Analyzing Benardete's comment on decimal notation
Classical Analysis and ODEs
2017-06-02 v1 History and Overview
Logic
Abstract
Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on the intelligibility of the continuum reveals challenging insights into number systems, the foundations of modern analysis, and mathematics education. A key concept here is, in Terry Tao's terminology, that of an ultralimit. Keywords: real analysis; infinitesimals; decimal notation; procedures vs ontology
Cite
@article{arxiv.1706.00191,
title = {Analyzing Benardete's comment on decimal notation},
author = {Jacques Bair and Piotr Blaszczyk and Karin U. Katz and Mikhail G. Katz and Taras Kudryk and David Sherry},
journal= {arXiv preprint arXiv:1706.00191},
year = {2017}
}
Comments
7 pages; to appear in Philosophy of Mathematics Education Journal