4 ms·

If you look at the definition on Wikipedia[1], you can see that a normal number, per definition, is base agnostic. [1]: https://en.wikipedia.org/wiki/Normal_nu

• danbruc 11y ago
  I think the question was whether it is possible for a number to be normal in one base but not in another. Intuitively I would say that randomness should transcend the base and therefore a number that is normal in one base should be normal in any other base and therefore absolutely normal. But if that were the case the distinction between normal in a specific base and absolutely normal would be unnecessary. So I don't know but would also be interested in an example in case one exists and is known. EDIT: It is easily possible for simply normal numbers, i.e. if you only consider single digit frequencies but not frequencies of digit pairs, triples and so on. 0.(0123456789) is simply normal in base 10 because every digit occurs with frequency one tenth but it is not normal in base 10 because only ten out of one hundred digit pairs occur. But it is also not simply normal in base 10¹⁰ because it then consists only of the single digit representing 0123456789 repeated indefinitely.
  • markild 11y ago
    Ah, yes. Brought up here as well: https://news.ycombinator.com/item?id=10966819 https://news.ycombinator.com/item?id=10966819
  • ecesena 11y ago
    This doesn't prove that the number in the edited example isn't simply normal in a base b for some b.
    • danbruc 11y ago
      I am not sure if I get your point. The number is simply normal in base 10 but is not simply normal in base 10¹⁰. And that is what Retr0spectrum asked with simply normal replaced with just normal, i.e. for a number that is normal in at least one base but not normal in at least one other base.
      • deleted 11y ago
        [deleted]
    • amadvance 11y ago
      That number is rational, and all rational numbers are not normal.
      • Fargren 11y ago
        But they can be simply normal. It's a much weaker property.