Infinite and Finite Sets

Infinite sets can behave more strangely than finite ones, at least from the perspective of 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, but this topic is beyond the scope of this text.