# 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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Please explain in your own words how the proof works; don't just copy the solution.

Please use words to describe the proof.

If you use a theorem, ...

#### Solution Summary

Bounded numbers are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.