I remember long time ago I faced with a question talking about real numbers which include all natural numbers in them after the decimal point. I don't remember the term for them and I cannot find them on web. Any help?

For example you if say $359$ then I can find it somewhere:



1 Answer 1


These are called 'normal numbers' (or at least i think that's what you mean :)) or you could even go to the more general 'disjunctive sequences'.

  • 2
    $\begingroup$ One simple example is due to Champernowne: .012345678910111213..., where you just concatenate the numbers 0, 1, 2, ..., 9, 10, 11, ... after the decimal point. $\endgroup$ Sep 19, 2013 at 13:12
  • $\begingroup$ does it grantee that all natural numbers would appear? $\endgroup$
    – faravish
    Sep 19, 2013 at 13:17
  • $\begingroup$ Yes: from my answer above: A disjunctive sequence is a sequence in which every finite string appears. A normal sequence is disjunctive, but a disjunctive sequence need not be normal. A rich number in base b is one whose expansion in base b is disjunctive. $\endgroup$ Sep 19, 2013 at 13:39

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