Mathematical Fallacies and Paradoxes (Dover Books on Mathematics)

From ancient Greek mathematics to 20thcentury quantum theory, paradoxes, fallacies and other intellectual inconsistencies have long puzzled and intrigued the mind of man. This stimulating, thoughtprovoking 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 Godels theorem of 1931 and decision problems in general), the work takes a look as well at the mindbending 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 (Aristotles Circle paradox), being led astray by algebra (De Morgans paradox), failing to comprehend real events through logic (the Swedish Civil Defense Exercise paradox), mistaking infinity (Eulers 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 mindexpanding, this volume will appeal to anyone looking for challenging mental exercises.