Overview

Set theory, and its transformation of mathematician's ideas of infinity, was mainly the work of one man, the nineteenth-century German mathematician Georg Cantor (1845-1918). Cantor found ways to work with infinite sets, which many believed could not exist. He further alarmed his contemporaries by demonstrating that while all infinite sets are indefinitely large, some are nonetheless larger than others.

Background

One of the earliest philosophers of infinity was Zeno of Elea (495-435 B.C.). His ponderings led him to paradoxes such as one in which Achilles running to overtake a crawling tortoise could never accomplish the feat. First, you see, he must reach the place where the tortoise started, and by that time the tortoise is no longer there. In fact, Zeno "proved" that the entire idea of motion was absurd. Finally, the local authorities...