Re: Ultimate debunking of Cantor's Theory

In article <1185296232.248874.21820@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
WM <mueckenh@xxxxxxxxxxxxxxxxx> wrote:

On 24 Jul., 14:49, "Dik T. Winter" <Dik.Win...@xxxxxx> wrote:
In article <1185220878.048152.35...@xxxxxxxxxxxxxxxxxxxxxxxxxxx> WM
<mueck...@xxxxxxxxxxxxxxxxx> writes:
> On 23 Jul., 20:44, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
...
> > > expressions like
> > > sum(N) = 0 and other strange things.
> >
> > Where do I find that expression in a set theory book?
>
> Not in that book. But if in general continuous functions can be
> determined by their limits at points where they are undefined,

No. They can not be determined by their limits at points where they
are undefined because at such points they are not defined and so such
points are not in the domain of the function.

Nevertheless they can be determined. Sum[k = 1 ... n] (1/2^k) is
undefined for n --> oo. Nevertheless this sum can be determined to be
less than 10 - without any further definition.

The partial sums can be determined, but the sum cannot be determined at
all without a definitions that " sum = limit" when the limit exists, and
mathematics does not require any such definition.

They can be *defined*
by the limit, extending the domain. However, the limit is not the
only value with which you can extend the domain.

For the above example and for P(x)/K(x) in the tree there is no chance
to get more than 10 at x = oo.

Sure there is. Since P(x)/K(x) has no value at all "at oo", one can
extend the definition from finite arguments to oo by giving it any value
at all at oo.

Since P(x)/K(x) is essentially a function on N, originally, there is no
issue of continuity at all to bother with. If WM wishes to extend the
definitions to reals, he, himself, introduces infinitely many
discontinuities, so his argument again fails.



A different definition is obviously
wrong - not for an arbitrary function, there everything may be
possible, but it is wrong with respect to the structure of the tree.
This is clear by application of very simple logic.

Regards, WM
.

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