The “L⁰ norm” is not a norm

Counting the nonzero entries of a vector is a useful measure of size, and some authors call it the “L⁰ norm”. The book calls that incorrect terminology: it is not a norm, because scaling the vector by α does not change the count, while a norm must scale with |α|.

The L¹ norm is often used as a substitute for the number of nonzero entries.