A guide to infinity : ten mathematical journeys / Edward R. Scheinerman.

Format:

Book

Author/Creator:

Scheinerman, Edward R., author.

Language:

English

Subjects (All):

Infinite.

infinity.

Physical Description:

1 online resource (xiv, 174 pages) : illustrations

Edition:

First edition.

Other Title:

Ten mathematical journeys

Place of Publication:

New Haven : Yale University Press, 2026.

Summary:

An accessible introduction to mathematical infinity for the endlessly curious. Infinity has traditionally been a topic for philosophers, physicists, and artists, and it can be large, scary, or highly metaphorical.

Contents:

Preface

Part I: Real Infinity. 1. Real Numbers, Extended. 1.1 Real numbers : Operations and properties ; 1.2 Two new numbers : ∞ and −∞ ; 1.3 Computing with ∞ and −∞ ; For your consideration

2. Infinite Decimals. 2.1 Place value notation ; 2.2 What is 0.3333 . . . ? ; 2.3 Infinite sums as sequences ; 2.4 Smaller terms but infinite sum ; For your consideration

3. Tropical Arithmetic. 3.1 New operations : ⊕ and ⊙ ; 3.2 Polynomials ; 3.3 Tropical algebraic curves ; For your consideration

4. Hyperreals. 4.1 Starting small ; 4.2 The transfer principle ; 4.3 Derivatives made easy ; For your consideration

Part II: Plane Infinity. 5. Complex Numbers, Extended. 5.1 Complex numbers ; 5.2 One infinity for all ; 5.3 Stereographic projection and the Riemann sphere ; 5.4 Linear fractional transformations ; For your consideration

6. Line at Infinity I : Projective Plane. 6.1 Parallel lines meet at infinity ; 6.2 The projective plane ; 6.3 Points and lines, algebraically ; 6.4 Desargues's theorem ; 6.5 Topology of the projective plane ; 6.6 Bézout's theorem ; For your consideration

7. Line at Infinity II : Hyperbolic Plane. 7.1 The parallel postulate ; 7.2 The hyperbolic plane ; 7.3 Tessellations ; 7.4 Distance and area in the hyperbolic plane ; For your consideration

Part III: Infinite Things. 8. Counting Infinity. 8.1 Counting things ; 8.2 Sets, functions, bijections ; 8.3 Finite and infinite sets ; 8.4 Comparing infinite sets ; 8.5 Transfinite cardinal numbers ; 8.6 Transcendental numbers ; For your consideration

9. Order Infinity. 9.1 Ordered sets ; 9.2 Well-ordered sets ; 9.3 Ordinal numbers ; For your consideration

10. Infinite Shapes. 10.1 Circles ; 10.2 How long is the diagonal of a square? ; 10.3 Sierpiński's carpet ; 10.4 Hilbert's space-filling curve ; 10.5 Mandelbrot set ; For your consideration.

Notes:

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Scheinerman, Edward R. A Guide to Infinity

ISBN:

9780300289626

0300289626

0-300-28962-6

OCLC:

1564337767