Dr. Dobb's Python-URL! - weekly Python news and links (Mar 17)

Erik Max Francis max at alcyone.com
Wed Mar 19 22:21:30 CET 2003


Robin Becker wrote:

> I assume absolute normality excludes the case where one expresses the
> number in itself as a base or am I being more than usually stupid.

When one talks about a number being b-normal, b is an integer.  It's
true that pi written in base pi is 10, but that's "cheating" in the
sense that integral bases are usually what is intended when one is
talking about writing numbers in different bases.

> Also I suppose that being non-random implies finiteness (in some
> sense)
> so are we just talking 'symbol' count or information. After all there
> are very small symbolic representations of pi, but are they smaller in
> information content etc etc.

No, non-random (in terms of non-normality) simply means that a number
does not terminate or repeat (thus it is irrational), but that the
distribution of digits (in whatever base(s) are being discussed) are not
uniform.

Digit expansions (in any base) have nothing to do with a number's
symbolic representation; there are probably an infinite number of
different symbolic representations for any number you can name, but the
digit expansion in base b is unique (or, well, at least mostly unique,
for cases like 0.999... = 1).

-- 
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