Is there a better notation for the norm of a vector? For example, if I have a set of vectors $X$, then the set of norms associated with it would be
$$ \{||x|| \mid x \in X\} $$
The vertical norm lines look identical to the set builder vertical line. The vertical lines only start to get more confusing from there. Say I want to get the number of vectors with their norm in a certain range $[r_1, r_2]$ (by set cardinality notation, which is also a vertical bar)
$$ |\{x \mid ||x|| \in [r_1, r_2]\}| $$
which seems very confusing. Any better notations?