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To Infinity and Beyond

A Cultural History of the Infinite

  • Book
  • © 1987

Overview

Authors:
  1. Eli Maor

    1. Department of Mathematical Sciences, Oakland University, Rochester, USA

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Table of contents (30 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Mathematical Infinity

    1. Front Matter

      Pages 1-1
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    2. First Steps to Infinity

      • Eli Maor
      Pages 2-9

    3. Towards Legitimation

      • Eli Maor
      Pages 10-16

    4. Convergence and Limit

      • Eli Maor
      Pages 17-24

    5. The Fascination of Infinite Series

      • Eli Maor
      Pages 25-28

    6. The Geometric Series

      • Eli Maor
      Pages 29-33

    7. More about Infinite Series

      • Eli Maor
      Pages 34-39

    8. Interlude: An Excursion into the Number Concept

      • Eli Maor
      Pages 40-43

    9. The Discovery of Irrational Numbers

      • Eli Maor
      Pages 44-52

    10. Cantor’s New Look at the Infinite

      • Eli Maor
      Pages 53-59

    11. Beyond Infinity

      • Eli Maor
      Pages 60-65

  3. Geometric Infinity

    1. Front Matter

      Pages 67-67
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    2. Some Functions and Their Graphs

      • Eli Maor
      Pages 68-87

    3. Inversion in a Circle

      • Eli Maor
      Pages 88-94

    4. Geographic Maps and Infinity

      • Eli Maor
      Pages 95-101

    5. Tiling the Plane

      • Eli Maor
      Pages 102-107

    6. A New Look at Geometry

      • Eli Maor
      Pages 108-117

    7. The Vain Search for Absolute Truth

      • Eli Maor
      Pages 118-134

  4. Aesthetic Infinity

    1. Front Matter

      Pages 135-135
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Keywords

About this book

The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite. . . - David Hilbert (1862-1943) Infinity is a fathomless gulf, There is a story attributed to David Hilbert, the preeminent mathe­ into which all things matician whose quotation appears above. A man walked into a vanish. hotel late one night and asked for a room. "Sorry, we don't have o Marcus Aurelius (121- 180), Roman Emperor any more vacancies," replied the owner, "but let's see, perhaps and philosopher I can find you a room after alL" Leaving his desk, the owner reluctantly awakened his guests and asked them to change their rooms: the occupant of room #1 would move to room #2, the occupant of room #2 would move to room #3, and so on until each occupant had moved one room over. To the utter astonish­ ment of our latecomer, room #1 suddenly became vacated, and he happily moved in and settled down for the night. But a numbing thought kept him from sleep: How could it be that by merely moving the occupants from one room to another, the first room had become vacated? (Remember, all of the rooms were occupied when he arrived.

Authors and Affiliations

  • Department of Mathematical Sciences, Oakland University, Rochester, USA

    Eli Maor

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