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Topic: ? 533 Proof
Replies: 46   Last Post: Aug 4, 2014 8:39 PM

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Posts: 437
Registered: 12/4/04
Re: ? 533 Proof
Posted: Aug 3, 2014 12:22 AM
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In article <lrk472$ahe$>,
Martin Shobe <> wrote:

> On 8/2/2014 4:19 PM, 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.
> Martin Shobe

I note that the frequently posted proof that Q is well-orderable and
that such a well-ordering of Q does precisely what WM claims is
impossible, is something to which WM is careful not to reply to.

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