English

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

R2 v1 2026-06-22T20:05:51.256Z