On Examples, Counterexamples, and Proof by Example

Thomas Mitchell
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Thomas Mitchell: Southern Illinois University at Carbondale

General Economics and Teaching from University Library of Munich, Germany

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.

Keywords: Proving theorems; special cases; Pi Mu Epsilon Journal (search for similar items in EconPapers)
JEL-codes: A (search for similar items in EconPapers)
Date: 1996-07-12
New Economics Papers: this item is included in nep-pke
Note: Type of Document - Tex; prepared on IBM PC; to print on HP;
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