A computational criterion for the irrationality of some real numbers [article]

Peyman Nasehpour
2019 arXiv   pre-print
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.
arXiv:1806.07560v4 fatcat:j3xuu7aqkrho5onxozrkae5ffi