Uses of Infinity

Leo Zippin

doi:10.5948/UPO9780883859247

The word 'infinity' usually elicits feelings of awe, wonder, and admiration; the concept infinity has fascinated philosophers and theologians. The author shows how professional mathematicians tame this unwieldy concept, come to terms with it, and use its various aspects as their most powerful tools of the trade. The early chapters are descriptive and intuitive, full of examples that not only illustrate some infinite processes, but that are worth studying for their own sake. Many questions are raised in the beginning, partially answered in various contexts throughout the book, and finally treated with the precision necessary to give the reader an excellent grasp of the fundamental notions used in the calculus as well as in virtually all other mathematical disciplines. The text is peppered with challenging problems whose solutions appear at the end of the book.

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Uses of Infinity

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

USES OF INFINITY
pp 1-2

Preface
pp 3-4

Chapter 1 - Popular and Mathematical Infinities
pp 5-13

Chapter 2 - From Natural Numbers to √2
pp 14-37

Chapter 3 - From √2 to the Transfinite
pp 38-58

Chapter 4 - Zig-Zags: To the Limit if the Limit Exists
pp 59-74

Chapter 5 - The Self Perpetuating Golden Rectangle
pp 75-95

Chapter 6 - Constructions and Proofs
pp 96-120

Solutions to Problems
pp 121-149

Bibliography
pp 150-151

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