On 8/2/2014 4:19 PM, firstname.lastname@example.org wrote: > 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.
This is ambiguous. Do you mean "Every finite initial segment is a proper subset of N.", or "There is something in N that isn't in at least one initial segment."?
In either case, your argument doesn't show that there are no bijections between N and Q+.
>> 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?
Nothing else is in N. But you were the one who labeled thinking that N isn't a finite initial segment of N as unmathematical. I just want to know what you think is unmathematical about it.
>>> 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.
I notice that your attempt to prove it is an ad hominem.
>>> 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.
Whatever your opinion is, it's still proven.
> A proof is a convincing argument. Your argument will not convince anybody without matheological indoctrination when being contrasted with mine.
So you don't know what a proof (in mathematics) is. That explains a lot.