Talk:Collection of All Ordered Sets is not Set

I'd like to add a proof based on the fact that the class of singletons is a proper class, as one can create an order on a single element, but have a few questions.

Firstly, should this be a proof that this is a proper class, or merely that it is not a set? Maybe it can prove that it isn't a set, then add a note below that extends this to a proof that it is a proper class.

Secondly, what kind of order is this talking about? Partial, total, and well-orders are all listed under the ordered set definition, and the above proof would work for any of them. It would also work for the strict versions of these orders, meaning this proof can be for any of 6 different statements. One approach would be to prove it for strict well orders, then extend it to a proof for strict total and partial orders as the class of well orders is a subset of them, then extend it to the non-strict versions by defining $a \leq b$ as $a < b \lor a = b$. --TheoLaLeo (talk) 07:14, 22 November 2021 (UTC)

The general ordering. If it meant a more specialised ordering, then it would have said so. Probably. --prime mover (talk) 20:28, 22 November 2021 (UTC)