> Sorry, but no - the explanation doesn't work. If you read my original
> long post, you'd see that the two cases are *identical*.

The mistake in your logic is assuming the probability of choosing 1 item 
from an infinite set is zero, it isn't, it is 1/infinity or "infinitely 
small".  In many cases this can be treated as zero, but when you start 
summing over an infinite number of items (ie what is the probability that I 
chose any of these items, or if I try an infinite times will I get this 
one?) there is an important difference.

The probability of you choosing 1.847 when asked to choose a number between 
0 and 1 is really zero.  Even if you try an infinite number of times, it's 
still zero probability.

> Getting a sequence of all heads forever is identical to picking a point
> from 0 to 1. Both have probability 0.

Mathematicians seem to disagree with you on that one.  1/infinity is not 
defined as zero (because it can often lead to problems like the above), 
however the infinite sum of 1/2+1/4+1/8+... (ie probability of getting no 
tails after infinite throws) is defined as 1.

Of course you can discuss how this relates to reality, but I'd rather not 
get involved in that one, it could an infinitely long time :-)

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