\begin{definition}[Definition:P-Norm]
Let $p \ge 1$ be a real number.
Let $\ell^p$ denote the $p$-sequence space.
Let $\mathbf x = \sequence {x_n} \in \ell^p$.
Then the '''$p$-norm''' of $\mathbf x$ is defined as:
:$\ds \norm {\mathbf x}_p = \paren {\sum_{n \mathop = 0}^\infty \size {x_n}^p}^{1/p}$
\end{definition}