Finite and Infinite Sets
Sets of many different sizes have been considered up to now; some have been finite and some infinite. In this section we will investigate what distinguishes finite from infinite and, in fact, because of the work of Georg Cantor (1845-1918), and others, we will even be able to draw distinctions between infinite sets on the basis of size. Then infinite sets of different sizes will be assigned different cardinal numbers. Finally, arithmetic and order properties of these numbers will be pursued.