, but the class of all sets is a proper class, not a set, and so we have not defined an equivalence relation on a proper class of sets. On the other hands, to talk of a set of sets, while perfectly correct, seemed inelegant in this context. Richard Pinch (talk) 21:17, 10 January 2015 (CET)