## An Isometry to a Metric Space

Theorem

Suppose we have a metric spaceSupposeis a Cauchy sequence in

Defineas follows:where

Thenis isometric to

Proof

Suppose

Then

and

Henceis isometric to

Theorem

Suppose we have a metric spaceSupposeis a Cauchy sequence in

Defineas follows:where

Thenis isometric to

Proof

Suppose

Then

and

Henceis isometric to