Re: Dedekind Cuts, Fundamental Sequences: why?

On Fri, 08 Jun 2007 21:58:04 -0400, Hatto von Aquitanien wrote:
Hatto von Aquitanien wrote:

Dave Seaman wrote:

I do not agree. One can talk about convergence to a rational limit.
It is possible to use the above quoted definitions of convergence in
conjunction with a test for abs(a_n-L)->0.

I specified that L is not rational in the paragraph above.

But that is not required in order to talk about limits and convergence.

I didn't say it was required. Here is my original statement, which you
snipped:


Actually, what you said is this:

"The number L that appears in the definition is called the limit of the
sequence.  I have been assuming that you were familiar with the
definitions, since you claimed to have taken a senior-level real analysis
course.  (Senior level in what, I might ask.  High School?)"

That's what immediately preceded the paragraph that I then quoted. I
actually said both those things.

But the paragraph you quoted here supports my claim that a Cauchy
sequence of rationals does not necessarily converge, because in some
cases there is no rational L that fits the definition.


--
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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