9780486470368

Satan, Cantor and Infinity Mind-Boggling Puzzles

by
  • ISBN13:

    9780486470368

  • ISBN10:

    0486470369

  • Format: Paperback
  • Copyright: 3/26/2009
  • Publisher: Dover Publications

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Supplemental Materials

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Summary

Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions.

Author Biography

Born in New York City in 1919, Raymond Smullyan is a philosopher and magician as well as a famous mathematician and logician. His career as a stage magician financed his undergraduate studies at the University of Chicago as well his doctoral work at Princeton. The author of several imaginative books on recreational mathematics, Smullyan is also a classical pianist.

Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919– ), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years.

In the Author's Own Words:
"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini."

"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'" — Raymond Smullyan

Critical Acclaim for The Lady or the Tiger:
"Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner

Table of Contents

Preface
PART I.  LOGICAL SORCERY
The Lie Detective
When I Was a Boy
The Abduction of Annabelle
How Kazir Won His Wife
A Plague of Lies
On the Other Hand
The Island of Partial Silence
PART II.  PUZZLES AND METAPUZZLES
Memories of the Sorcerer's Uncle
The Planet Og
Metapuzzles
PART III.  SELF-REPRODUCING ROBOTS
The Island of Robots
The Quaint System of Professor Quincy
From the Ridiculous to the Simple
PART IV.  GÖDELIAN PUZZLES
Self-Reference and Cross-Reference
The Sorcerer's Miniature Gödelian Language
PART V.  HOW CAN THESE THINGS BE?
Something to Think About!
Of Time and Change
PART IV.  A JOURNEY INTO INFINITY
What Is Infinity?
Cantor's Fundamental Discovery
But Some Paradoxes Arise!
Resolutions
The Continuum Problem
PART VII.  HYPERGAME, PARADOXES, AND A STORY
Hypergame
Paradoxical?
Satan, Cantor, and Infinity

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