6 Number Theory

In the Chapter 4, we defined the natural numbers and the integers and looked at some of their basic properties and representations. The subject of Number Theory is the detailed study of the set of Integers and their operations. In this chapter we will combine the properties of the Integers studied in Chapter 4 with the ideas of function and cardinality in Chapter 5 to focus on a few topics of number theory, particularly issues related to divisibility and counting arguments. We will leave some important properties of the integers, including the Fundamental Theorem of Arithmetic, for Section 8.1 in order to see the connection with the set of polynomials.