Talk:Ultrametric space

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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.

[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.

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