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arXiv · 1806.07560

A computational criterion for the irrationality of some real numbers

Peyman Nasehpour
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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.

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Peyman Nasehpour. 2018-06-20. A computational criterion for the irrationality of some real numbers. https://arxiv.org/abs/1806.07560

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