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9781568812137

The Pea and the Sun: A Mathematical Paradox

by
  • ISBN13:

    9781568812137

  • ISBN10:

    1568812132

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2005-04-29
  • Publisher: A. K. Peters

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Summary

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a manner that would to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the Sun by breaking something so small as a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Wapner writes in an engaging style that catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox, making one of the most intriguing problems of advanced mathematics accessible to the non- math-ematician.

Author Biography

Leonard Wapner is a professor of mathematics at El Camino College in Torrance, California.

Table of Contents

History : a cast of charactersp. 1
Georg Cantor - the founder of modern set theoryp. 5
Stefan Banach and Alfred Tarskip. 18
Kurt Godel - the consistency of the axiom of choicep. 28
Paul Cohen - the independence of the axiom of choicep. 34
Jigsaw fallacies and other curiositiesp. 49
Paradoxes and antinomiesp. 49
Jigsaw fallaciesp. 57
Preliminariesp. 69
Set theoryp. 70
Isometriesp. 79
Scissors congruencep. 87
Equidecomposabilityp. 98
Baby BTsp. 107
Shifting to infinityp. 112
Stretchingp. 117
Cantor dustp. 126
The Vitali construction paradoxesp. 132
Stewart's infinite dictionaryp. 135
The Sierpinski-Mazurkiewicz paradoxp. 138
Statement and proof of the theoremp. 143
Statementp. 143
Proofp. 144
Resolutionp. 165
The real worldp. 173
Yesterday, today, and tomorrowp. 191
Table of Contents provided by Blackwell. All Rights Reserved.

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