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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Universidad Católica del Norte, Departamento de Matemáticas
2006
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oai:scielo:S0716-091720060001000022006-06-07ON NORMAL NUMBERSPELLEGRINO,DANIELA 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 normalinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.25 n.1 20062006-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100002en10.4067/S0716-09172006000100002 |
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English |
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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 |
| author |
PELLEGRINO,DANIEL |
| spellingShingle |
PELLEGRINO,DANIEL ON NORMAL NUMBERS |
| author_facet |
PELLEGRINO,DANIEL |
| author_sort |
PELLEGRINO,DANIEL |
| title |
ON NORMAL NUMBERS |
| title_short |
ON NORMAL NUMBERS |
| title_full |
ON NORMAL NUMBERS |
| title_fullStr |
ON NORMAL NUMBERS |
| title_full_unstemmed |
ON NORMAL NUMBERS |
| title_sort |
on normal numbers |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2006 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000100002 |
| work_keys_str_mv |
AT pellegrinodaniel onnormalnumbers |
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