An example for a seminorm on $\mathbb{R}^n$ Can any one come up with an example of a seminorm that is not a norm on $\mathbb{R}^n$ ?
A seminorm on a real vector space $V$ is a function $N:V\rightarrow \mathbb{R}$
that satisfies that
1) $N(x)\geq 0$, $x\in V$
2) $N(\alpha x)=|\alpha|N(x)$, $x\in V$, $\alpha\in \mathbb{R}$
3) $N(x+y)\leq N(x)+N(y)$, $x,y\in V$
So a seminorm generalizes a norm as it does not require the condition 
$$N(x)=0\Longrightarrow x=0$$.

Take $N(x,y) = |x|$ on $\mathbb{R}^2$.
