Can you take the (Euclidean) norm of a scalar quantity (non-vector)?

Question

Context: This question

My question is whether or not you can take the (Euclidean) norm of a scalar non-vector quantity. My intuition is no, but I just wanted to confirm it.

I understand that a norm in essence gives you a 'length' or 'magnitude' which is a scalar quantity, so if you already had a scalar quantity $k$, does $\Vert k \Vert = k$ where $\Vert . \Vert$ is a norm?

Thanks.

Answer 1

Every norm $\|\cdot\|$ on $\Bbb R$ is related to the absolute value $|\cdot|$ via the silly computation $\|x\| = \|x1\| = |x|\|1\| = \|1\||x|$, since you can regard the "vector" $x$ as the number it actually is. Corollary: the only norm $\|\cdot\|$ in the vector space $\Bbb R$ with $\|1\| = 1$ is $\|\cdot\| = |\cdot|$.