Definition talk:Ordering

It is unclear to me what is gained by defining "ordering" to be what most sources would call a "poset" and then (consistently but oddly) adopting a non-standard definition of "poset" (i.e., that it *must* be partial). This in addition seems to leave the site with no term for a preorder that is not an equivalence relation but also is not antisymmetric (i.e., what other sources would call an "ordering" or an "order relation"). Anyone tempted to say that "preorder" is the term is dismissive of the need for the convenience provided by specificity.