Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 0 Prelude
- 1 Fundamentals
- 2 ℕ: Natural Numbers
- 3 ℤ: Integers
- 4 ℤm: Modular Arithmetic
- 5 ℚ: Rational Numbers
- 6 ℝ: Real Numbers I, Dedekind Cuts
- 7 ℝ: Real Numbers II, Cauchy Sequences
- 8 ℝ: Real Numbers III, Complete Ordered Fields
- 9 ℂ: Complex Numbers
- 10 Further Extensions
- Answers to Exercises
- Bibliography
- Index
2 - ℕ: Natural Numbers
Published online by Cambridge University Press: 05 December 2024
- Frontmatter
- Dedication
- Contents
- Preface
- 0 Prelude
- 1 Fundamentals
- 2 ℕ: Natural Numbers
- 3 ℤ: Integers
- 4 ℤm: Modular Arithmetic
- 5 ℚ: Rational Numbers
- 6 ℝ: Real Numbers I, Dedekind Cuts
- 7 ℝ: Real Numbers II, Cauchy Sequences
- 8 ℝ: Real Numbers III, Complete Ordered Fields
- 9 ℂ: Complex Numbers
- 10 Further Extensions
- Answers to Exercises
- Bibliography
- Index
Summary
We define the natural numbers as equivalence classes of finite sets and their basic properties. We make mention of the Peano axioms. We conclude with important results on prime numbers.
- Type
- Chapter
- Information
- From Counting to ContinuumWhat Are Real Numbers, Really?, pp. 23 - 52Publisher: Cambridge University PressPrint publication year: 2024