Let (X,D)be a metric space and let A and B be subset of X.Define D(A,B)=in f{D(a,b):aA,bB} Prove that if some sequence of points in A converges to a...

 Let (X,D)be a metric space and let A and B be subset of X.Define D(A,B)=in f⁡{D(a,b):a∈A,b∈B}

Prove that if some sequence of points in A converges to a point in B,then D(A,B)=0.that if some sequence of points in A converges to a point in B,then D(A,B)=0.

Hint: Proof by contradiction