Definition

The 1-Norm, denoted as $\|\cdot\|$ is defined as follows for any arbitrary $v\in V$ where $v=(v_{1},\ldots,v_{n})$ $$\begin{align*} \mathbb{F}^{n}&: \ \|v\|=|v_{1}|+\cdots+|v_{n}|\\ \mathbb{F}^{\infty}&:\|(v_{i})_{i\in\mathbb{N}}\|=\sum\limits_{i=1}^{\infty}|v_{i}|\\ C^{0}([a,b];\mathbb{F})&:\|f\|=\int_{a}^{b}|f(x)|dx \end{align*}$$