Question

Prove that in any metric space every finite set is closed

Answer 1

I have a metric space (X,d) and I am trying to prove that any finite subset F={x1,…,xn} of X is closed. What I have by now is a proof that a subset F of a metric space X is closed if and only if it contains all of its accumulation points. What I think is that if I prove that my set F contains all of it's accumulation points, then F would be closed, right? But I have problems in prooving that F contains all of its accumulation points.