Talk:Idempotent relation

Example

Could the example be clarified, it is not clear what is meant. --SomethingKdVI (talk) 12:00, 10 June 2015 (UTC)[reply]

Clarity

At Binary relation a distinction is made between the set of departure of a relation and its domain. The difference is important for inverse elements which arise in semigroups and are not full inverses like in a group. Viktor Wagner worked with partial functions to motivate inverse semigroups. For a given relation in ${\mathcal {B}}(X)$ the domain may well be less than X, in which case its compostion with its converse yields an idempotent which is an "inverse element" in the sense of semigroups. Introduction of the full class of binary relations on X emphasizes that a relation may have a domain less than the whole set of departure. Further, the use of backwards notation for relational composition has been criticised on the appropriate Talk page. — Rgdboer (talk) 21:34, 19 July 2019 (UTC)[reply]

@Rgdboer: The 1st lead sentence introduces "binary relation on a set X" in the same sense as you are introducing "B(X)", so I still consider the notation as unnecessary formalism. - Tacit use of "Q R" for "R \circ Q" must lead to confusion; a critics on some "appropriate Talk page" (which you are apparently unable to find) is of no help to a reader. It would have been less worse if you'd changed the composition notation of the whole article to "Q R".

Although you reverted them, you didn't comment on the following parts of my edit summary:

avoid "consider";
avoid 3rd link to composition of relations;
avoid adjacent formulas;
suggest to use main title serial relation;
not sure about domain;
link identity relation;
"in X \times X" --> "on X";
unable to follow proof idea immediately, requesting citation

Please comment these subsequently. - Jochen Burghardt (talk) 16:46, 20 July 2019 (UTC)[reply]

Thank you Jochen Burghardt for flagging the several problems with that contribution. Now it is replaced with another contribution also requiring review. The relation suggested at first is no idempotent, so the whole notion is now erased but for the diffs in History. Again, your awareness is appreciated. — Rgdboer (talk) 21:33, 20 July 2019 (UTC)[reply]