1. The problem statement, all variables and given/known data The Wikipedia part of question 5 here: http://www.dpmms.cam.ac.uk/site2002/Teaching/IB/MetricTopologicalSpaces/2007-2008/Examples1.pdf [Broken] 2. Relevant equations All relevant information is given in the question above. 3. The attempt at a solution I'm trying to simplify the problem by considering only 2-dimensional vectors rather than n-dimensional ones. But I've considered dozens of combinations of vectors, norms and metrics, none of which are working. I think that what Wikipedia says is correct in that d-tilde(x, y) = 0 <=> x = y, and d-tilde(x, y) = d-tilde(y, x), so the problem lies in the triangle inequality being violated I presume. But after two days of trying so many things out (and killing lots of trees for paper :P ) I still haven't come up with a single counter-example. Can someone please tell me which vector/norm/metric combination I should be considering? Thanks a lot!