By Gary L. Wise, Eric B. Hall

A counterexample is any instance or end result that's the contrary of one's instinct or to regularly held ideals. Counterexamples may have nice academic price in illuminating advanced subject matters which are tough to give an explanation for in a rigidly logical, written presentation. for instance, rules in mathematical sciences that will look intuitively seen can be proved unsuitable with using a counterexample. This monograph concentrates on counterexamples to be used on the intersection of chance and genuine research, which makes it distinct between such remedies. The authors argue convincingly that likelihood thought can't be separated from actual research, and this ebook includes over three hundred examples with regards to either the idea and alertness of arithmetic. a number of the examples during this assortment are new, and plenty of outdated ones, formerly buried within the literature, at the moment are available for the 1st time. unlike numerous different collections, all the examples during this publication are thoroughly self-contained--no info are befell to vague outdoors references. scholars and theorists throughout fields as varied as actual research, likelihood, statistics, and engineering will need a reproduction of this book.

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