Finite Sets and Infinite Sets

Abstract

Infinite sets appear to behave more strangely than finite ones, at least from our perspective as human beings, whose daily experience is of the finite. The difficulty of dealing with infinite sets was raised by the ancient Greek Zeno in his four “paradoxes”; see [Ang94, Chapter 8] or [Boy91, pp. 74–76] for details. From a modern perspective Zeno’s paradoxes are not paradoxes at all, and can be resolved using tools from real analysis, developed long after Zeno. However, these paradoxes had a historical impact on the study of the infinite, and they indicate how much trickier it is to understand the infinite than the finite.