# Let A be a nonempty set of real numbers which

## Homework Statement

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

## Homework Equations

Definitions of upper bound, lower bound, least upper bound, and least lower bound.

## The Attempt at a Solution

Here's what I have so far:

Almost there! I just need to derive a contradiction on my assumption that gamma is an upper bound for -A.