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Bounded Numbers

Let A be a nonempty set of real numbers which is bounded below. Let -A be the set of all numbers -x where x E A.
Prove that inf A = -sup(-A)
(Please see the attached file for the fully formatted problem.)

Included in the attachment is a copy of the solution, but please explain in your own words how the proof works; don't just copy the solution out. Please use words to describe the proof. If you use a theorem, please state what it is and if possible, where you got it.


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