Hi, I have the following problem... I know the second bit of it, but I have no clue how to prove the first bit. I know B is bounded below (it is basically set A but with opposite signs, so the supremum of A will be the lowest number of set B, its infimum), but I don't know how to express it mathematically. Thanks for any help you can give me!

"Let A be a non-empty subset of R that is bounded above. Let

B = {-x : x ϵ A}.

Show that B is bounded below. How are sup A (supremum of A) and inf B (infimum) related?"

I don't know how to prove that B is bounded below, but for the question "How are sup A (supremum of A) and inf B (infimum) related?", I have the following:

sup A = -inf B.