1. Let [itex] A [/itex] be a nonempty set of real numbers which is bounded below. Let [itex] -A [/itex] be the set of numbers [itex] -x [/itex], where [itex] x \in A [/itex]. Prove that [itex] \inf(A) = -\sup(-A) [/itex]. Intuitively this makes sense if you draw it on a number line. But I am not sure how to formally prove it.