Convergent Real Sequence has Unique Limit/Proof 2

Theorem
Let $\left \langle {s_n} \right \rangle$ be a real sequence.

Then $\left \langle {s_n} \right \rangle$ 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.