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Table of contents

  1. Front Matter
    Pages i-vii
  2. Paul R. Halmos
    Pages 1-3
  3. Paul R. Halmos
    Pages 4-7
  4. Paul R. Halmos
    Pages 8-11
  5. Paul R. Halmos
    Pages 12-16
  6. Paul R. Halmos
    Pages 17-21
  7. Paul R. Halmos
    Pages 22-25
  8. Paul R. Halmos
    Pages 26-29
  9. Paul R. Halmos
    Pages 30-33
  10. Paul R. Halmos
    Pages 34-37
  11. Paul R. Halmos
    Pages 38-41
  12. Paul R. Halmos
    Pages 42-45
  13. Paul R. Halmos
    Pages 46-49
  14. Paul R. Halmos
    Pages 50-53
  15. Paul R. Halmos
    Pages 54-58
  16. Paul R. Halmos
    Pages 59-61
  17. Paul R. Halmos
    Pages 62-65
  18. Paul R. Halmos
    Pages 66-69
  19. Paul R. Halmos
    Pages 70-73
  20. Paul R. Halmos
    Pages 74-77
  21. Paul R. Halmos
    Pages 78-80
  22. Paul R. Halmos
    Pages 81-85
  23. Paul R. Halmos
    Pages 86-89
  24. Paul R. Halmos
    Pages 90-93
  25. Paul R. Halmos
    Pages 94-98
  26. Paul R. Halmos
    Pages 99-102
  27. Back Matter
    Pages 102-104

About this book

Introduction

Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set­ theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.

Keywords

addition arithmetic Cardinal number Countable set Lemma Peano axioms set theory

Authors and affiliations

  • Paul R. Halmos
    • 1
  1. 1.Department of MathematicsSanta Clara UniversitySanta ClaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-1645-0
  • Copyright Information Springer-Verlag New York 1974
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-90104-6
  • Online ISBN 978-1-4757-1645-0
  • Series Print ISSN 0172-6056
  • Buy this book on publisher's site