A computational criterion for the irrationality of some real numbers
Commutative Algebra
2020-08-19 v4 Number Theory
Abstract
In this paper, we compute the asymptotic average of the decimals of some real numbers. With the help of this computation, we prove that if a real number cannot be represented as a finite decimal and the asymptotic average of its decimals is zero, then it is irrational. We also show that the asymptotic average of the decimals of simply normal numbers is 9/2.
Cite
@article{arxiv.1806.07560,
title = {A computational criterion for the irrationality of some real numbers},
author = {Peyman Nasehpour},
journal= {arXiv preprint arXiv:1806.07560},
year = {2020}
}
Comments
Minor update. Some new references were added. 6 pages