Talk:Lower set

Proposed merge

Upper set and lower set are dual notions, and so both articles necessarily basically say the same just with "greater then or equal" switched with "less than or equal" etc. I think it makes sense to merge both articles into one article Lower set and upper set with appropriate redirects. — Tobias Bergemann 08:48, 28 August 2006 (UTC)

It's not just that they're the same concepts: they're almost the same objects, as complementation puts the lower sets and upper sets of any partial order into 1-1 correspondence. (In the case of finite orders they also correspond 1-1 with the Antichains but that's not true more generally e.g. for the total order on Q an antichain is a single rational while a lower or upper set is a Dedekind cut.) And the redundancy would make it awkward to keep the articles in synch in the case of any changes. So I agree with the proposed merge. I think Maximal element would make a good model: it is a single article, named after one of the two dual concepts, but its dual name is just a redirect to the same page. —David Eppstein 06:15, 12 September 2006 (UTC)