If A is a nonempty subset of R that is bounded below, show that A has a greatest lower bound. That is, show that there is a number satisfying: 1) m is a lower bound for A; and 2) if x is a lower bound for A, then x<=m. [Hint: Consider the set -A={ } and show that m = -sup(-A) works.]

The hint is confusing me, I'm really not good at proving, any help is appreaciated!