Set theory : a first course
Author(s)
Bibliographic Information
Set theory : a first course
（Cambridge mathematical textbooks）
Cambridge University Press, 2016
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Note
Includes bibliographical references (p. [241]) and index
Description and Table of Contents
Description
Set theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
Table of Contents
- 1. Introduction
- 2. Basic set building axioms and operations
- 3. Relations and functions
- 4. The natural numbers
- 5. On the size of sets
- 6. Transfinite recursion
- 7. The axiom of choice (revisited)
- 8. Ordinals
- 9. Cardinals.
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