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The Mysterious World of Normal Numbers

  • Jean-Marie De KoninckEmail author
Conference paper
  • 416 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9310)

Abstract

Given an integer \(q\ge 2\), a q-normal number (or a normal number) is a real number whose q-ary expansion is such that any preassigned sequence of length \(k\ge 1\), of base q digits from this expansion, occurs at the expected frequency, namely \(1/q^k\). Even though there are no standard methods to establish if a given number is normal or not, it is known since 1909 that almost all real numbers are normal in every base q. This is one of the many reasons why the study of normal numbers has fascinated mathematicians for the past century. We present here a brief survey of some of the important results concerning normal numbers.

Keywords

Algebraic Number Irrational Number Abnormal Number Infinite Word Liouville Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Département de Mathématiques et de StatistiqueUniversité LavalQuébecCanada

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