@John #40: thanks. I've updated the diagram accordingly, though a side effect is your post now shows the new version (apologies). You can use [https://raw.githubusercontent.com/sfinnie/CategoryTheoryCourseNotes/6bbcc770474a8945ee4e47e273a65909f979b818/posets/img/orderVennDiagram.gif](https://raw.githubusercontent.com/sfinnie/CategoryTheoryCourseNotes/6bbcc770474a8945ee4e47e273a65909f979b818/posets/img/orderVennDiagram.gif) to access the original in your post.
It was something I considered in drawing the diagram. I decided on "Unordered" as a disjoint set, on the basis that there are some which are explicitly *not* ordered. So those that obey the rule:
* ***unordered***: for all \\(x\\) and \\(y\\), there exists no \\(x, y\\) such that \\(x \le y \\).
I think the "Set" rectangle in the revised diagram now means "Possibly ordered". It still caters for unordered sets, but doesn't assert any properties about them. Is that correct?