Partial Order

Partial Order is a Relation R on a set S that is reflexive, anti-symmetric and transitive.

For example, $\leq$ on the integers is a partial order: \leq a$, if \leq b$ and \leq a$ then = b$, and if \leq b$ and \leq c$ then \leq c$. "a divides b" on the positive integers is another one.

It's called "partial" because not every pair of elements has to be comparable. For "divides", neither 2 nor 3 divides the other. When every pair is comparable, it's a Total Order. See Week 18 - Relations B.