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A computational criterion for the irrationality of some real numbers

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.

preprint2019arXivOpen access
Peyman Nasehpour
math.ACmath.NT
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Peyman Nasehpour

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