Hilbert Sequence Space is Metric Space/Proof 1

Theorem
Let $A$ be the set of all real sequences $\left\langle{x_i}\right\rangle$ such that the series $\displaystyle \sum_{i \mathop \ge 0} x_i^2$ is convergent.

Let $\ell^2$ be the Hilbert sequence space on $\R$.

Then $\ell^2$ is a metric space.

Proof
$\ell^2$ is a particular instance of the general $p$-sequence space $\ell^p$.

Hence $p$-Sequence Space of Real Sequences is Metric Space can be applied directly.