# Talk:Ultrametric space

I suppose that even for an ultrametric space you need that distances be non-negative. Is that right?

Yes I will fix definition. Paul August 03:05, July 15, 2005 (UTC)

Its the fist condition.

--Lzap 08:20, 19 May 2006 (UTC)

I think it's more common to use the word "sphere" for a set of points equidistant from a given point. "Ball" sounds bizarre.—Preceding unsigned comment added by Akiezun (talkcontribs) 15:58, 1 November 2006

These are two different things - look at ball (mathematics). — MFH:Talk 19:13, 10 April 2008 (UTC)

## Missing criterion

I think the formal definition lacks a condition. d(x,z) <= max{ d(x,y), d(y,z) } but also d(x,y) = d(y,z), or more succinctly, d(x,z) <= d(x,y) = d(y,z). Otherwise, it seems all we've asserted is that there exists an edge shorter or equal to the longest edge. This, at least to me, seems like a trivial assertion.—Preceding unsigned comment added by 71.204.144.5 (talk) 20:53, 15 March 2007

No: this asserts that *any* side of a triangle is not longer than the longer one of the two others, which is not the case in Euclidean space.— MFH:Talk 19:08, 10 April 2008 (UTC)

## Cleanup

I suggest putting all the equations in LaTeX format. Tony (talk) 16:22, 21 March 2011 (UTC)

I agree that more consistent formatting would be an improvement. But I prefer {{math}} over LaTeX formatting when possible, because LaTeX makes the math characters much bigger than the article text. —David Eppstein (talk) 21:06, 21 March 2011 (UTC)
So we wouldn't use HTML tricks, but yet another way of rendering? In other words, was the previous version written with that template? Tony (talk) 22:24, 21 March 2011 (UTC)
The previous version appears to be written using several different inconsistent rendering methods, probably not including that one. —David Eppstein (talk) 00:39, 22 March 2011 (UTC)
OK, I will try to take a look at it when I have time. Also, please double-check my entries, as you are more qualified than me. Tony (talk) 15:15, 22 March 2011 (UTC)

## Redirection from Krull valuation

There is a redirection from "Krull valuation" to "ultrametric space". This is rather confusing, since one point about Krull valuation is that the distances do not take values in ℝ but in some possibly bigger group. I think it would make more sense if "krull valuation" redirects to "valuation"; then one could add a section about Krull valuations to the valuation page.

128.176.181.38 (talk) 08:47, 2 September 2011 (UTC)