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when the Lab is back, could somebody please remember to remove the redirect setoid from equivalence relation and have it instead point to Bishop set ? Thanks.
Redirect: relation of equivalence.
Link to a new page tolerance relation (stub to be created in minutes).
Following discussion in another thread (here) I have truncated the paragraph
A set equipped with an equivalence relation is sometimes called a setoid; however the term setoid is primarily used for a pseudo-equivalence relation instead, and the usage on the nLab follows the latter.
after the semicolon. The claim that “the nLab follows” some convention is generally dubious but particularly here where the nLab wasn’t even told about it (the Anonymous edit in rev 38 was not announced).
While we are at it: I don’t find the paragraph that follows was adding clarity:
This terminology is particularly common in foundations of mathematics where quotient sets don't always exist and the above equivalence to a set cannot be carried out. However, arguably this is a terminological mismatch, and such people should say ’set’ where they say ’setoid’ and something else (such as ’preset’, ’type’, or ’completely presented set’) where they say ’set’. (See Bishop set and page 9 of these lecture notes.)
I find this more than less confusing: Who is meant with “such people”? In any case, these are matters that should be sorted out at setoid. So I took the liberty of just deleting this paragraph and in its place adding, after the link to “setoid”, the words: “see there for more”.
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