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
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
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