Talk:Partial equivalence relation

I feel that the second sentence of the "Properties and applicatons" section is imprecisely stated. Here is the first part of that sentence, as it stands:

> However, given a set ${\displaystyle X}${\displaystyle X} and a subset ${\displaystyle Y\subseteq X}${\displaystyle Y\subseteq X}, an equivalence relation on ${\displaystyle Y}${\displaystyle Y} need not be a PER on ${\displaystyle X}${\displaystyle X}...

I think that the following would be more correct:

> However, given a set ${\displaystyle X}${\displaystyle X} and a subset ${\displaystyle Y\subseteq X}${\displaystyle Y\subseteq X}, a relation on ${\displaystyle X}${\displaystyle X} that is an equivalence relation when restricted on ${\displaystyle Y}${\displaystyle Y} need not be a PER on ${\displaystyle X}${\displaystyle X}...

This is a nontrivial change because a relation on ${\displaystyle X}${\displaystyle X} that is a proper subset (as a binary relation) of ${\displaystyle Y\times Y}${\displaystyle Y\times Y} is in fact a PER on ${\displaystyle X}${\displaystyle X}.

--Jasha10 (talk) 04:47, 26 May 2022 (UTC) [reply ]

Done - I agree with you and have changed the text accordingly. - Jochen Burghardt (talk) 12:41, 26 May 2022 (UTC) [reply ]

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