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

But is the probability that it hit any rational number (vs any 
irrational number) non-zero at that point?  If you do it countably many 
times, will you *ever* hit *any* rational number?

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

That's pretty much exactly what the axiom of choice is. Given an 
infinite set of sets, can you create a set by picking one element from 
each subset?

-- 
Darren New / San Diego, CA, USA (PST)
  Helpful housekeeping hints:
   Check your feather pillows for holes
    before putting them in the washing machine.

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