All arrangemets are equally likely, but the probability is, of course, zero.
So with probability one you don't get only zeros.

There is a theorem that says that any finite arbitrary configuration will
appear an infinite number of times in an infinite random sequence with
probability one.


Neil Lion wrote:
> 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
> define without an infinite description (semantic paradoxs
> aside).. which one assumes, are 'truly' random.
> >From: Norman Samish <[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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