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Re: Effect of gravitation in set theory
Posted:
Nov 25, 2011 1:03 PM
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On 25 Nov., 17:34, Tonico <Tonic...@yahoo.com> wrote:
> is possible to say: ALL the elements of S_k, for any k, are contained
> in any S_(k+j),
>
> for all j > 0.
So it is.
>
> From where "the theorem" follows: no single S_K can contain ALL the
> natural numbers,
>
> so....how eaxctly have you proved that all the naturals are contained
> in one single
>
> S_k, again?
I proved that in order to contain the actual infinite set |N no S_k is
necessary. That includes that not more than one S_k are necessary.
That is what I need in order to show those wrong, who claim infinitel
many S_k would be necessary.
>
> More important, perhaps: how the above gets even slightly close to
> proving that the
>
> union of all S_k is NOT the whole set IN??
Obviously the union is not necessary (and not sufficient).
>
> How can anyone after high school mathematics (well taught and well
> learnt, of course)
>
> can believe, before or after the above, what you wrote at the
> beginning of the post
>
> "Same holds for my proof.
> The set of natural numbers that is not covered by one finite initial
> segment *alone* is empty." ???
The actually infinite set |N does not exist. If it would exist it
would have to have infinite numbers. Those are not available in any
S_k. That is the essence of my proof.
Regards, WM
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