In mathematics, a set can be thought of as a well defined collection of objects. The "objects" with which we will be concerned are abstract entities such as numbers or other sets. Until late in the nineteenth century, there were few references to sets in the mathematical literature, but this was to change dramatically due to the work of one brilliant German mathematician, Georg Cantor (1845-1918). The official birth of set theory can be traced to an 1874 article by Cantor in Crelle's Journal, one of the most influential mathematics journals of its time. In this article, Cantor suggested that there were different kinds of infinite sets and different orders of infinity. This idea stirred up tremendous controversy among some editors of the journal and among mathematicians in general. Prior to this publication, all infinite sets had been considered alike. No one had ever suggested that there were different...