It's undefinable. You're just as likely to get all zeros,
or all ones, as you are to get any arrangement of numbers you care to
mention (or can mention); the probability being 0 for each, I suppose. The
difference is, there are some infinite binary strings of numbers you cannot
define without an infinite description (semantic paradoxs
aside).. which one assumes, are 'truly' random.

##
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>From: Norman Samish <[EMAIL PROTECTED]>
>To: [EMAIL PROTECTED]
>Subject: The infinite list of random numbers
>Date: Thu, 08 Nov 2001 20:41:30 -0800
>
>Suppose an ideal random number generator produces, every microsecond,
>either
>a zero or a one and records it on a tape. After a long time interval one
>would expect the tape to contain a random mix of zeroes and ones with the
>number of zeroes equal to the number of ones. Is this necessarily true?
>Is
>it possible that, even after an infinite time had passed, that the tape
>could
>contain all zeroes or all ones? Or MUST the tape contain an equal number
>of
>zeroes and ones? Why? If you have a reference dealing with this topic,
>please let me know. Thanks,
>Norm Samish
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