# Stevin Numbers and Reality

@article{Katz2012StevinNA, title={Stevin Numbers and Reality}, author={Karin U. Katz and M. Katz}, journal={Foundations of Science}, year={2012}, volume={17}, pages={109-123} }

We explore the potential of Simon Stevin’s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.

#### 33 Citations

Real numbers as infinite decimals -- theory and computation

- Computer Science, Mathematics
- 2018

This article is devoted to solving the historical problem of how to perform arithmetic directly on infinite decimals, which has seen the popular degeometrisation of real numbers since the first constructions were published in around 1872. Expand

Defining arithmetical operations on infinite decimals

- Mathematics
- 2018

Completing Loo-Keng Hua's approach to the real number system pioneered in 1962, this paper defines arithmetical operations directly on infinite decimals without appealing to any ordering structure.… Expand

Real numbers as infinite decimals

- Mathematics
- 2021

Stemming from an idea put forward by Loo-Keng Hua in 1962, this article describes an original way to perform arithmetic directly on infinite decimals. This approach leads to a new and elementary… Expand

The real numbers--A survey of constructions

- Mathematics
- 2015

We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known… Expand

Analyzing Benardete's comment on decimal notation

- Computer Science, Mathematics
- 2017

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. Expand

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

- Philosophy
- 2015

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… Expand

A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography

- Philosophy, Mathematics
- 2012

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis… Expand

Toward a History of Mathematics Focused on Procedures

- Computer Science, Mathematics
- 2016

The proposed formalisations indicate that Robinson’s framework is more helpful in understanding the procedures of the pioneers of mathematical analysis than a Weierstrassian framework, but this does not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians. Expand

Ten Misconceptions from the History of Analysis and Their Debunking

- Mathematics, Philosophy
- 2013

The widespread idea that infinitesimals were “eliminated” by the “great triumvirate” of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number… Expand

Gregory’s Sixth Operation

- Sociology, Mathematics
- 2016

AbstractIn relation to a thesis put forward by
Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny.… Expand

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