Discouraging "Proof by Example"

Thomas Mitchell
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Thomas Mitchell: Southern Illinois University at Carbondale

GE, Growth, Math methods from University Library of Munich, Germany

Abstract: One of the difficult and frustrating aspects of teaching mathematics is getting students to think logically and develop an ability to prove theorems. Too frequently, students resort to what might be called "proof by example." A classic illustration of "proof by example" comes from years of teaching "mathematics for economists." The exercise is to prove a general principle about sets; for example: "show that for arbitrary sets A and B, the sets A \setminus B, B \setminus A, and A \intersect B are pairwise disjoint." Too frequently the student "proof" begins with: "Let A = {1,3,5,7} and B = {2,4,6,8}. Then ..." Other examples, in other areas of mathematics, no doubt abound. This note presents an obviously preposterous "theorem" and "proves" it with many examples. This "theorem," once "proved" in class, successfully discourages future proofs "by example."

JEL-codes: C6 D5 D9 (search for similar items in EconPapers)
Pages: 10 pages
Date: 1995-06-05
Note: 10 pages; LaTeX 2.09; three files FTP'ed: DVI, PostScript, and TeX input file; Report_no: SIUC Discussion Paper #90-07
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