Darren New <dne### [at] sanrrcom> wrote:
> >     Well, your probability of hitting a given real number is also 0. 
> > Same amount of weirdness.

> Yes. But I meant my probability of hitting *any* rational number is zero.

  I think that this confuses people because they think that if the
probability for something is 0, that means that it's *impossible* for
that something to happen.

  This is indeed so in the discrete case. However, in this case the
probability is 0 because the total probability of 1 has been divided
among an *infinite* amount of numbers. Thus, mathematically, the resulting
probability of hitting a given number is 0, as 1/infinite = 0.

  *After* you have thrown the dart, the probability to hit the number
the dart did hit grows to 1 (or 100%).

  Or if we say the same thing in another way: Even though there is an
infinite amount of numbers, that doesn't mean you can't choose one.

  (I really wonder if this has any relation whatsoever to the so-called
axiom of choice.)

-- 
                                                          - Warp

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