>> So you would also agree then that 1/2 + 1/4 + 1/8 + ... equals 1 with
>> infinitely many terms?  You see where this is going?
>
>  I agree with it, and no, I don't see your point.

That the sequence is also the probability of a head being tossed after N 
tries of throwing a coin.  After 1 try it's 1/2, after 2 tries it's 1/2 + 
1/4, etc.  So after infinitely many tries the probability is *equal* to 1.

Now simply replace "head being tossed" with "this sequence of characters 
being the works".

>  I honestly don't understand.

If you are choosing numbers in the range 0...1, 0.5 has an infinitesimally 
small probability of being chosen, 1.5 has a zero probability of being 
chosen, they are not the same probability.  (In some situations you can call 
the probability of 0.5 being chosen "zero", but you must remember that the 
zero came from 1/infinity and not "real" zero incase you use it in later 
calculations).

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