A new construction of the real numbers by alternating series
Number Theory
2013-10-31 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1208.1434,
title = {A new construction of the real numbers by alternating series},
author = {Soichi Ikeda},
journal= {arXiv preprint arXiv:1208.1434},
year = {2013}
}
Comments
15 pages, 0 figure. Section 4 was added