"Darren New" <dne### [at] sanrrcom> wrote:
> Do you have a citation for this assertion? Because the wikipedia entry on 
> Normal_numbers disagrees with you. If you have an equal probability for 
> all 1-symbol elements to appear in an infinite string (i.e., if every 
> symbol appears an infinite number of times) then you have an equal 
> probability of every subsequence to show up - i.e., all possible 
> combinations show up an infinite number of times.

While the probability is equal, it doesn't mean all possible combinations 
necessarily show up an infinite number of times in an arbitrary sequence. 
The aforementioned 0102030405..9596979899 is technically a possible random 
number with each digit 0-9 having an equal probability of occurring.  An 
infinite sequence could be considered that fails to meet the 'all possible 
combinations' feature.

> If you have an infinite number of trials and the letter 'a' never shows 
> up, it means it's impossible for the letter 'a' to show up.

Not really.  Randomly picking an infinite amount from the set {a,b} *could* 
result in nothing but bbb..bbb.  That doesn't mean it's impossible for the 
letter 'a' to show up, only that the bbb..bbb sequence isn't very 
likely...except it's exactly the same probability as any other sequence of 
infinite length:  1/infinity.

-- 
Tim Cook
http://empyrean.freesitespace.net

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