In article <email@example.com>, firstname.lastname@example.org wrote:
> On Thursday, 7 August 2014 17:40:44 UTC+2, Zeit Geist wrote: > > > > > I think the following: For all natural numbers I have shown that > > > uncounted rationals remain. > > > > All Natural Numbers are Finite, too. > > > > Is N Finite? > > If infinity can be finished, then N is ""all natural numbers. I have assumed > that and have shown that then rationals remain uncounted.
AS usual, WM's claimed proofs are not valid anywhere outside of WM's worthless world of WMytheology.
While proofs valid in all standard mathematics that the SET of ALL rationals can be well-ordered order-isomorphically to the SET of ALL naturals (neither of which can exist as sets in WM's worthless world of WMytheology) are valid everywhere outside of WM's worthless world of WMytheology.
> But since it is > impossible to identify remaining rationals
All of them are identifiable in standard mathematics, and none elude well-ordering by
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 them by increasing values of abs(m)+n, and within equal values of abs(m)+n by increasing values of m, if any. 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 well-ordering 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 well-ordering, everywhere outside of WM's worthless world of WMytheology.
> the original assumption has been > contradicted.
WM can contradict all he wants, but he alwasy fails yo prove his conradictions valid anywhere in the wide wide world of mathematics outside of WM's wee worthless world of WMytheology
> well established as reliable from hundreds of years of mathematics.) > Therefore finished infinity has been contradicted. "All natural numbers" is a > meaningless notion.
Not anywhere as meaningless as WM's wee worthless world of WMytheology,
> So we must say: N contains every natural number. Since > there is not a largest one, N is without end, we call it endless or infinite
> Correct, since there are not "all natural numbers".
Then WM must have been extraordinlarilyy careless with them the inside his WM's worthless world of WMytheology since outside that worthless world of WMytheology they are still all accounted for in N.
And until WM has produced and posted as complete and coherent a set of axioms for his idiot version of a set theory as ZF or ZFC are for standard set theories, he is in no positon to make claims about what must hold or not hold in any such theory.
Put up or shut up! -- Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)