ABSTRACT
This chapter assumes the existence of the ordered field of real numbers and presents a few examples to develop some tools for exploring sequences of real numbers. It shows that a sequence is Cauchy and discusses the properties of Cauchy sequences. The chapter provides a number of propositions about Cauchy sequences of real numbers that are analogous to propositions about convergent sequences of real numbers. Such analogues exist because, in the real number system, a sequence is convergent if and only if it is Cauchy. The chapter also includes some exercise problems related to the sequences of real numbers.
