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- Title
ON NORMAL NUMBERS.
- Authors
Pellegrino, Daniel
- 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 ŋ̄ = 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 ŋ̄ is normal or not, and we also discuss the normality (or not) of ŋ̄ when η fails to be normal.
- Subjects
NORMAL numbers; REAL numbers; NUMBER theory; GEOMETRIC series; COMPLEX numbers
- Publication
Proyecciones - Journal of Mathematics, 2006, Vol 25, Issue 1, p19
- ISSN
0716-0917
- Publication type
Article