Virgil
Posts:
8,833
Registered:
1/6/11


Re: Effect of gravitation in set theory
Posted:
Nov 23, 2011 2:25 AM


In article <9fb19006a6344a88b256d11560cae372@w7g2000yqc.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, 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. 

