Yes I suppose so, there are an infinite number of ways to arrange an
infinite number of zeros (or ones), but it's little odds, because they
are essentially the same string as far as we are concerned. Each infinite 
arrangement with zeros and ones together is distinct however.
More generally, all the definable arrangements of zeros and ones,
would have prob. 0.

>From: "Saibal Mitra" <[EMAIL PROTECTED]>
>To: "everything" <[EMAIL PROTECTED]>
>Subject: Re: The infinite list of random numbers
>Date: Fri, 9 Nov 2001 18:45:15 +0100
>All arrangemets are equally likely, but the probability is, of course, 
>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. 
> > 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 
> > >would expect the tape to contain a random mix of zeroes and ones with 
> > >number of zeroes equal to the number of ones.  Is this necessarily 
> > >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 
> > >of
> > >zeroes and ones?  Why?  If you have a reference dealing with this 
> > >please let me know.  Thanks,
> > >Norm Samish
> >
> >
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