# Analyzing Benardete's comment on decimal notation

## TL;DR

This paper explores Benardete's critique of decimal notation and zero, offering insights into the foundations of analysis and number systems, with implications for mathematics education and the concept of ultralimits.

## Contribution

It provides a philosophical and mathematical analysis of Benardete's comments, connecting them to modern concepts like ultralimits and foundational issues in analysis.

## Key findings

- Benardete's critique challenges conventional views on decimal notation.
- The paper links philosophical insights to modern analysis concepts.
- Implications for mathematics education and understanding of the continuum.

## 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