Definiteness of a norm
= Definiteness of a norm
{title2=$\|v\|=0\iff v=0$}
Definiteness says that a <norm> vanishes only at the zero <vector>. The <box norm> on a nonempty finite <Cartesian product> is definite because its defining sum of squares includes equal-column terms, each of which is the square of an average of squares. Omitting repeated coordinates would destroy this proof and can produce a different quantity.