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Some representations of real numbers using integer sequences

Published online by Cambridge University Press:  14 October 2022

Loïc Mazo*
Affiliation:
ICube, Université de Strasbourg, CNRS, Strasbourg, France
Marie-Andrée Da Col-Jacob
Affiliation:
ICube, Université de Strasbourg, CNRS, Strasbourg, France
Laurent Fuchs
Affiliation:
XLIMM, Université de Poitiers, CNRS, Poitiers, France
Nicolas Magaud
Affiliation:
ICube, Université de Strasbourg, CNRS, Strasbourg, France
Gaëlle Skapin
Affiliation:
XLIMM, Université de Poitiers, CNRS, Poitiers, France
*
*Corresponding author. Email: loic.mazo@laposte.net

Abstract

The paper describes three models of the real field based on subsets of the integer sequences. The three models are compared to the Harthong–Reeb line. Two of the new models, contrary to the Harthong–Reeb line, provide accurate integer “views” on real numbers at a sequence of growing scales $B^n$ ( $B\ge2$ ).

Type
Paper
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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