Virgil
Posts:
3,521
Registered:
12/6/04
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Re: Grrrr! (was): infinite dimensional vector space
Posted:
Jun 29, 2003 3:40 PM
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In article <VLGLa.52470$XG4.77426@rwcrnsc53>,
Martin Cohen <mjcohen@acm.org> wrote:
> Virgil wrote:
> > In article
> > <8irKa.11$612.581@dfw-service2.ext.raytheon.com>,
> > Martin Cohen <martin_j_cohen@west.raytheon.com> wrote:
> >
> > would be much less confusion about Cantor's nonsense.
> >
> >>How do you know that you can't select alternately 4 and 5
> >>as the digit that does not match the n-th digit of the
> >>n-th number. If you can do this, you get
> >>.4545454545.... which is rational (45/99 = 5/11).
> >>
> >>Martin Cohen
> >>
> >
> >
> > As long as 45/99 = 5/11 is not listed in the range of the
> > function you could, but not if 5/11 is already in that range.
>
> Just replace the digit you get at 5/11 with anything.
> The rest of the generated number will be alternately
> 4 and 5 and thus rational.
>
The point is that, whatever listing of the reals (mapping from the
naturals to the reals) you make, there are reals missing from that
list.
In fact "more" reals will be missing than present.
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