Counterexamples

by Bernard R. Gelbaum, John M. H. Olmsted

These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the ...

by Lynn Arthur Steen, J. Arthur Seebach Jr.

According to the authors of this highly useful compendium, focusing on examples is an extremely effective method of involving undergraduate mathematics students in actual research. It is only as a ...

by Jordan M. Stoyanov

Most mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study ...

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