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On 06/08/2011 20.58, Roberto Ierusalimschy wrote:
Real numbers provide completeness (every Cauchy sequence has a limit)
just fine. You do not need Complex numbers for that.

Yes, that's why Gavin said complex numbers extend _integers_ in _two_ ways!

Integers are already complete. (Any Cauchy sequence within integers
must become constant after some index and therefore converge to that

I gave for understood Gavin was talking about sets that are also fields, i.e. C is a *field* that includes the *field* R and they are both *complete fields*.

IIRC (too many years since my exams of advanced calculus :-) completeness is non-trivial (i.e. interesting from a mathematical POV) only in the context of the theory of fields or normed spaces over a field (R or C, specifically), or am I mistaken?

> -- Roberto
-- Lorenzo