On Saturday, 2 August 2014 22:54:24 UTC+2, Martin Shobe wrote:
> Less unambiguously, you can show that every finite initial segment of N > is not sufficient.
And *if there is more in |N* than every finite initial segment, then the limit shows that even this "more" is not sufficient. But who would confess his belief that |N contains more than every finite natural number (tantamount to every finite segment)? He would become ridiculous in mathematics because he cannot answer what this "more" should be. >
> Therefore you must believe in something unmathematical. > > What's unmathematical about thinking that N isn't a finite initial > segment of N.
You are trying to cheat again and again. |N is not a finite initial segments but all finite initials segments or numbers. What else? >
> > It follows from the proof that every natural numbers fails. Enough for a mathematician. >
> Go ahead and prove that "the rationals cannot be enumerated by the > naturals" follows from "The number of unit intervals, each one > containing infinitely many rationals without index =< n, increases > infinitely".
No problem. The fact already that you are trying to cheat would make every objective reader suspicious. > > > > For that "proof" you have to assume that every is tantamount with all. This, however, is a very naive way of thinking that infinite sets can > be exhausted like finite sets.
> > It's still proven. > It is proven to be very naive.
A proof is a convincing argument. Your argument will not convince anybody without matheological indoctrination when being contrasted with mine.