The foundations of mathematics / Ian Stewart and David Tall.

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Bibliographic Details
Main Authors: Stewart, Ian, 1945- (Author), Tall, David Orme (Author)
Language:English
Published: Oxford : Oxford University Press, 2015.
Edition:Second edition.
Subjects:
Mathematics.
Logic, Symbolic and mathematical.
Physical Description:xvi, 391 pages : illustrations ; 22 cm
Format: Book
Contents:
  • Part I. The intuitive background
  • 1. Mathematical thinking
  • 2. Number systems
  • Part II. The beginnings of formalisation
  • 3. Sets
  • 4. Relations
  • 5. Functions
  • 6. Mathematical logic
  • 7. Mathematical proof
  • Part III. The development of axiomatic systems
  • 8. Natural numbers and proof by induction
  • 9. Real numbers
  • 10. Real numbers as a complete ordered field
  • 11. Complex numbers and beyond
  • Part IV. Using axiomatic systems
  • 12. Axiomatic systems, structure theorems, and flexible thinking
  • 13. Permutations and groups
  • 14. Cardinal numbers
  • 15. Infinitesimals
  • Part V. Strengthening the foundations
  • 16. Axioms for set theory.