9780486470368

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.

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

PrefacePART I. LOGICAL SORCERYThe Lie DetectiveWhen I Was a BoyThe Abduction of AnnabelleHow Kazir Won His WifeA Plague of LiesOn the Other HandThe Island of Partial SilencePART II. PUZZLES AND METAPUZZLESMemories of the Sorcerer's UncleThe Planet OgMetapuzzlesPART III. SELF-REPRODUCING ROBOTSThe Island of RobotsThe Quaint System of Professor QuincyFrom the Ridiculous to the SimplePART IV. GÖDELIAN PUZZLESSelf-Reference and Cross-ReferenceThe Sorcerer's Miniature Gödelian LanguagePART V. HOW CAN THESE THINGS BE?Something to Think About!Of Time and ChangePART IV. A JOURNEY INTO INFINITYWhat Is Infinity?Cantor's Fundamental DiscoveryBut Some Paradoxes Arise!ResolutionsThe Continuum ProblemPART VII. HYPERGAME, PARADOXES, AND A STORYHypergameParadoxical?Satan, Cantor, and Infinity

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Satan, Cantor and Infinity Mind-Boggling Puzzles

Satan, Cantor and Infinity Mind-Boggling Puzzles

0486470369

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