ON NORMAL NUMBERS
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 num...
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| Autor principal: | |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2006
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| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100002 |
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| Sumario: | 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 <img border=0 width=14 height=22 id="_x0000_i1026" src="http:/fbpe/img/proy/v25n1/1.jpg" > or = 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 <img border=0 width=14 height=22 id="_x0000_i1027" src="http:/fbpe/img/proy/v25n1/1.jpg">is normal or not, and we also discuss the normality (or not) of <img border=0 width=14 height=22 id="_x0000_i1028" src="http:/fbpe/img/proy/v25n1/1.jpg">when η fails to be normal |
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