1.Let $\displaystyle A $ be a nonempty set of real numbers which is bounded below. Let $\displaystyle -A $ be the set of numbers $\displaystyle -x $, where $\displaystyle x \in A $. Prove that $\displaystyle \inf(A) = -\sup(-A) $.

Intuitively this makes sense if you draw it on a number line. But I am not sure how to formally prove it.