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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?

Yuxi L
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  • You know the notation ${\lVert x\rVert:x\in X}$ exists, right? Also use \| or friends instead of ||. – user10354138 Oct 15 '23 at 12:43
  • The norm notation is pretty standard. What you can do is change the vertical bar in the set builder notation to a colon, I.e. ${|x| : x \in X}$, which is also standard. – Sambo Oct 15 '23 at 12:50
  • Great idea, user10354138 and Sambo! – Yuxi L Oct 15 '23 at 13:13
  • I am also considering the double bar cardinality notation. i.e. $|X| = \overline{\overline{X}}$, from Wikipedia article on cardinality (link) – Yuxi L Oct 15 '23 at 13:34

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