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Bryan Bunch

Mathematical Fallacies and Paradoxes

Mathematics may seem to be the embodiment of certainty, but in Mathematical Fallacies and Paradoxes Brian Bunch shows that you sometimes have to watch your step.In the first chapter he demonstrates that the circumference of a circle doesn't always seem to be 2πr, as well as proving that 1=0. This is followed by a look at the paradoxical nature of infinity, and a chapter on arguing by contradiction. Bunch then gets on to self reference and the paradoxes of set theory, leading up to a well written explanation of Gödel's incompleteness theorem.

Gödel's incompleteness theorem would have made a good finale for the book, but Bunch then moves on to paradoxes of space and time, where he gets a bit lost - in particular his explanation of Schwarz paradox is wide of the mark, and his relativistic race between Achilles and the tortoise is very muddled. (There is also a flash of illogic earlier in the book concerning intuitionism and the contrapositive of Goldbach's conjecture). But if you don't mind the occasional lapse when Bunch is trying too hard to find a paradox where there isn't one, then you will find that most of the book provides and enjoyable and informative read.

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Paperback 240 pages  
ISBN: 0486296644
Salesrank: 251331
Weight:0.55 lbs
Published: 1997 Dover Publications
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Amazon.co.uk info
Paperback 224 pages  
ISBN: 0486296644
Salesrank: 767644
Weight:0.55 lbs
Published: 2003 Dover Publications Inc.
Amazon price £7.99
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Amazon.ca info
Paperback 240 pages  
ISBN: 0486296644
Salesrank: 304177
Weight:0.55 lbs
Published: 1997 Dover Publications
Amazon price CDN$ 14.75
Marketplace:New from CDN$ 14.75:Used from CDN$ 0.01
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Product Description

From ancient Greek mathematics to 20th-century quantum theory, paradoxes, fallacies and other intellectual inconsistencies have long puzzled and intrigued the mind of man. This stimulating, thought-provoking compilation collects and analyzes the most interesting paradoxes and fallacies from mathematics, logic, physics and language.
While focusing primarily on mathematical issues of the 20th century (notably Godel's theorem of 1931 and decision problems in general), the work takes a look as well at the mind-bending formulations of such brilliant men as Galileo, Leibniz, Georg Cantor and Lewis Carroll ― and describes them in readily accessible detail. Readers will find themselves engrossed in delightful elucidations of methods for misunderstanding the real world by experiment (Aristotle's Circle paradox), being led astray by algebra (De Morgan's paradox), failing to comprehend real events through logic (the Swedish Civil Defense Exercise paradox), mistaking infinity (Euler's paradox), understanding how chance ceases to work in the real world (the Petersburg paradox) and other puzzling problems. Some high school algebra and geometry is assumed; any other math needed is developed in the text. Entertaining and mind-expanding, this volume will appeal to anyone looking for challenging mental exercises.