Recent content by bxn4

Yes, it is the supremum. I am using the fact that E is compact to show that there is a subsequence that converges in E. Then I'd want to say that the limit of d(x_n_j, y_n_j) is \Delta but not sure how to show it. We have not talked about continuous functions. We have only studied sequences so...

I am struggling to prove the following: Let E be a compact nonempty subset of R^k and let delta = {d(x,y): x,y in E}. Show E contains points x_0,y_0 such that d(x_0,y_0)=delta.