Empty Set Madness | Upper Bounds, Least Upper Bounds, and Contradictions | Intro To Analysis

Feel free to comment with alternative proofs. Note: This is Problem 9 in Chapter 2 - Properties of the Real Number System - of Maxwell Rosenlicht's book Introduction to Analysis The trick at the end where I supposed that "a" was a LUB and then took a number smaller than it was inspired by a trick I saw used by Michael Loss.