Math Help - Partial Order

1. Partial Order

I had an extra credit question for my my math class:

Why is partial order interesting and why is it important?

Partial orders are interesting and important because they appear often everywhere in mathematics. Real numbers are ordered by the partial order $\leq.$ Natural numbers are ordered by the same order but also by the order $\mid$ (divisibility). Subsets of any set are ordered by the order $\subseteq.$