Virgil
Posts:
10,821
Registered:
6/8/11


Re: � 534 Finis
Posted:
Aug 9, 2014 8:11 AM


In article <1e0fd76d1bae4651b327ad9537494dc7@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Saturday, 9 August 2014 00:14:28 UTC+2, Zeit Geist wrote: > > On Friday, August 8, 2014 2:07:28 PM UTC7, muec...@rz.fhaugsburg.de > > wrote:
> > > I have a proof about all natural numbers.
It is only about EACH natural number, which WM acknowledges is quite different.
> > In that you Show something for Each Set of Cardinality n e N.
Not even thatn, only for FISONs! >
> > You show Nothing for the Set N. > > I show it for all natural numbers.
Only for each, not for all.
> > > It applies to all natural numbers.
Only for each, not for all.
> > P(x) is True For All x e N, does Not imply P(N) is Necessarily True. > > Nobody is interested in P(N).
Everyone other than WM is! > > > > For you, P(y) is a Set of Cardinality y can Not Exhaust The Set Q. > > > All natural numbers cannot exhaust all rational numbers.
N enueates W when Q has been wellordered SA dollows: Once again, since WM is having so much trouble understanding it:
Each member of Q has UNIQUE representation as m/n, with m being an integer, n being a positive integer, and with m and n having no common factor greater than 1.
Order Q by increasing values of abs(m)+n, and within equal values of abs(m)+n by increasing values of m.
Note that for positive m, m/1 has successor (m+1)/1. For any other form, m/n will have successor of form (m + k)/(n  k) for some natural k with 0 < k < n.
This is a wellordering of Q with a first rational, 0/1, and for each rational a uniquely defined successor rational, and with no rationals left out.
Thus each rational is now enumerated by the natural number marking its position in the above wellordering, everywhere outside of WM's worthless world of WMytheology.
> > > It shows that "all natural numbers" is a nonexisting notion in > > > mathematics. The SET of all natural numbers certainly is an existing notion everywhere outside of WM's worthless world of WMytheology.
> Most set theorists call it N. > > > > > > > > BTW, have you Figured out how to Wriggle Out of the Fact that your System > > shows that the Set N, which contains More Elements than Any Natural Number, > > is Finite? > > It is potentially infinite. That means it is not actually infinity.
Outside of WM's worthless world of WMytheology, N is actually infinite in the sense that one can inject N into a proper subset of N. E,g., f: N > N: n > 2*n is such a function.
> what I have proven (and known for a long time already) Is mostly false in proper mathematics. > > Regards, WM  Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)

