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dc.rights.licenseopenen_US
hal.structure.identifierEnvironnements et Paléoenvironnements OCéaniques [EPOC]
dc.contributor.authorFALLOT, Laurent
dc.date.accessioned2024-03-07T09:12:32Z
dc.date.available2024-03-07T09:12:32Z
dc.date.created2023-12-08
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/188615
dc.description.abstractEnThis 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.isoENen_US
dc.rights.urihttp://creativecommons.org/licenses/by-sa/
dc.subject.ensequence of rational numbers
dc.subject.enrational numbers
dc.subject.enrecord holders
dc.subject.ensubset dense
dc.subject.enCollatz problem
dc.title.enTHE MONOID OF NUMBERS OF THE FORM 1 <= a^q /b^p < a
dc.typeDocument de travail - Pré-publicationen_US
dc.subject.halMathématiques [math]/Topologie générale [math.GN]en_US
dc.identifier.arxiv2312.06248en_US
bordeaux.hal.laboratoriesEPOC : Environnements et Paléoenvironnements Océaniques et Continentaux - UMR 5805en_US
bordeaux.institutionUniversité de Bordeauxen_US
bordeaux.institutionCNRSen_US
bordeaux.teamPROMESSen_US
bordeaux.import.sourcehal
hal.identifierhal-04332248
hal.version1
hal.popularnonen_US
hal.audienceInternationaleen_US
hal.exportfalse
workflow.import.sourcehal
dc.rights.ccCC BY-SAen_US
bordeaux.subtypePrepublication/Preprinten_US
bordeaux.COinSctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.au=FALLOT,%20Laurent&amp;rft.genre=preprint


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