Mueen Nawaz wrote:
>         Let's say that instead of a 2 sided coin, I have a three state
> random generator, which generates each state with equal probability.
> 
>         Now I had already shown that the likelihood of getting a
> _particular_ infinite sequence was the same as getting a _particular_
> value between 0 and 1. (That is, the likelihood is zero - I'm arguing
> purely mathematically - let's put the "real" world aside).
> 
>         Intuitively, that's because a point is infinitely smaller than
> the interval [0,1].
> 
>         In fact, if I were to ask the probability of getting a rational
> number, the answer is still 0. While the set of rationals is infinite,
> it's still infinitely smaller than the unit interval - the latter is of
> a higher infinity.

I think this is relevant:
http://en.wikipedia.org/wiki/Almost_surely

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