Re: infinity

Randy Poe said:
>
> 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.
Even though there is no end to the possible values for a natural number, and
yet you apply the label "finite" to natural numbers? This is the root of the
problem here. I am only saying the apparently unending set is finite because
you are claiming the apparently unending set of values is finite. You allow
infinite naturals and this problem goes away.
>
> > > 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.
Faith-based? I have offered nothing but numerical arguments and caclulations to
support my position. You offer gedankens and verbiage, and no math.
>
> > 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 the recursive definition of the natural numbers defines a finite set. Be
serious.
>
> > then incrementing the values in it can
> > just as easily produce an infinite value.
>
> It can't.
Look up infinite series, for god's sake.
>
> - Randy
>
>

--
Smiles,

Tony
.

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