# Real Convergent Sequence is Cauchy Sequence/Proof 2

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## 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.

$\blacksquare$