Upper Bounds Example Problem | Proving a Set Has No Upper Bound | Intro to Real Analysis

Introduction to Analysis by Rosenlicht | Chapter 2 - The Real Number System | Problem 11

Videos I reference:

Proof (using the least upper bound property) that there exist arbitrarily large powers of 2

Proof of addition inequality tool:

Proof of multiplication inequality tool:

A roundabout proof that there exists arbitrarily small rational numbers:

Proof that a greater than b implies a-b is in the positive reals (part of the Order Property of the Real Numbers):