Re: Dedekind Cuts, Fundamental Sequences: why?

On Wed, 06 Jun 2007 15:30:43 -0400, Hatto von Aquitanien wrote:
David C. Ullrich wrote:

The rationals are not complete -

By what criteria of completeness? I have presented two possible ways of
viewing the rational numbers as being incomplete, and hinted at a third.

Completeness of the reals means that the least upper bound axiom is specified.
Equivalently, that every Cauchy sequence converges.

we want to extend them to a complete ordered field, so that we can prove
the basic theorems of analysis.

That statement merely begs the question. Quite honestly, my senior level
real analysis course bored the piss out of me because most of it was
blatantly obvious.

Then you must find the study of incomplete ordered fields (such as the
rationals) to be even more obvious. So all your objections apply to that
case in spades.


--
Dave Seaman
Oral Arguments in Mumia Abu-Jamal Case heard May 17
U.S. Court of Appeals, Third Circuit
<http://www.abu-jamal-news.com/>
.

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