From: Tomaz Kristan (tomaz.kristan@gmail.com)
Date: Tue Aug 24 2004 - 14:13:58 MDT
On Mon, 23 Aug 2004 16:11:59 -0700, J. Andrew Rogers
<andrew@ceruleansystems.com> wrote:
> So in a sense, I don't have a problem with
> infinities as long as they are never expressible as a
> practical matter.
Yes, but I would go further than that. I can sketch an antinomy inside
a countable infinite set. Shake the set of all naturals! Shake it
well, infinitely many times. Now, what do you expect you will see at
the first 1000 places? What their average is going to be?
On one hand, it should be greater than any N. N much has already been
after only a finite number of shakes. Later on, this first 1000
places' average only increases.
On the other hand, every average of all finite naturals is a finite number.
A paradox. Therefore I don't see a possibility for any kind of infinity.
p.s.
I could formulate this paradox in a strict math language, but it's
enough for a glimpse.
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