Virgil
Posts:
4,482
Registered:
1/6/11
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Re: Effect of gravitation in set theory
Posted:
Nov 23, 2011 2:20 AM
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In article
<2eb4c45f-bf1c-4d84-855e-3e9acbb1b568@g7g2000vbd.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!
H_K = Union{S_k: k in H} will work for any H which is not a subset of
any S_k.
In particular, H_N = Union{S_k: k in N} does so trivially since for
every n in N, n is also in S_n, so the union of all such S_n's will
cover all n''s in N.
>
> Proof:
The alleged proof of something that is already proven false is of no
interest except as an example of flawed proofs.
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