I'm not really sure where to start with this problem, because the sets we're talking about here are infinite. I guess the root would be the empty set, then 0, etc., but how do you show it for 0..n and 0..m?Given totally ordered sets 0..n and 0..m with the ordinary $\displaystyle \leq$ orders, consider the Cartesian product of these sets, with $\displaystyle (a, b) \leq (c, d) \Leftrightarrow (a \leq c) \wedge (b \leq d)$. Draw the Hasse diagram showing the partial order relation.

Thanks!