Total Order
Total Order is a Partial Order R on a set S where every pair of elements is comparable: for all , b \in S$, either \ R \ b$ or \ R \ a$.
For example, on the integers is a total order, since for any two integers one is always less than or equal to the other. "a divides b" is a partial order but not a total order, since 2 and 3 don't divide each other. See Week 18 - Relations B.