# Talk:Set Equivalence behaves like Equivalence Relation

## This theorem is too broad as stated to match Definition:Equivalence Relation

Definition:Equivalence Relation defines equivalence relations on sets. The statement of this theorem makes no mention of the set involved. So either this needs to refer to a broader definition of equivalence relation (allowing relations, e.g., on the (proper) class of all sets), or the theorem needs to be narrowed to say that if $S$ is a set of sets, then set equivalence is an equivalence relation on $S$. --Dfeuer (talk) 04:01, 12 December 2012 (UTC)

I vote for both, but while I like the first one better, it must be remarked that under current terminology it isn't strictly speaking an equivalence. --Lord_Farin (talk) 15:48, 12 December 2012 (UTC)
I vote for the second for the reason L_F mentioned. Please be very clear on this page if you have to change it and use the concept of equivalence class. Although it should be done in this case I question the usefulness of setting up a UoD for everything. Please do not get carried away and change theorems like Union is Associative to include statements like:
$\forall A,B,C \in U: A \cup \paren {B \cup C} = \paren {A \cup B} \cup C$
--Jshflynn (talk) 16:58, 12 December 2012 (UTC)
Sadly, I don't understand either answer to my question. Lord Farin, why is it not an equivalence? Jshflynn, the definition of equivalence class on this site (currently) is defined in terms of equivalence relations, so that doesn't give any extra strength. --Dfeuer (talk) 18:09, 12 December 2012 (UTC)
An equivalence relation is defined as a binary relation on a set $S$. One suggestion you made was that we introduce set equivalence as a binary relation on the proper class of all sets. So technically it wouldn't be an equivalence relation. I believe this was LF's point.
My point was to be careful with the term "equivalence class" if you had to use it in your reworking of the article. This is because the it contains the word "class" and so could cause confusion.

Work is in progress to try and bring some consistency to this area. --prime mover (talk) 06:34, 28 June 2021 (UTC)

Right, that should be adequate. We have started to make some inroads into the question of how to present class theory, but it's slow work because of the intellectual limitations of the one working on it. --prime mover (talk) 06:18, 30 June 2021 (UTC)