
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 constant).
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 nontrivial (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 > > > Cheers.  Lorenzo