Virgil
Posts:
4,486
Registered:
1/6/11
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Re: Effect of gravitation in set theory
Posted:
Nov 23, 2011 2:25 AM
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In article
<9fb19006-a634-4a88-b256-d11560cae372@w7g2000yqc.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 22 Nov., 23:32, William Hughes <wpihug...@gmail.com> wrote:
>
> Here is all that is to be said about that topic.
>
> S_k = {1, 2, 3, ..., k}
>
> Definition: S_k is necessary <==> S_k contains a natural number n that
> is not in any S_(k+j), j > 0.
>
> Theorem. *If it is possible* to have all natural numbers in the union
> of a set of S_k we need not more than one S_k.
It is possible, since {S_k: k in N} does it quite throrougly.
So now it is up to WM to show how one and only one of the S_k's can
cover N.
>
> Proof:
> S_1 is not necessary.
> If S_n is not necessary, then als S_(n+1) is not necessary.
I do not know in what system of illogic WM thinks that this is even
close to being a proof of his false claim, but it does not float in any
standard form of mathematics.
And should not float even in WM's matheological Wolkenmuekenheim.
>
> This holds for every n in |N.
Except that it doesn't hold anywhere outside of WM's matheological
Wolkenmuekenheim.
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