Talk:Lower set

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Proposed merge[edit]

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)