Generalized Number Derivatives

Michael Stay

Generalized Number Derivatives

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arxiv math/0508364 v1 pith:Y5UX4V7K submitted 2005-08-19 math.NT

Michael Stay This is my paper · ORCID

classification math.NT

keywords derivativenumberexaminebasicconceptdeformationdeformedderivatives

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We generalize the concept of a number derivative, and examine one particular instance of a deformed number derivative for finite field elements. We find that the derivative is linear when the deformation is a Frobenius map and go on to examine some of its basic properties.

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Hyperreal differentiation with an idempotent ultrafilter
math.LO 2024-11 conditional novelty 7.0 of 10

A derivative operator on hyperreals is well-defined when the ultrafilter is idempotent and favors small positive intervals, with applications to a strengthened Hindman's theorem.

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