## complete metric space

<*theory*> 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].

Last updated: 1998-07-05

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**Nearby terms:**

**complete metric space**» completeness » complete partial ordering » complete theory

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