## Seminorm

### Set

 context $F$ … subfield of $\mathbb{C}$ context $V$ … $F$-vector space definiendum $p\in \mathrm{SemiNorm}(V)$ postulate $p:V\to \mathbb R$ $v,w\in V$ postulate $p(v+w) \le p(v)+p(w)$ $\lambda\in F$ postulate $p(\lambda\cdot v) = |\lambda|\cdot p(v)$

#### Discussion

A Norm is a seminorm with the adition axiom

$p(v)=0 \implies v=0$

(which I also write as $p(!0)=0$.)

Wikipedia: Norm