\\(\forall x\in X, x \leq x\\) looks like a standard poset to me, not just a preorder

\\(\forall x,y \in X, x \leq y \\) and \\( y \leq x \\) implies \\(x \leq x \\)

Incidentally, have we diverged from Fong & Spivak in these lectures, i.e. do we use poset and preorder with their standard meanings?