"Darren New" <dne### [at] sanrrcom> wrote:
>> While the probability is equal, it doesn't mean all possible combinations 
>> necessarily show up an infinite number of times in an arbitrary sequence.
> Why do you say that?

Because 0.50000000... is one possible arbitrary sequence, and nowhere in it 
contains the sequence 123.

>>> 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.
> Do you have a cite to support this contention?

Observe:  the number set of decimals from 0 to 1 (inclusive) is infinitely 
large, with each element containing an infinite amount of decimal places, 
each having an equal probability of being a digit 0-9.  This set contains 
the number 0.000...  QED.

>> 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.
> That's not my understanding of how the math works. Do you have any 
> citation as evidence for this? Because if the letter 'a' doesn't show up 
> after an *infinite* number of trials, you clearly don't have any 
> probability for it to show up at all, and indeed that's what the math 
> pages I've cited already say.

See above.  The probability of selecting any particular number is 
effectively zero, but that number exists and so *can* be chosen.

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

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