Real Convergent Sequence is Cauchy Sequence/Proof 2

From ProofWiki
Jump to navigation Jump to search

Theorem

Every convergent real sequence in $\R$ is a Cauchy sequence.


Proof

From Real Number Line is Complete Metric Space, $\R$ under the usual metric is a metric space.

The result then follows as a special case of Convergent Sequence is Cauchy Sequence.

$\blacksquare$