# Sequence is Cauchy iff Convergent

## Theorem

### Real Case

Let $\sequence {a_n}$ be a sequence in $\R$.

Then $\sequence {a_n}$ is a Cauchy sequence if and only if it is convergent.

### Complex Case

Let $\sequence {z_n}$ be a complex sequence.

Then $\sequence {z_n}$ is a Cauchy sequence if and only if it is convergent.