Let $p$ be a real number $\ge 1$. Let $x=(x_1,x_2,\ldots x_n)$ be a vector of a vector space \(V\) over the field of real numbers \(\mathbb R\) or the field of complex numbers \(\mathbb C\).
The maximum norm.
$||x||_\infty:=\max(|x_1|,|x_2|,\ldots,|x_n|)$
is the limit of a p-norm for $p\to\infty,$ formally
$$||x||_\infty=\lim_{p\to\infty}||x||_p.$$
Proofs: 1
Definitions: 1
