I do not even have an idea how to prove the following. Could you please help me?
We say that a set of real numbers $A$ is bounded below if there is a number $d$ such that $d \leq x$ for all $x \in A$; then $d$ is called lower bound of $A$. Every nonempty bounded below set of real numbers has greatest lower bound which is denoted by $\inf A$. Prove that:
$\inf A = −\sup(−A)$, where $−A = \{−x : x \in A\}$.
Thanks in advance
Amadeus