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Topic: Grrrr! (was): infinite dimensional vector space
Replies: 25   Last Post: Jun 30, 2003 11:02 AM

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Virgil

Posts: 3,521
Registered: 12/6/04
Re: Grrrr! (was): infinite dimensional vector space
Posted: Jun 29, 2003 3:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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.



Date Subject Author
6/24/03
Read Grrrr! (was): infinite dimensional vector space
Kent Paul Dolan
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Julien Santini
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
David C. Ullrich
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Lee Rudolph
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
James Dolan
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
David C. Ullrich
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Virgil
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
David C. Ullrich
6/27/03
Read Re: Grrrr! (was): infinite dimensional vector space
Michael Stemper
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
David Petry
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Martin Cohen
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Virgil
6/29/03
Read Re: Grrrr! (was): infinite dimensional vector space
Martin Cohen
6/29/03
Read Re: Grrrr! (was): infinite dimensional vector space
Virgil
6/25/03
Read Re: Grrrr! (was): infinite dimensional vector space
Kent Paul Dolan
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Michael Hochster
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Virgil
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Denis Feldmann
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Denis Feldmann
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Kent Paul Dolan
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Denis Feldmann
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
David C. Ullrich
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
Kent Paul Dolan
6/26/03
Read Re: Grrrr! (was): infinite dimensional vector space
David C. Ullrich
6/26/03
Read al owens
yee22uuyee
6/30/03
Read Re: al owens
llaa1100

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