Proof That a Subsequence of a Cauchy Sequence is Cauchy
Theorem
Letbe a Cauchy sequence in a metric spaceand letbe a subsequence.
Thenas
Proof
LetSinceis Cauchy, there existssuch that
Butand
Henceas
Theorem
Letbe a Cauchy sequence in a metric spaceand letbe a subsequence.
Thenas
Proof
LetSinceis Cauchy, there existssuch that
Butand
Henceas