1. The problem statement, all variables and given/known data Show that d and p are equivalent metrics on X where p=d(x,y)/(1+d(x,y)) 2. Relevant equations ive proved already that p is indeed a metric too (if d is a metric). 3. The attempt at a solution I believe im supposed to use the Lipschitz condition where there exits constants A and B st for all x,y, Ap<=d<=Bp but i think i can actually prove that one of these two constants cannot exist... and i using the wrong definitions? Thanks!