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- Title
Proofs and Retributions, Or: Why Sarah Can't Take Limits.
- Authors
Kanovei, Vladimir; Katz, Karin; Katz, Mikhail; Schaps, Mary
- Abstract
The small, the tiny, and the infinitesimal (to quote Paramedic) have been the object of both fascination and vilification for millenia. One of the most vitriolic reviews in mathematics was that written by Errett Bishop about Keisler's book Elementary Calculus: an Infinitesimal Approach. In this skit we investigate both the argument itself, and some of its roots in Bishop George Berkeley's criticism of Leibnizian and Newtonian Calculus. We also explore some of the consequences to students for whom the infinitesimal approach is congenial. The casual mathematical reader may be satisfied to read the text of the five act play, whereas the others may wish to delve into the 130 footnotes, some of which contain elucidation of the mathematics or comments on the history.
- Subjects
MATHEMATICAL research; CALCULUS; MATHEMATICAL analysis; MATHEMATICAL literature; LITERATURE reviews
- Publication
Foundations of Science, 2015, Vol 20, Issue 1, p1
- ISSN
1233-1821
- Publication type
Article
- DOI
10.1007/s10699-013-9340-0