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
10 - Further Extensions
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
This chapter presents a variety of other types of numbers including how infinity may be incorporated into the real or complex numbers, the quaternions, transfinite ordinals and cardinals, and p-adic numbers.
- Type
- Chapter
- Information
- From Counting to ContinuumWhat Are Real Numbers, Really?, pp. 153 - 170Publisher: Cambridge University PressPrint publication year: 2024