Philosophy of Numbers

Contents: Preface. Acknowledgements. 1. The numbers we know. 2. The natural numbers -- the serial concept. 3. Sets and classes. 4. The Algebra of sets. 5. Relations. 6. The natural numbers and logic. 7. Mapping. 8. The natural numbers and mapping. 9. Abstract Algebra. 10. Order. 11. Finite and infinite numbers. 12. Relation number and structure. 13. The integers and rationals as relations. 14. The integers as classes. 15. Rational numbers as classes. 16. Real numbers--Dedekind's Theory. 17. Sequences. 18. The real numbers. 19. The real numbers and infinite continuum. 20. The complex numbers. 21. Infinite cardinals and ordinals. 22. The elusive primes. 23. Numbers and secret communications. 24. The mystical perfect numbers. 25. The Fermat's last theorem. 26. Some intriguing numbers. 27. The grammar of numbers. 28. The treacherous infinity. 29. Wrestling with numbers. 30. Numbers: reality and mysticism. 31. The nature of numbers. Bibliography. Index.

"This book is about numbers and so many questions relating to them. What is the nature of numbers? Are they discovered or invented? What is mystical about them? Mathematicians develop a hierarchy of numbers in which mysterious dichotomies appear. For example, the integer 5 is not the same as the rationale 5 which in turn is different from the real 5. The author explains how this conceptual maze does not affect the layperson's arithmetic. He also discusses such fascinating topics as primes, perfect numbers, inaccessible numbers and many other unsolved problems relating to the treacherous terrain of infinity, which have baffled mathematicians and philosophers alike." (jacket)