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On Examples, Counterexamples, and Proof by Example

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  • Thomas Mitchell

    (Southern Illinois University at Carbondale)

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    Abstract

    This note is motivated by two seemingly unrelated items that have recently appeared in the Pi Mu Epsilon Journal (http://www.wpi.edu/~pme/journal.html). In one, the editor of the Journal wrote of "mathematical cranks" and how frustratingly difficult it can be sometimes to get would-be "circle-squarers" and "angle- trisectors" to see the errors in their "proofs." The first part of this paper illustrates--by way of example!--how futile is a "proof" that is attempted with one or more examples. The second part of the paper follows up on a recent article in the PME Journal, "How Economists Use Mathematics to Show Why Some People Work So Much For So Little," and shows that the author's result is a consequence of the special characteristics of the Cobb-Douglas utility function.

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    Bibliographic Info

    Paper provided by EconWPA in its series General Economics and Teaching with number 9607001.

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    Date of creation: 12 Jul 1996
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    Handle: RePEc:wpa:wuwpgt:9607001

    Note: Type of Document - Tex; prepared on IBM PC; to print on HP;
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    Web page: http://128.118.178.162

    Related research

    Keywords: Proving theorems; special cases; Pi Mu Epsilon Journal;

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