Applications of full covers in real analysis

Abstract

In this paper we briefly introduce the reader to the concept of full covers and indicate how it can be used to prove theorems in an undergraduate analysis course. The technique exposes the student to the idea of covering an interval $\left[a,b\right]$ with a collection of sets and then extracting from this collection a subcollection that partitions $\left[a,b\right]$. As a consequence, the student is furnished with a unifying thread that ties together and simplifies the proofs of many theorems.