On normal numbers


  • Daniel M. Pellegrino Universidade Federal de Campina Grande.




Normality, real numbers, normalidad, números reales.


A real number ? 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 ? 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 ? = 0,a1a2a3a4... is a normal number, then ?? = 0, a1a1a2a1a2a3a1a2a3a4... is also normal. On the other hand, if ? 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 ? fails to be normal.

Author Biography

Daniel M. Pellegrino, Universidade Federal de Campina Grande.

Depto de Matemática e Estatística.


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How to Cite

D. M. Pellegrino, “On normal numbers”, Proyecciones (Antofagasta, On line), vol. 25, no. 1, pp. 19-30, May 2017.