Abstract. The metric (edge metric) dimension is the cardinality of the smallest ordered set of vertices that uniquely identifies every pair of distinct vertices (edges) by means of distance vectors to such a set. We show that for every r,t\ge 2, r\ne t, there is n_0 such that, for every n\ge n_0 there exists a graph of order n with metric dimension r and edge metric dimension t. We also show that it is not possible to bound edge metric dimension of a graph by some constant factor of its metric dimension.