Integer-detecting sequences
type: Item
instance of: scholarly article
title: Integer-detecting sequences
zbMATH Open document ID: 0920.11043
DOI: 10.1016/S0019-3577(98)80026-8
published in: Indagationes Mathematicae. New Series
publication date: 1999-04-07T00:00:00Z
review text: Let \(\|\alpha\|\) denote the distance from the real number \(\alpha\) to the nearest integer. Let \(\varepsilon>0\). A sequence \(\{m_n\}\) of positive integers is called integer-detecting of height \(\varepsilon\) if every rational number \(r\), such that \(\| m_nr\|<\varepsilon\) for all \(n\geq 0\) is an integer. A sequence of positive integers is called integer-detecting if it is integer-detecting of height \(\varepsilon\) for some \(\varepsilon>0\). The paper deals with several criteria of integer-detecting sequences.
Mathematics Subject Classification ID: 11J71
Mathematics Subject Classification ID: 11B83
zbMATH DE Number: 1251270
zbMATH Keywords: integer-detecting sequences
author: J. W. Sander
author: John Steinig
reviewed by: Jaroslav Hančl
MaRDI profile type: Publication
cites work: Q3318963
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description: scientific article; zbMATH DE number 1251270