Re: Dedekind Cuts, Fundamental Sequences: why?

Dave Seaman wrote:

On Thu, 07 Jun 2007 07:54:50 -0400, Hatto von Aquitanien wrote:

I guess one could argue that even if we do have Cauchy sequences in which
some of the representations have irrational elements, they must all have
representations which are purely rational due to the fact that the real
numbers were completely defined by the latter. That is, of course,
assuming that such a construction actually took place.

Yes, a sequence of reals has a representation as a sequence of sequences
of rationals.

Is such a sequence of sequences of rational numbers a real number?

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