Real Convergent Sequence is Cauchy Sequence/Proof 2

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 in Metric Space is Cauchy Sequence.

$\blacksquare$