On normal numbers

  • Daniel M. Pellegrino Universidade Federal de Campina Grande.
Palabras clave: Normality, real numbers, normalidad, números reales.


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.

Biografía del autor/a

Daniel M. Pellegrino, Universidade Federal de Campina Grande.
Depto de Matemática e Estatística.


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Cómo citar
D. Pellegrino, On normal numbers, PJM, vol. 25, n.º 1, pp. 19-30, may 2017.

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