Cauchy complete

A metric space $(M,d)$ is called complete, a Cauchy space or Cauchy complete space if every Cauchy sequence of points of $M$ has a limit in $M$.

A Cauchy sequence is a sequence $\{x_i\}\subset M$ such that for every $ϵ>0$ there is a index $N$ such that for $n,m\ge N$ we have