On normal numbers

• Pellegrino, Daniel M. ^[1]
  1. [1] Universidade Federal de Campina Grande

     Universidade Federal de Campina Grande

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 1, 2006, págs. 19-30
• Idioma: inglés
• Enlaces
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• Resumen

  • 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.