Talk:Characterisation of Non-Archimedean Division Ring Norms

In the proof of the sufficient condition, the computation introduces the term:
 * $\size{B \paren{n + 1}}$

but this term is, in part, a summation over the real numbers and so the premise:
 * $\forall n \in \N_{>1}: \left\vert{n \cdot 1_k}\right\vert \le 1$

does not hold and can't be used in the next line, and so you are left with the $\paren{n + 1}$ term. You have to take the nth-root of the terms and then let $n \to \infty$ to get the desired result.

Also the bound $B$ is a bound in the real numbers, but not in the field $k$ --Leigh.Samphier (talk) 16:40, 26 January 2019 (EST)


 * Can it be put right? This dates back to work done by User:Linus44 (sadly no longer active) and went a bit over my head, so unfortunately I can't help. --prime mover (talk) 16:59, 26 January 2019 (EST)
 * I shouldn't have mentioned it. I was only trying to add weight to the proposal to delete the page since wants to replace Absolute Values on Fields with Norms on Division Rings. I have introduced a replacement page Characterisation of Non-Archimedean Division Ring Norms and have now redirected Characterisation of Non-Archimedean Absolute Values to Characterisation of Non-Archimedean Division Ring Norms. The replacement page has the issues above addressed. --Leigh.Samphier (talk) 21:24, 26 January 2019 (EST)


 * Good job. Incidentally, it's always a good idea when renaming pages to move the talk page along with it (that is, this one) so that when we delete the original page, we don't leave the talk page orphaned. If the material on the page becomes irrelevant, we can clean that up at a later stage, which is better than having talk pages scattered in limbo. --prime mover (talk) 05:22, 27 January 2019 (EST)
 * I'll take that on board. --Leigh.Samphier (talk) 06:45, 27 January 2019 (EST)