Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Virgil Posts: 3,521 Registered: 12/6/04
Re: Grrrr! (was): infinite dimensional vector space
Posted: Jun 29, 2003 3:40 PM

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 Kent Paul Dolan
6/25/03 Julien Santini
6/25/03 David C. Ullrich
6/25/03 Lee Rudolph
6/25/03 James Dolan
6/25/03 David C. Ullrich
6/25/03 Virgil
6/25/03 David C. Ullrich
6/27/03 Michael Stemper
6/25/03 David Petry
6/25/03 Martin Cohen
6/25/03 Virgil
6/29/03 Martin Cohen
6/29/03 Virgil
6/25/03 Kent Paul Dolan
6/26/03 Michael Hochster
6/26/03 Virgil
6/26/03 Denis Feldmann
6/26/03 Denis Feldmann
6/26/03 Kent Paul Dolan
6/26/03 Denis Feldmann
6/26/03 David C. Ullrich
6/26/03 Kent Paul Dolan
6/26/03 David C. Ullrich
6/26/03 yee22uuyee
6/30/03 llaa1100