On normal numbers
Author
Pellegrino, Daniel M.
Full text
https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/154710.4067/S0716-09172006000100002
Abstract
A real number α is said to be normal to base 10 if, for every natural number L, each finite sequence of L digits appears in the decimals of α with frequency 1/10L. Even intuitive results concerning normal numbers presents complicated formalizations and to decide whether a given number is normal or not is sometimes almost impossible. In this paper we prove that if η = 0; a1a2a3a4... is a normal number, then = 0, a1a1a2a1a2a3a1a2a3a4... is also normal. On the other hand, if η fails to be normal, there are some technical difficulties in order to decide whether is normal or not, and we also discuss the normality (or not) of when η fails to be normal.