1. The problem statement, all variables and given/known data Let [a,b] be an interval and let A be a subset of [a,b]. and Suppose that A is an infinite set. Let z be the unique point that belongs to all of the intervals [an, bn]. Show that if I is any interval that contains z, then A intersect I is infinite. 2. Relevant equations I don't know where to start this problem but I think I can use the fact that a set that contains an infinite subset is infinite. Any help would be appreciate. 3. The attempt at a solution I know I is an infinite interval, I think. I also know the set of intervals [an, bn] intersect A is infinite. I believe I can say that [an, bb] is a subset of [a,b] and that [a,b] is infinite.