Naive Set Theory
eBook - ePub

Naive Set Theory

  1. 112 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Naive Set Theory

About this book

This classic by one of the twentieth century's most prominent mathematicians offers a concise introduction to set theory. Suitable for advanced undergraduates and graduate students in mathematics, it employs the language and notation of informal mathematics. There are very few displayed theorems; most of the facts are stated in simple terms, followed by a sketch of the proof. Only a few exercises are designated as such since the book itself is an ongoing series of exercises with hints. The treatment covers the basic concepts of set theory, cardinal numbers, transfinite methods, and a good deal more in 25 brief chapters.
"This book is a very specialized but broadly useful introduction to set theory. It is aimed at 'the beginning student of advanced mathematics' … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics." — Allen Stenger, The Mathematical Association of America, September 2011.

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Yes, you can access Naive Set Theory by Paul R. Halmos in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Preface
  5. Contents
  6. Section 1: The Axiom of Extension
  7. Section 2: The Axiom of Specification
  8. Section 3: Unordered Pairs
  9. Section 4: Unions and Intersections
  10. Section 5: Complements and Powers
  11. Section 6: Ordered Pairs
  12. Section 7: Relations
  13. Section 8: Functions
  14. Section 9: Families
  15. Section 10: Inverses and Composites
  16. Section 11: Numbers
  17. Section 12: The Peano Axioms
  18. Section 13: Arithmetic
  19. Section 14: Order
  20. Section 15: The Axiom of Choice
  21. Section 16: Zorn’s Lemma
  22. Section 17: Well Ordering
  23. Section 18: Transfinite Recursion
  24. Section 19: Ordinal Numbers
  25. Section 20: Sets of Ordinal Numbers
  26. Section 21: Ordinal Arithmetic
  27. Section 22: The Schroder-Bernstein Theorem
  28. Section 23: Countable Sets
  29. Section 24: Cardinal Arithmetic
  30. Section 25: Cardinal Numbers
  31. Index