If infinitely many points then then contains at least one point.
What don't you understand?
I read the following definition of a limit in some lectures notes:
"Suppose that A⊆X (in a metric space). The point is a limit point of A if for every neighborhood , of xo, the set is an infinite set."
Well, the definition I know is: is a limit point of a set A if every deleted neighborhood of intersects A in at least one point.
Can someone explain to me the first definition? I can't make the link between the two definitions