# Convergent Real Sequence has Unique Limit/Proof 2

## Theorem

Let $\sequence {s_n}$ be a real sequence.

Then $\sequence {s_n}$ can have at most one limit.

## Proof

We have that the real number line is a metric space

The result then follows from Convergent Sequence in Metric Space has Unique Limit‎.

$\blacksquare$