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Satan Cantor Infinity

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486470369
Size: 50.25 MB
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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.

Satan Cantor And Infinity And Other Mind Bogglin

Author: Raymond M. Smullyan
Publisher: Knopf
ISBN: 0307819825
Size: 60.13 MB
Format: PDF
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More than two hundred new and challenging logic puzzles—the simplest brainteaser to the most complex paradoxes in contemporary mathematical thinking—from our topmost puzzlemaster (“the most entertaining logician who ever lived,” Martin Gardner has called him). Our guide to the puzzles is the Sorcerer, who resides on the Island of Knights and Knaves, where knights always tell the truth and knaves always lie, and he introduces us to the amazing magic—logic—that enables to discover which inhabitants are which. Then, in a picaresque adventure in logic, he takes us to the planet Og, to the Island of Partial Silence, and to a land where metallic robots wearing strings of capital letters are noisily duplicating and dismantling themselves and others. The reader’s job is to figure out how it all works. Finally, we accompany the Sorcerer on an alluring tour of Infinity which includes George Cantor’s amazing mathematical insights. The tour (and the book) ends with Satan devising a diabolical puzzle for one of Cantor’s prize students—who outwits him! In sum: a devilish magician’s cornucopia of puzzles—a delight for every age and level of ability.

Logical Labyrinths

Author: Raymond Smullyan
Publisher: CRC Press
ISBN: 143986537X
Size: 78.80 MB
Format: PDF, Docs
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This book features a unique approach to the teaching of mathematical logic by putting it in the context of the puzzles and paradoxes of common language and rational thought. It serves as a bridge from the author’s puzzle books to his technical writing in the fascinating field of mathematical logic. Using the logic of lying and truth-telling, the author introduces the readers to informal reasoning preparing them for the formal study of symbolic logic, from propositional logic to first-order logic, a subject that has many important applications to philosophy, mathematics, and computer science. The book includes a journey through the amazing labyrinths of infinity, which have stirred the imagination of mankind as much, if not more, than any other subject.

Who Knows

Author: Raymond M. Smullyan
Publisher: Indiana University Press
ISBN: 9780253109682
Size: 41.46 MB
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Is there really a God, and if so, what is God actually like? Is there an afterlife, and if so, is there such a thing as eternal punishment for unrepentant sinners, as many orthodox Christians and Muslims believe? And is it really true that our unconscious minds are connected to a higher spiritual reality, and if so, could this higher spiritual reality be the very same thing that religionists call "God"? In his latest book, Raymond M. Smullyan invites the reader to explore some beautiful and some horrible ideas related to religious and mystical thought. In Part One, Smullyan uses the writings on religion by fellow polymath Martin Gardner as the starting point for some inspired ideas about religion and belief. Part Two focuses on the doctrine of Hell and its justification, with Smullyan presenting powerful arguments on both sides of the controversy. "If God asked you to vote on the retention or abolition of Hell," he asks, "how would you vote?" Smullyan has posed this question to many believers and received some surprising answers. In the last part of his treasurable triptych, Smullyan takes up the "beautiful and inspiring" ideas of Richard Bucke and Edward Carpenter on Cosmic Consciousness. Readers will delight in Smullyan's observations on religion and in his clear-eyed presentation of many new and startling ideas about this most wonderful product of human consciousness.

King Arthur In Search Of His Dog And Other Curious Puzzles

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486474356
Size: 31.61 MB
Format: PDF, Kindle
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This fanciful, original collection for readers of all ages features arithmetic puzzles, logic problems related to crime detection, and logic and arithmetic puzzles involving King Arthur and his Dogs of the Round Table.

The G Delian Puzzle Book

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 0486315770
Size: 55.24 MB
Format: PDF, ePub, Mobi
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These logic puzzles provide entertaining variations on Gödel's incompleteness theorems, offering ingenious challenges related to infinity, truth and provability, undecidability, and other concepts. No background in formal logic necessary.

To Mock A Mockingbird

Author: Raymond M. Smullyan
Publisher: Oxford University Press, USA
ISBN: 9780192801425
Size: 21.62 MB
Format: PDF, ePub
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In this entertaining and challenging collection of logic puzzles, Raymond Smullyan - author of Forever Undecided - continues to delight and astonish us with his gift for making available, in the thoroughly pleasurable form of puzzles, some of the most important mathematical thinking of our time. In the first part of the book, he transports us once again to that wonderful realm where knights, knaves, twin sisters, quadruplet brothers, gods, demons, and mortals either always tell thetruth or always lie, and where truth-seekers are set a variety of fascinating problems. The section culminates in an enchanting and profound metapuzzle in which Inspector Craig of Scotland Yard gets involved in a search for the Fountain of Youth on the Island of Knights and Knaves. In the second part of To Mock a Mockingbird, we accompany the Inspector on a summer-long adventure into the field of combinatory logic (a branch of logic that plays an important role in computer science and artificial intelligence). His adventure, which includes enchanted forests, talking birds, bird sociologists, and a classic quest, provides for us along the way the pleasure of solving puzzles of increasing complexity until we reach the Master Forest and - thanks to Godel's famous theorem - the final revelation.

The Unimaginable Mathematics Of Borges Library Of Babel

Author: William Goldbloom Bloch
Publisher: Oxford University Press
ISBN: 9780199715169
Size: 75.99 MB
Format: PDF
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"The Library of Babel" is arguably Jorge Luis Borges' best known story--memorialized along with Borges on an Argentine postage stamp. Now, in The Unimaginable Mathematics of Borges' Library of Babel, William Goldbloom Bloch takes readers on a fascinating tour of the mathematical ideas hidden within one of the classic works of modern literature. Written in the vein of Douglas R. Hofstadter's Pulitzer Prize-winning G?del, Escher, Bach, this original and imaginative book sheds light on one of Borges' most complex, richly layered works. Bloch begins each chapter with a mathematical idea--combinatorics, topology, geometry, information theory--followed by examples and illustrations that put flesh on the theoretical bones. In this way, he provides many fascinating insights into Borges' Library. He explains, for instance, a straightforward way to calculate how many books are in the Library--an easily notated but literally unimaginable number--and also shows that, if each book were the size of a grain of sand, the entire universe could only hold a fraction of the books in the Library. Indeed, if each book were the size of a proton, our universe would still not be big enough to hold anywhere near all the books. Given Borges' well-known affection for mathematics, this exploration of the story through the eyes of a humanistic mathematician makes a unique and important contribution to the body of Borgesian criticism. Bloch not only illuminates one of the great short stories of modern literature but also exposes the reader--including those more inclined to the literary world--to many intriguing and entrancing mathematical ideas.

Geometric Magic Squares

Author: Lee C.F. Sallows
Publisher: Courier Corporation
ISBN: 0486290026
Size: 41.24 MB
Format: PDF
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This innovative work replaces magic square numbers with two-dimensional forms. The result is a revelation that traditional magic squares are now better seen as the one-dimensional instance of this self-same geometrical activity.

The Lady Or The Tiger

Author: Raymond M. Smullyan
Publisher:
ISBN: 9780192801432
Size: 41.66 MB
Format: PDF, ePub
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This text presents a series of logic puzzles, ranging from the simplest problems to the most tantalizing complexities. An array of imaginary characters - sane and insane vampires, psychiatrists, dreamers, hermits, kings, knights and knaves - pose questions, giving just enough information to enable the reader to solve problems of increasing difficulty.