Talk:Ultrametric space
From Wikipedia, the free encyclopedia
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 (talk • contribs) 15:58, 1 November 2006
- These are two different things - look at ball (mathematics). — MFH:Talk 19:13, 10 April 2008 (UTC)
[edit] 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
