Satan Cantor And Infinity And Other Mind Bogglin

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.

From Simon & Schuster, This Book Needs No Title is Raymond Smullyan's budget of living paradoxes—the author of What is the Name of This Book? Including eighty paradoxes, logical labyrinths, and intriguing enigmas progress from light fables and fancies to challenging Zen exercises and a novella and probe the timeless questions of philosophy and life.

Have you ever wondered why we do certain things in mathematics? Why do we count decimal points when multiplying with decimals or why do we ?invert and multiply? when multiplying with fractions? Or, were you frustrated when you asked for a reason why we convert mixed numbers to improper fractions that way, and the teacher simply said, ?That is the way I learned how.?? This book attempts to answer these questions along with dozens more. If you have ever wondered why we do something in mathematics, this is the book for you. Here are a few of the mysteries that are ?unraveled? in this book: What can?t we divide by zero? Why do we move the decimal point when dividing by a decimal? Why is a ?negative times a negative a positive?? Why is any number raised to the zero power equal to zero?

A study of the cognitive science of mathematical ideas.

In his new book, Raymond Smullyan, grand vizier of the logic puzzle, joins Scheherazade, a charming young woman of “fantastic logical ingenuity,” to give us 1001 hours of brain-teasing fun. Scheherazade, we find, has gotten back into hot water with the king, and is once more in danger of losing her head at down. But, thinking quickly, she tempts the king to stay her execution by posing him the most delightfully devious mathematical and logic puzzle ever invented. They keep him guessing for many more nights until the fatal hour has passed, and she keeps her head. The Riddle of Scheherazade includes several wonderful old chestnuts and many fiendishly original puzzles, 225 in all. There are logic tricks and number games, metapuzzles (puzzles about puzzles), liar/truth-teller exercises, Gödelian brian twisters, baffling paradoxes, and an excursion, under Scheherazade’s expert guidance, into an amusing new field invented by Smullyan, called “coercive” logic, in which the answer to a problem can actually change the fate of the puzzler! An absolute must for all puzzle fans—from the middle-school whiz to the sophisticated mathematician or computer scientist.

A lively and engaging look at logic puzzles and their role in mathematics, philosophy, and recreation Logic puzzles were first introduced to the public by Lewis Carroll in the late nineteenth century and have been popular ever since. Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself. In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt Gödel's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data. Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the "Hardest Logic Puzzle Ever," metapuzzles, paradoxes, and the logic puzzles in detective stories.