For a subset $A$ of $\mathbb{R}$ define $-A=\{-x : x \in A\}$. Suppose that S is a non-empty bounded subset of $\mathbb{R}$
Prove:
1) $-S$ is bounded below
2) $\inf(-S)=-\sup(S)$
3) From (2) conclude that the greatest upper bound property implies the least upper bound property
I am not looking for answers is $S$ supposed to be $-A$? The wording of the question is confusing