Alex Kreitzberg #20: Yeah, I should have specified that I meant the subset with ordering.

Can we define a hierarchy of ordering within posets in order to make a totally ordered set? So given a poset made up of two types of objects, one letters and one numbers, both with the natural ordering for each type, then can we define a higher ordering to say letters are always less than numbers to make a totally ordered set, and would that still be a poset? Or does that not make sense within the concept of a poset?

Can we define a hierarchy of ordering within posets in order to make a totally ordered set? So given a poset made up of two types of objects, one letters and one numbers, both with the natural ordering for each type, then can we define a higher ordering to say letters are always less than numbers to make a totally ordered set, and would that still be a poset? Or does that not make sense within the concept of a poset?