The Real and Complex Number Systems

Sections 4.1 and 4.2 show how the real numbers can either be defined axiomatically, or constructed all the way from the natural numbers, to the integers, to the rational numbers, and finally to the real numbers using equivalence relations introduced in Chapter 3. The Dedekind cut is introduced in Section 4.2, which defines the real numbers in terms of the rational numbers. Finally in 4.3 a brief tutorial on the complex numbers, a subject often overlooked in the undergraduate curricula.