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. Classic Set Theory gives students sufficient
grounding in a rigorous approach to the revolutionary results of
set theory as well as pleasure in being able to tackle significant
problems that arise from the theory.
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