Talk:Ultrametric space

Non-negative
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 &#9742; 03:05, July 15, 2005 (UTC)

Its the fist condition.

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

Sphere vs ball
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 (talk • contribs) 15:58, 1 November 2006
 * These are two different things - look at ball (mathematics). &mdash; 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.&mdash; 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)

“… do not make sense”
The illustration present in the article for ten years is suddenly removed by a user without a single contribution to this (and related) article. Is this problem really about the image? May it be located on the opposite side of monitors and keyboards? Incnis Mrsi (talk) 13:35, 23 February 2018 (UTC)
 * One of my initial objections was that the triangle on the right was nearly equilateral, so the figure was not very clear. Meanwhile I also realized that a graphic representation of distance is more confusing than clarifying with this kind of metric: here distance is not an arc length of a line or curve between the two points. - Patrick (talk) 21:02, 23 February 2018 (UTC)
 * Restored with different caption, the image itself is not confusing. Nicolas Perrault (talk) 17:52, 25 May 2018 (UTC)

I really struggled to get this
For a start, the points on the green triangle are unlabelled which threw me. I went to the  which said "At least two of d(x,y), d(y,z), and d(x,z) are the same".

OK, now that starts to make sense. Having that made explicit in this article would have been very helpful. I'm not a mathematician. Thanks 2.98.219.46 (talk) 15:19, 24 July 2018 (UTC)
 * It was there at the start of the "Properties" section already, but another editor broke that part last May by changing all the ors to ands. I have fixed it, I hope. Note however that this is not a defining property of an ultrametric space: the three points of an obtuse isosceles triangle in the Euclidean plane have distances obeying this property, but do not form a three-point ultrametric space. (Acute isosceles triangles are ultrametric, however.) —David Eppstein (talk) 19:40, 24 July 2018 (UTC)
 * Appreciated, thanks 92.0.17.233 (talk) 10:26, 6 August 2018 (UTC)

"Krull valuation" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Krull valuation and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 July 5 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 00:17, 5 July 2022 (UTC)