0

The definition of a disjunctive sequence is an infinite sequence (in some base $b$), which contains all finite base $b$ words at least once. However, does that automatically imply it contains all finite base $b$ words infinitely many times?

user107952
  • 20,508
  • 2
    The following special case is sufficient for the general case. Consider the digit string $33871.$ Since the sequence is disjunctive, the digit string $3387133871$ appears somewhere, and the digit string $338713387133871$ appears somewhere, and the digit string $33871338713387133871$ appears somewhere, etc. So not only does $33871$ appear infinitely often, every finitely-iterated concatenation of $33871$ appears (hence, every finitely-iterated concatenation of $33871$ appears infinitely often). FYI, this collection of links may be of interest. – Dave L. Renfro Apr 14 '23 at 19:50

0 Answers0