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The 4th way the article states the condition for equivalence of 2 metrics is:
* there exists a strictly increasing, continuous, and subadditive f:R_{+} \to R such that d_{2} = f \circ d_{1}.[2]
Surely this is not true? For instance on the real line if d_1(x,y)=|x-y| and d_2(x,y)=|x^3-y^3| then d_1 and d_2 are equivalent but there is no f such that d_2(x,y)=f(d_1(x,y)).Fathead99 (talk) 15:16, 25 May 2011 (UTC)