I suppose you'd just have to be more careful with the definition. The digits 0, 1, and 2 should occur with frequency 1/pi, while 3 should occur with frequency 1-3/pi. The strings 00, 01, 02, 10, 11, 12, 20, 21, 22 should occur with frequency 1/pi^2, etc. I imagine all the proofs about non-normal numbers having measure 0 would carry over mutatis mutandis. Charles Greathouse Analyst/Programmer Case Western Reserve University On Sun, Oct 13, 2013 at 2:24 PM, Hans Havermann <gladhobo@teksavvy.com>wrote:
Keith F. Lynch: "No, the digits of seventeen *in base pi*, 120.220021101020230020003… This of course never repeats or terminates."
MathWorld's article on 'base' cautions that "the representation of a given integer in an irrational base may be nonunique" (but this is true also of integer bases: 1=.999… in base ten). More relevant perhaps is the issue of normalcy. My understanding of the concept is that it cannot be applied to irrational bases. What then is the frequency distribution of the digits (0, 1, 2, 3) of seventeen in base pi? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun