Re: [MLUG - DISCUSSION] fun math thing

[Stephen Montgomery-Smith <EMAIL:PROTECTED>]

Mike Miller wrote:
> 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.

Well I would counter that they are correct - it is possible that the 
random number is rational, just that the probability of it being so is zero.

I similar event which is theoretically possible but has probability zero 
is to keep tossing a coin, and it never comes up with a head.

Stephen

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