ABSTRACT
This chapter discusses properties of the natural numbers and integers in more detail, as well as the construction of the rational numbers from the integers. It provides representations of some small natural numbers in different bases and develops an algorithm for expressing a given natural number in terms of a fixed base. The chapter defines modular arithmetic carefully and explores some elementary properties. It provides a definition of rational numbers that incorporates into it the notion that a given rational number can be represented by more than one ratio of integers. The chapter gives a brief introduction to the variety of algebraic structures, with a focus on routine verification proofs. It also includes some exercise problems related to number systems and algebraic structures.
