Mathematical Fallacies and Paradoxes

Mathematical Fallacies and Paradoxes.

Hardcover with dust jacket. Zustand: Sehr gut. xi, 216 p., Ill. Das Exemplar ist in einem sehr guten und sauberen Zustand ohne Anstreichungen. / The copy is in a very good and clean condition without markings. -- Contents -- Preface -- Thinking Wrong about Easy Ideas -- Thinking Wrong about Infinity -- Using a Wrong Idea to Find Truth -- Speaking with Forked Tongue -- Paradoxes That Count -- The Limits of Thought? -- Misunderstanding Space and Time -- Moving against Infinity -- Selected Further Reading -- Index -- (Publishing text:) Misconceptions fallacies. contradictions paradoxes. By reconciling these or attempting to reconcile them we better understand both the possibilities and limita- tions of the world and human intelligence. We're also invigorated and delighted along the way. Bryan Bunch's Mathematical Fallacies and Paradoxes illuminates the tantalizing inconsis- tencies and loopholes in human thought that have perplexed, dumbfounded, and thrilled man since he first exercised the power of reason. In the tradition of Douglas Hofstad- ter's Pulitzer prize-winning Godel, Escher, Bach: an Eternal Golden Braid, Bunch's ex- amination is a cerebral treat for anyone with an interest though not necessarily an ex- tensive background in mathematics. Focusing firmly on the central mathematical issues of the 20th century, Mathematical Fallacies and Paradoxes nevertheless reviews the formulations of mankind's most daring and original thinkers down through the ages and describes them in readily accessible terms. The mind-benders and thought-twist- ers of such brilliant innovators as Galileo, Leibniz, Kurt Gödel, Georg Cantor, Charles Lutwidge Dodgson (a.k.a. Lewis Carroll), and others are all here. Seminal concepts such as one-to-one correspondence, com- pleted infinities, the notions of limit and continuity, decidability, and many more are fully clarified within the context of mathe- matical reality. Bunch elucidates methods for misunderstand- ing the real world by experiment (Aristotle's Circle paradox) being led astray by alge- bra (De Morgan's paradox) failing to comprehend real events through logic (the Swedish Civil-Defense Exercise paradox). mistaking infinity (Euler's paradox) and grasping how chance ceases to work in the real world (the Petersburg paradox). Intriguing discussions are included of the first paradox, Eublides' "The Liar," and the per- sistent paradoxes of Zeno of Elea, first arti- culated in 450 B.C. Among the volume's un- usual features are paradoxes from quantum theory and relativity presented from a math- ematical perspective and the first popular account of the Banach-Tarski paradox in English in forty years! Mathematical Fallacies and Paradoxes a stimulating, endlessly entertaining look at many of the most ticklish questions ever to arouse man's curiosity and besiege his intellect. About the Author: Bryan H. Bunch divides his time between writing and consulting work with textbook publishers. He is currently engaged in co- authoring algebra 1 and 2 textbooks to be published by McDougal, Littell & Company. For eight years he was the Chief Mathema- tics Editor in the School Department of Har- court Brace Jovanovich. He was also Editor- in-Chief and Senior Vice-President of Ameri- can Book Company. As a freelancer, Mr. Bunch edited college textbooks in mathema- tics and logic for the Bobbs-Merrill Company and wrote the articles "Number," "Numer- ation," "Mathematics," and "Sets" for The New Book of Knowledge (Grolier, Inc.). More recently, he has written "Introduction to the Mathematics Volume," "Arithmetic," and "New Concepts in Mathematics" for The Volume Library (Southwestern). A member of the National Council of Teachers of Mathematics, Mr. Bunch studied mathe- matics for several years at the Courant Insti- tute of Mathematical Sciences, New York University. ISBN 9780442249052 Sprache: Englisch Gewicht in Gramm: 509. Artikel-Nr. 1262105

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