A Computational Criterion for the Irrationality of Some Real Numbers

نویسندگان
Nasehpour, Peyman ID 1

1 Department of Engineering Science, Golpayegan University of Technology, Golpayegan, Iran

doi
10.22059/jac.2020.76471
چکیده

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.

کلیدواژه‌ها
Asymptotic average of the decimals, Cesaro summation, Irrational numbers, Simply normal numbers