Talk:Pólya-Vinogradov Inequality

This theorem claims that the mapping $\norm x$ defined as the difference between $x$ and the closest integer to $x$, i.e.:
 * $\displaystyle \norm x = \inf_{z \mathop \in \Z} \set {\size {x - z} }$

is a non-Archimedean norm (previously non-Archimedean absolute value) but this mapping fails to be Definition:Positive Definite (Ring) since for any integer $n: \norm n = 0$.

So at best it is a Definition:Seminorm. The proof doesn't seem to be reliant on either fact, only on the definition of $\norm x$ as the difference between $x$ and the closest integer to $x$, so it might be possible to just drop the comment that it is a non-Archimedean norm. --Leigh.Samphier (talk) 00:46, 28 January 2019 (EST)


 * If that's what needs to be done. I admit I posted it up without knowing too much about what I was doing, probably just wanted to make sure I had a "name" theorem for the guys in question. --prime mover (talk) 01:36, 28 January 2019 (EST)