publication . Preprint . Article . 2018

Hyperreal Numbers for Infinite Divergent Series

Jonathan Bartlett; Logan Gaastra; David Nemati;
Open Access English
  • Published: 30 Apr 2018
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.
Subjects
free text keywords: Mathematics - General Mathematics, 40C99, Hyperreal number, Pure mathematics, Divergent series, Mathematics

[1] J. M. Henle and E. M. Kleinberg, Infinitesimal Calculus. Dover Publications, 2003.

[2] J. Keisler, Elementary Calculus: An Infinitesimal Approach. Dover Books, second ed., 2012.

[3] L. Gaastra, “Omega: How hilbert's infinite hotel can be used to evaluate divergent series,” GRCC Student Mathematics Seminars, 2016.

[4] S. Schmidt, Life of Fred: Kidneys. Polka Dot Publishers, 2012.

[5] E. W. Weisstein, “Wheat and chessboard problem,” Mathworld-A Wolfram Web Resource, 2018.

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publication . Preprint . Article . 2018

Hyperreal Numbers for Infinite Divergent Series

Jonathan Bartlett; Logan Gaastra; David Nemati;