If you start with an infinite set, you can have a sequence of nested sets which converge to a single point. (ie Intersection of (-1/n, 1/n) as n->infinity))
However, at no time during the sequence is there a first element with only one point. In fact, for any finite (but unbounded) n, the number of points in the interval is uncountably large. So, how do you understand the idea that this infinite intersection contains just one point? How do you make sense of it?