Re: Lua evolution and C99

[Lorenzo Donati <lorenzodonatibz@...>]

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 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
>
>
>
Cheers.
-- Lorenzo