Natural Numbers and Integers

In this chapter, we recall how natural numbers and integers may be constructively defined, and how to prove the basic rules of computation we learn in school. The purpose is to give a quick example of developing a mathematical theory from a set of very basic facts. The idea is to give the reader the capability of explaining to her/his grandmother why, for example, 2 times 3 is equal to 3 times 2. Answering questions of this nature leads to a deeper understanding of the nature of integers and the rules for computing with integers, which goes beyond just accepting facts you learn in school as something given once and for all. An important aspect of this process is the very questioning of established facts that follows from posing the why,which may lead to new insight and new truths replacing the old ones.