I notice I didn't respond to your first question in this post. So...

On 5/3/2010 7:41 PM, Rex Allen wrote:
Probablistic statements are always about measure.  What you write above is
true, but it is also true if you substitute "finite" for "infinite".  It's
just that when you have a finite set or you are generating a potentially
inifinite set, then the cardinality and the relative rate of generation
provides a canonical measure.  But it's not the only one and not even
necessarily the right one depending on the problem - did you read the paper
I sent?

So I did read your handout on probability.  And I'm *still* not an
expert on the subject.  SO.  Epic fail on your part.

Trying the impossible does tend to epic failure.

So, given eternal recurrence, there are an infinite number of Rexs.
And an infinite number of not-Rexs.  Let's pair the Rexs off in a
one-to-one correspondence with the not-Rexs.  Then, let's go down the
list and put an "A" sticker on the Rexs.  And a "B" sticker on the
not-Rexs.  Then lets randomly arrange them in an infinitely long row
and select one at random.  What's the probability of selecting a Rex?
What's the probability of selecting an "A" sticker?

I suppose your intent is to assign equal measure to each position on
the list so, for any finite subsection of the list the measure of As
and Bs will be equal.

If that was my intent, what would your response be?

The usual way of dealing with "infinity" is to use a measure that works for finite cases and converges in the limit as the number is arbitrarily increased. Notice that there is no way to "randomly arrange" the infinite sets, except by some process that "randomly" selects elements and places them on the list. So you're really back the generating frequency.

Brent

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