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THE MONOID OF NUMBERS OF THE FORM 1 <= a^q /b^p < a
| dc.rights.license | open | en_US |
| hal.structure.identifier | Environnements et Paléoenvironnements OCéaniques [EPOC] | |
| dc.contributor.author | FALLOT, Laurent | |
| dc.date.accessioned | 2024-03-07T09:12:32Z | |
| dc.date.available | 2024-03-07T09:12:32Z | |
| dc.date.created | 2023-12-08 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/188615 | |
| dc.description.abstractEn | This paper is a study of the set of rational numbers of the form 1 <= a^q /b^p < a with a and b co-prime integers. The set F (a,b) of these numbers, with an appropriate binary law, is a monoid isomorphic to (N, +, 0). We identify the sequences of minimum and maximum record holders in F (a,b) and prove that the first one converges to 1 while the second one converges to a. We conclude that F (a,b) is dense in the set of the real numbers comprise between 1 and a. | |
| dc.language.iso | EN | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-sa/ | |
| dc.subject.en | sequence of rational numbers | |
| dc.subject.en | rational numbers | |
| dc.subject.en | record holders | |
| dc.subject.en | subset dense | |
| dc.subject.en | Collatz problem | |
| dc.title.en | THE MONOID OF NUMBERS OF THE FORM 1 <= a^q /b^p < a | |
| dc.type | Document de travail - Pré-publication | en_US |
| dc.subject.hal | Mathématiques [math]/Topologie générale [math.GN] | en_US |
| dc.identifier.arxiv | 2312.06248 | en_US |
| bordeaux.hal.laboratories | EPOC : Environnements et Paléoenvironnements Océaniques et Continentaux - UMR 5805 | en_US |
| bordeaux.institution | Université de Bordeaux | en_US |
| bordeaux.institution | CNRS | en_US |
| bordeaux.team | PROMESS | en_US |
| bordeaux.import.source | hal | |
| hal.identifier | hal-04332248 | |
| hal.version | 1 | |
| hal.popular | non | en_US |
| hal.audience | Internationale | en_US |
| hal.export | false | |
| workflow.import.source | hal | |
| dc.rights.cc | CC BY-SA | en_US |
| bordeaux.subtype | Prepublication/Preprint | en_US |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=FALLOT,%20Laurent&rft.genre=preprint |
