@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?

Thanks.

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?

Thanks.