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

 Messages: [ Previous | Next ]
 Martin Cohen Posts: 128 Registered: 12/7/04
Re: Grrrr! (was): infinite dimensional vector space
Posted: Jun 25, 2003 8:40 PM

David Petry wrote:
> David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<68bjfv0qpm20kt7fgnup431sch6ii38hus@4ax.com>...
>
>

>>(Or maybe I'm wrong - how _does_ one give a proof that there
>>exist irrational numbers by "diagonalization"?

>
>
> Start with a list of rational numbers between 0 and 1, and
> diagonalize over the decimal expansions of those numbers. It
> works just fine. The technical detail of what to do with
> numbers that end in either all 9's or all 0's is easily
> handled, and in the end you get an honest-to-god irrational
> number.
>
> Comment: if the above proof were more widely known, there
> 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

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