
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.
The
book is designed for students studying on their own, without access to
lecturers and other reading, along the lines of the internationally
renowned courses produced by the Open University. There are thus a large
number of exercises within the main body of the text designed to help
students engage with the subject, many of which have full teaching
solutions. In addition, there are a number of exercises without answers
so students studying under the guidance of a tutor may be assessed
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