Let M = R with d1(x, y) = x - y and d2(x,y) 1+1-y (You may assume without proof that these are valid metrics.) (a) Show that Vz, y eR, dz(x, y) _d1(x,y). (c) Show that a sequence an +x in (R, d.) if and only if it converges in (R, d). n->00 (d) Show that the set A = [0, 0) is closed and bounded in (R, d2). (e) Is A compact in (R, d2)? If yes, explain briefly. If no, find a sequence in A with no convergent subsequence