Question

Prove that every finite subset of a metric space is closed

Answer 1

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