Another Least Upper Bound Practice Problem | Introduction to Real Analysis

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Introduction to Analysis by Rosenlicht | Chapter 2 - The Real Number System | Problem 13

I received a little help on this problem from Michael Loss's Analysis 1 webpage.

Here's the link to the video where I prove the little inequality trick that if a is greater than b
and c greater than or equal to d then a+c is greater than b+d

Always feel free to comment with questions, alternative proofs, or any fun thoughts you would like to share.
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Great video, thanks for being so thorough.

nicoinghilleri