Hyperreal Numbers for Infinite Divergent Series

Bartlett, Jonathan, Logan Gaastra, and David Nemati. 2020. "Hyperreal Numbers for Infinite Divergent Series." Communications of the Blyth Institute 2(1):7-15.

9 Pages Posted: 5 Oct 2019 Last revised: 12 Feb 2020

See all articles by Jonathan Bartlett

Jonathan Bartlett

ITX Corp; The Blyth Institute; Bradley Center for Natural and Artificial Intelligence

Logan Gaastra

University of Michigan at Ann Arbor

David Nemati

The Blyth Institute

Date Written: April 15, 2019

Abstract

Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent series in a more comprehensive and tractable way.

Keywords: divergent series, hyperreal numbers, infinity

Suggested Citation

Bartlett, Jonathan and Gaastra, Logan and Nemati, David, Hyperreal Numbers for Infinite Divergent Series (April 15, 2019). Bartlett, Jonathan, Logan Gaastra, and David Nemati. 2020. "Hyperreal Numbers for Infinite Divergent Series." Communications of the Blyth Institute 2(1):7-15., Available at SSRN: https://ssrn.com/abstract=3459243 or http://dx.doi.org/10.2139/ssrn.3459243

Jonathan Bartlett (Contact Author)

ITX Corp ( email )

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Pittsford, NY 14534
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The Blyth Institute ( email )

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Bradley Center for Natural and Artificial Intelligence ( email )

208 Columbia Street
Seattle, WA 98104
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Logan Gaastra

University of Michigan at Ann Arbor ( email )

David Nemati

The Blyth Institute

8835 S Kingston Ave
Tulsa, OK 74137
United States

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