Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:
- The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbers
- Defining natural numbers in terms of sets
- The potential paradoxes in set theory
- The Zermelo-Fraenkel axioms for set theory
- The axiom of choice
- The arithmetic of ordered sets
- Cantor’s two sorts of transfinite number – cardinals and ordinals – and the arithmetic of these.
