The diameter of a nonempty subset EEE of a metric space (X,ρ)(X,\rho)(X,ρ) is given by the supremum diam(E)=sup{ρ(x,y)∣x,y∈E}.\text{diam}(E) = \sup\{\rho(x,y)\mid x,y \in E\}.diam(E)=sup{ρ(x,y)∣x,y∈E}.