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Topic: Foundations of real numbers
Replies: 26   Last Post: Oct 14, 2012 7:35 PM

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Robin Chapman

Posts: 282
Registered: 5/29/08
Re: Foundations of real numbers
Posted: Oct 11, 2012 3:58 AM
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On 10/10/2012 18:30, Paul wrote:
> It seems ridiculous to me to define the real numbers by using the
> least-upper-bound property as an axiom,


> So the Cauchy sequence definition is much better, and I like the
> Dedekind cuts definition too.


The first approach is a way to *characterize* R.

The other approaches are ways to *construct* R.

Here's a nice paper:
http://uk.arxiv.org/abs/1204.4483


Date Subject Author
10/10/12
Read Foundations of real numbers
Paul
10/10/12
Read Re: Foundations of real numbers
Ken.Pledger@vuw.ac.nz
10/13/12
Read Re: Foundations of real numbers
Graham Cooper
10/13/12
Read Re: Foundations of real numbers
Frederick Williams
10/13/12
Read Re: Foundations of real numbers
Graham Cooper
10/11/12
Read Re: Foundations of real numbers
Peter Webb
10/11/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/11/12
Read Re: Foundations of real numbers
Michael Stemper
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/12/12
Read Re: Foundations of real numbers
Virgil
10/12/12
Read Re: Foundations of real numbers
LudovicoVan
10/12/12
Read Re: Foundations of real numbers
Michael Stemper
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/12/12
Read Re: Foundations of real numbers
Shmuel (Seymour J.) Metz
10/12/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Peter Webb
10/13/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Robin Chapman
10/11/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Frederick Williams
10/11/12
Read Re: Foundations of real numbers
Herman Rubin
10/11/12
Read Re: Foundations of real numbers
Michael Stemper
10/11/12
Read Re: Foundations of real numbers
Brian Q. Hutchings
10/12/12
Read Re: Foundations of real numbers
G. A. Edgar
10/14/12
Read Re: Foundations of real numbers
gnasher729
10/14/12
Read Re: Foundations of real numbers
Graham Cooper

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