Proofs and Retributions, Or: Why Sarah Can’t Take Limits

Vladimir Kanovei; Karin U. Katz; Mikhail G. Katz; Mary Schaps

doi:10.1007/s10699-013-9340-0

Proofs and Retributions, Or: Why Sarah Can’t Take Limits

Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Mary Schaps

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Foundations of Science
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s10699-013-9340-0
State	Published - Mar 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media Dordrecht.

Funding

The work of V. Kanovei was partially supported by RFBR grant 13-01-00006. M. Katz was partially funded by the Israel Science Foundation grant no. 1517/12. The authors are grateful to Antonio Montalban for expert advice in matters of note 115. The influence of Hilton Kramer (1928–2012) is obvious.

Funders	Funder number
Israel Science Foundation
Russian Foundation for Basic Research
Russian Foundation for Basic Research	13-01-00006
Israel Science Foundation	1517/12

Keywords

Abraham Robinson
Errett Bishop
Hyperreals
Infinitesimals
Intuitionists
Petard

Access to Document

10.1007/s10699-013-9340-0

Cite this

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Proofs and Retributions, Or: Why Sarah Can’t Take Limits

Abstract

Bibliographical note

Funding

Keywords

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