The Free On-line Dictionary of Computing (30 December 2018):

complete metric space

    A metric space in which every sequence that
   converges in itself has a limit.  For example, the space of
   real numbers is complete by Dedekind's axiom, whereas the
   space of rational numbers is not - e.g. the sequence a[0]=1;
   a[n_+1]:=a[n]/2+1/a[n].

   (1998-07-05)