On Thu, Dec 6, 2018 at 10:02 AM Mike Stay <metaweta@gmail.com> wrote:
It's normal to base 10. I think the claim is that nobody knows a specific number to be normal to every base. That said, the claim has to be restricted to computable numbers, since an algorithmically random real like the halting probability of a prefix-free universal Turing machine has to be normal to every base; if not, you could predict infinitely many (not necessarily contiguous) digits of it, which contradicts the definition of algorithmically random.
I don't follow this. If I tell you that X has no 3s in it's base-10 expansion, which means it is not normal, how does this let you predict infinitely many digits (or even one digit!) of X? Andy Latto
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com