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Arithmetic Subderivatives: Discontinuity and Continuity
University of Tampere, Finland.
University of Tampere, Finland.
Luleå University of Technology, Department of Arts, Communication and Education, Education, Language, and Teaching.ORCID iD: 0000-0002-7494-4632
2019 (English)In: Journal of Integer Sequences, ISSN 1530-7638, E-ISSN 1530-7638, Vol. 22, no 7, article id 19.7.4Article in journal (Refereed) Published
Abstract [en]

We first prove that any arithmetic subderivative of a rational number defines a function that is everywhere discontinuous in a very strong sense. Second, we show that although the restriction of this function to the set of integers is continuous (in the relative topology), it is not Lipschitz continuous. Third, we see that its restriction to a suitable infinite set is Lipschitz continuous. This follows from the solutions of certain arithmetic differential equations.

Place, publisher, year, edition, pages
Ontario, Canada: University of Waterloo, , 2019. Vol. 22, no 7, article id 19.7.4
National Category
Mathematics Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:ltu:diva-76401OAI: oai:DiVA.org:ltu-76401DiVA, id: diva2:1361355
Note

Validerad;2019;Nivå 2;2019-10-21 (johcin)

Available from: 2019-10-15 Created: 2019-10-15 Last updated: 2019-10-21Bibliographically approved

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https://cs.uwaterloo.ca/journals/JIS/VOL22/Merikoski/meri6.html

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Tossavainen, Timo

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