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In this rich, thorough account of all things infinite, Joel David Hamkins combines playful thought experiments with mathematically precise exposition to explore the vast, fascinating spectrum of paradoxes and conundrums of infinity. Written with equal parts wonder and rigor, the book moves from classical paradoxes (Zeno, Hilbert’s hotel, Aristotle’s wheel) to Cantor’s transfinite arithmetic, the continuum hypothesis, surreal numbers, infinitesimals, epistemic logic puzzles, and contemporary debates about potential vs. actual infinity. Twenty-five lively, self-contained chapters are enriched by extensive illustrations, diagrams, figures, and Fermi-style estimation puzzles. Highly readable and pedagogically rich, The Book of Infinity is ideal for undergraduate philosophy and math students and enthusiasts of logical and mathematical curiosities alike.
- Approaches a wide range of ideas with both rigor and delight
- Renders deep mathematical ideas accessible to beginners
- Emphasizes intuition and deep conceptual understanding
- Integrates historical perspectives and contemporary issues
- Suits anyone interested in paradoxes, large numbers, and conceptual puzzles
In this rich, thorough account of all things infinite, Joel David Hamkins combines playful thought experiments with mathematically precise exposition to explore the vast, fascinating spectrum of paradoxes and conundrums of infinity. Written with equal parts wonder and rigor, the book moves from classical paradoxes (Zeno, Hilbert’s hotel, Aristotle’s wheel) to Cantor’s transfinite arithmetic, the continuum hypothesis, surreal numbers, infinitesimals, epistemic logic puzzles, and contemporary debates about potential vs. actual infinity. Twenty-five lively, self-contained chapters are enriched by extensive illustrations, diagrams, figures, and Fermi-style estimation puzzles. Highly readable and pedagogically rich, The Book of Infinity is ideal for undergraduate philosophy and math students and enthusiasts of logical and mathematical curiosities alike.
- Approaches a wide range of ideas with both rigor and delight
- Renders deep mathematical ideas accessible to beginners
- Emphasizes intuition and deep conceptual understanding
- Integrates historical perspectives and contemporary issues
- Suits anyone interested in paradoxes, large numbers, and conceptual puzzles
Preface
About the Author
1 The Book of Numbers
2 The sand reckoner
3 Zeno’s paradox
4 The method of exhaustion
5 Supertasks
6 The infinite coastline paradox
7 The paradox of giants
8 The paradox of the largest tweetable number
9 Potential versus actual infinity
10 Equinumerosity and comparison of size
11 What is the infinite?
12 Hilbert’s Grand Hotel
13 Uncountable infinity
14 How to count
15 Transfinite recursive constructions
16 Slaying the hydra
17 The continuum hypothesis
18 Throwing darts at the real line
19 The orders of infinity
20 The surreal numbers
21 The axiom of choice
22 Infinitary hat puzzles and the Aftermath
23 The guessing-box puzzle
24 We can predict the future
25 Infinite liars
26 Common knowledge
Bibliography
Index
| Erscheinungsjahr: | 2026 |
|---|---|
| Fachbereich: | Allgemeines |
| Genre: | Importe, Philosophie |
| Jahrhundert: | Antike |
| Rubrik: | Geisteswissenschaften |
| Thema: | Lexika |
| Medium: | Taschenbuch |
| Inhalt: | Einband - flex.(Paperback) |
| ISBN-13: | 9780262054010 |
| ISBN-10: | 0262054019 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Hamkins, Joel David |
| Hersteller: | The MIT Press |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 224 x 178 x 27 mm |
| Von/Mit: | Joel David Hamkins |
| Erscheinungsdatum: | 25.08.2026 |
| Gewicht: | 0,708 kg |
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