Set Theory
eBook - PDF

Set Theory

A First Course

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Set Theory

A First Course

About this book

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.

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Yes, you can access Set Theory by Daniel W. Cunningham in PDF and/or ePUB format, as well as other popular books in Matematica & Logica nella matematica. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Half title
  3. Series
  4. Title
  5. Copyright
  6. Contents
  7. Preface
  8. The Greek Alphabet
  9. 1 Introduction
  10. 2 Basic Set-Building Axioms and Operations
  11. 3 Relations and Functions
  12. 4 The Natural Numbers
  13. 5 On the Size of Sets
  14. 6 Transfinite Recursion
  15. 7 The Axiom of Choice (Revisited)
  16. 8 Ordinals
  17. 9 Cardinals
  18. Notes
  19. References
  20. Index of Special Symbols
  21. Index