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 η̅ = 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 η̅ is normal or not, and we also discuss the normality (or not) of η̅ when η fails to be normal.
Universidad Católica del Norte.
Derechos de autor 2006 Proyecciones. Journal of Mathematics
Proyecciones. Journal of Mathematics; Vol 25 No 1 (2006); 19-30
Proyecciones. Revista de Matemática; Vol. 25 Núm. 1 (2006); 19-30