Skip to Main content Skip to Navigation
Journal articles

Integer calculus on the Harthong-Reeb Line

Abstract : In this work, we give a presentation of the so-called Harthong-Reeb line. Only based on integer numbers, this numerical system has the striking property to be roughly equivalent to the continuous real line. Its definition requires the use of a natural number w which is infinitely large in the meaning of nonstandard analysis. Following the idea of G. Reeb, we show how to implement in this framework the Euler scheme. Then we get an exact representation in the Harthong-Reeb line of many real functions like the exponential. Since this representation is given with the help of an explicit algorithm, it is natural to wonder about the global constructivity of this numerical system. In the conclusion, we discuss this last point and we outline some new directions for getting analogous systems which would be more constructive
Document type :
Journal articles
Complete list of metadatas

Cited literature [6 references]  Display  Hide  Download

https://hal.inria.fr/hal-01277784
Contributor : Coordination Episciences Iam <>
Submitted on : Tuesday, February 23, 2016 - 11:13:09 AM
Last modification on : Monday, May 4, 2020 - 5:02:04 PM
Long-term archiving on: : Tuesday, May 24, 2016 - 11:55:18 AM

File

arima00928.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01277784, version 1

Collections

Citation

Guy Wallet. Integer calculus on the Harthong-Reeb Line. Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées, INRIA, 2008, 9, pp.517-536. ⟨hal-01277784⟩

Share

Metrics

Record views

138

Files downloads

781