Virgil
Posts:
7,005
Registered:
1/6/11


Re: Effect of gravitation in set theory
Posted:
Nov 23, 2011 2:20 AM


In article <2eb4c45fbf1c4d84855e3e9acbb1b568@g7g2000vbd.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.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. 

