Let A be a nonempty set of real numbers which

[Jamin2112]

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.

 

[Jamin2112]

[URL]http://www.threadbombing.com/data/media/8/bummmp.gif[/URL]
By the way, if you help me with this problem I'll give you another one.