Re: infinity
- From: "Randy Poe" <poespam-trap@xxxxxxxxx>
- Date: 7 Sep 2005 08:21:56 -0700
aeo6 Tony Orlow wrote:
> > But the set of all k can be Cantor-infinite even though each k in that
> > set is finite.
> Yes, even though you have a finite number of finite terms, the sum is Cantor-
> infinite. Doesn't that indicate a problem with Cantor's definitions/
No. What's the problem? As you have repeatedly admitted,
there is no end to a list of the values in such a set.
Most of us have no problem calling a thing which is
unending "infinite", and have a great deal of trouble
understanding how anybody could apply the adjectives
"finite" and "unending" to the same thing.
> > But the sum over all finite k is the sum over a Cantor-infinite set of
> > values, the Cantor-infinite set of finite naturals.
> Yes, based on the misconception that you can have an infinite set of unique
> finite naturals
Despite your faith-based assertions that you can't, the
actual proofs that you can are elementary.
> If adding one natural to the set at a time can produce an infinite set by
> incrementing the set size repeatedly,
It can't.
> then incrementing the values in it can
> just as easily produce an infinite value.
It can't.
- Randy
.
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