Definition talk:Dual Ordering

I note that this as a separate page to Definition:Inverse Relation, but they are in fact exactly the same thing, except for the fact that a "dual ordering" is what some sources call it when the relation in question is specifically an ordering (possibly subsuming the concept of a strict ordering as well).

My proposal is that this page be merged with Definition:Inverse Relation, with the term "dual ordering" being added into the "also known as" section on that page. "When $\mathcal R$ is an ordering, its inverse is referred to in some sources (e.g. the Birkhoff work cited in the subpage?) as the dual ordering sort of thing.

Thoughts? --prime mover (talk) 05:56, 6 April 2015 (UTC)


 * Not everyone using orderings will have encountered relations. For ease of reference, I would recommend keeping this page separate. Naturally, the two pages should be linked, but I think even a transclusion would be too much here. Just links would be my preferred approach. &mdash; Lord_Farin (talk) 16:03, 7 April 2015 (UTC)


 * (Noticed the notation subpages on Inverse Relation.) I think the notation subpages on inverse relation should be on this page. This is where they belong. &mdash; Lord_Farin (talk) 16:05, 7 April 2015 (UTC)


 * Two rebuttals: a) only the majority of sources (of those I've seen) refer to the "the inverse (of the) ordering" and don't mention the term "dual ordering" (even Cohn doesn't use the term "dual ordering"), and b) all the rigorous treatments of an ordering that I've seen define the ordering as a relation with those particular properties (antisymmetry, transitivity, reflexivity), so in a certain sense you can't encounter orderings (at least, at this level) without encountering relations.


 * In the context of numbers, the ordering relations $\le$ etc. are taken for granted anyway, and there is never a need to go from there to the abstract properties of orderings -- and if there is a need to analyse the properties of orderings on numbers, still the only way to approach them is to discuss "relations with properties".


 * My motivation for merging them is to emphasise the fact that the two definitions (inverse relation and dual ordering) are the same thing.


 * The reason I put the notation pages on inverse relation rather than here was purely in anticipation of the future merge as I sort of took it for granted that it would be a done thing. --prime mover (talk) 18:05, 7 April 2015 (UTC)


 * I concede. Do as you please. &mdash; Lord_Farin (talk) 21:55, 7 April 2015 (UTC)


 * Revisiting this after all this time ... I'm inclined to leave it as it is. --prime mover (talk) 21:35, 9 May 2021 (UTC)