Arithmetic Subderivatives

Discontinuity and Continuity

Document identifier: oai:DiVA.org:ltu-76401
Keyword: Natural Sciences, Mathematics, Naturvetenskap, Matematik, Social Sciences, Educational Sciences, Didactics, Samhällsvetenskap, Utbildningsvetenskap, Didaktik, Mathematics Education, Matematik och lärande
Publication year: 2019
Abstract:

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.

Authors

Pentti Haukkanen

University of Tampere, Finland
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Jorma K. Merikoski

University of Tampere, Finland
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Timo Tossavainen

Luleå tekniska universitet; Pedagogik, språk och Ämnesdidaktik
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