Suppose and is an infinite set. Show that A is an accumulation point of .

Let and Q be a neighborhood of A. There is an such that .

Since A = sup and if c is an upper bound,

Let

Assume there are finitely many .

Now, let

Since x' is the max, x' is an upper bound of . Therefore, , but which is a contradiction. Thus, A is an accumulation point.

Correct?