Theorem
Let
be a Cauchy sequence in a metric space
and let
be a subsequence.
Then
as
Proof
Let
Sinceis Cauchy, there exists
such that
But
and
Henceas
Call Us 07766496223
Theorem
Letbe a Cauchy sequence in a metric spaceand letbe a subsequence.
Thenas
Proof
LetSinceis Cauchy, there existssuch that
Butand
Henceas