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To Infinity and Beyond

A Cultural History of the Infinite

  • Eli Maor

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Mathematical Infinity

    1. Front Matter
      Pages 1-1
    2. Eli Maor
      Pages 2-9
    3. Eli Maor
      Pages 10-16
    4. Eli Maor
      Pages 17-24
    5. Eli Maor
      Pages 25-28
    6. Eli Maor
      Pages 29-33
    7. Eli Maor
      Pages 34-39
    8. Eli Maor
      Pages 60-65
  3. Geometric Infinity

    1. Front Matter
      Pages 67-67
    2. Eli Maor
      Pages 68-87
    3. Eli Maor
      Pages 88-94
    4. Eli Maor
      Pages 95-101
    5. Eli Maor
      Pages 102-107
    6. Eli Maor
      Pages 108-117
    7. Eli Maor
      Pages 118-134
  4. Aesthetic Infinity

    1. Front Matter
      Pages 135-135
    2. Eli Maor
      Pages 136-138
    3. Eli Maor
      Pages 139-148
    4. Eli Maor
      Pages 149-154
    5. Eli Maor
      Pages 155-163
    6. Eli Maor
      Pages 179-182
  5. Cosmological Infinity

    1. Front Matter
      Pages 183-183
    2. Eli Maor
      Pages 184-189
    3. Eli Maor
      Pages 190-198
    4. Eli Maor
      Pages 199-203
    5. Eli Maor
      Pages 204-211
    6. Eli Maor
      Pages 212-223
    7. Eli Maor
      Pages 224-226
    8. Eli Maor
      Pages 227-230
  6. Epilogue

    1. Front Matter
      Pages 231-231
    2. Eli Maor
      Pages 232-234
  7. Back Matter
    Pages 235-278

About this book

Introduction

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.

Keywords

Cantor cosmology cultural history function geometry Mathematica number concept philosophy

Authors and affiliations

  • Eli Maor
    • 1
  1. 1.Department of Mathematical SciencesOakland UniversityRochesterUSA

Bibliographic information