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.:
 * $\displaystyle \norm{x} = \inf_{z \mathop \in \Z} \left\{ {\left|{x - z}\right|}\right\}$

is a non-Archimedean norm (previosuly non-Archimedean absolute value) but this mapping fails to be Definition:Positive Definite (Division 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)