Re: [MLUG - DISCUSSION] fun math thing

[Mike Miller <EMAIL:PROTECTED>]

On Thu, 1 Jun 2006, Stephen Montgomery-Smith wrote:

> I am guessing that "absolutely normal" means all b digits appear with 
> equal frequency when written in base b, and this for every base 
> b=2,3,... at the same time.
>
> If you pick a real number between 0 and 1 using the uniform probability, 
> then with probability 1 the number you pick will be absolutely normal. 
> (You can prove this using the law of large numbers.)

I can see that.  A similar idea is that the probability is zero that the 
number will be rational.  I tell people this and they don't believe me. 
I will tell them that it is impossible for the randomly selected number to 
be rational and they will counter that the rational numbers are there, so 
it must be possible to pick one.  I guess it is counterintuitive for some 
people but it seems obvious to me.


> However there is no naturally occuring number, like pi or e or sqrt(2), 
> that is known to be absolutely normal.  (It is conjectured that most 
> naturally occuring irrational numbers are normal, but I don't think that 
> anyone is even close to providing a proof.)

Fascinating.  I did not know that.  Do you remember from about 10 years 
ago that some genius came up with a formula for the nth digit of pi?  But 
it was in base 16.  Still, I was stunned.  Anyway, maybe that development 
made it possible to say something about normality of pi in base 16 (if 
that's even what it is called).  I just looked it up:

http://mathworld.wolfram.com/BBPFormula.html

Mike

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