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.
Nasehpour, P. (2020). A Computational Criterion for the Irrationality of Some Real Numbers. Journal of Algorithms and Computation, 52(1), 97-104. doi: 10.22059/jac.2020.76471
MLA
Peyman Nasehpour. "A Computational Criterion for the Irrationality of Some Real Numbers". Journal of Algorithms and Computation, 52, 1, 2020, 97-104. doi: 10.22059/jac.2020.76471
HARVARD
Nasehpour, P. (2020). 'A Computational Criterion for the Irrationality of Some Real Numbers', Journal of Algorithms and Computation, 52(1), pp. 97-104. doi: 10.22059/jac.2020.76471
VANCOUVER
Nasehpour, P. A Computational Criterion for the Irrationality of Some Real Numbers. Journal of Algorithms and Computation, 2020; 52(1): 97-104. doi: 10.22059/jac.2020.76471
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