Tim Cook wrote:
> "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.

The probability of a 1 showing up anywhere is zero, so yes, the probability 
of 123 showing up anywhere is zero.

> 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.  

Yep.

> This set contains the number 0.000...  QED.

And that's why the probability of picking a number like that is zero. :-)

>> 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.

Sorry, that's not a citation. I.e., I read experts who say you're wrong. 
You're trying to convince me using intuitive reasoning that infinity works 
in a way the experts say it doesn't work. I see that both arguments are 
perfectly reasonable given certain assumptions about how infinity works.

Now, if you find something that explains *why* it's reasonable to pick an 
infinite number of random digits and get all zeros, I'll look at it, but 
right now we're both just asserting the truth of our own positions. :-)

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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