ABSTRACT
This chapter describes the Cauchy sequences of a set of real numbers. If a sequence converges, then the sequence is referred to as a Cauchy sequence. The topic of completeness is quite abstract. It is really about a set of objects for which one has a way of measuring distance between objects and what happens to Cauchy sequences in this set. Given a set of objects, there is often more than one way to measure the distance between two objects. There are many pairings between a set of objects and a way to measure distance. Such a pairing needs to be described as the set plus its way of measuring distance. Cauchy sequences of rationals need not converge to a rational number. A real sequence is a cauchy sequence if and only if it converges. Continuity on a compact domain implies uniform continuity.
