arXiv Analytics

Sign in

arXiv:1208.1434 [math.NT]AbstractReferencesReviewsResources

A new construction of the real numbers by alternating series

Soichi Ikeda

Published 2012-08-07, updated 2013-10-30Version 3

We put forward a new method of constructing the complete ordered field of real numbers from the ordered field of rational numbers. Our method is a generalization of that of A. Knopfmacher and J. Knopfmacher. Our result implies that there exist infinitely many ways of constructing the complete ordered field of real numbers. As an application of our results, we prove the irrationality of certain numbers.

Comments: 15 pages, 0 figure. Section 4 was added
Categories: math.NT
Subjects: 11U99, 11J72
Related articles: Most relevant | Search more
arXiv:1102.4644 [math.NT] (Published 2011-02-23)
On the convergence of some alternating series
arXiv:2009.14644 [math.NT] (Published 2020-09-30)
Irrationality and Transcendence of Alternating Series Via Continued Fractions
arXiv:1006.3125 [math.NT] (Published 2010-06-16, updated 2014-12-07)
The big de Rham-Witt complex

Links

Toolbox