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The article is called "greatest element", but it talks as much about the greatest element as it does about the least element. (Naturally, as they are duals.) I propose to rename the article to "greatest and least element". (Or maybe even to "greatest and least element of a partially ordered set"?) —
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The definition is slightly more general. The special case of a partial order is handled in its 3rd paragraph. I added an "even" to emphasize the special/general relation between both cases. In the lead, I think it is ok to mention just the partial-order case since it is best known. -
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Should a mention to the well-ordering relation be made since the subject of this article (specifically a least element) is what makes a well-order from a total order?
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Yes, there is some intersection. I think the two articles look at things from a bit different perspectives though, but I am not sure. Let us see if a specialist in
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which affects this page. Please participate on that page and not in this talk page section. Thank you. —
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I consider this a good idea. For now, I just added an annotated link under "See also". -
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It is confusing that the intro speaks of a poset, and the definition of a preorderd set.
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