1.1 Overview

In Chapter 1, I set up some notation, introduce the well-ordered property of the natural numbers and, as an application of the well-ordered property, I also prove the Fundamental Theorem of Arithmetic (Theorem 1.8). The first proof I give is Zermelo’s direct proof, which uses only the well-ordered property avoiding Euclid’s Lemma (Lemma 1.9. As such, I think it is a good example of how powerful the well-ordered property can be. On the other hand, as the usual proof using Euclid’s Lemma is nice too, I give the standard proof in Section 1.5.