hey all,

I read the following definition of a limit in some lectures notes:

"Suppose that A⊆X (in a metric space). The point $\displaystyle x_0 \in X$ is a limit point of A if for every neighborhood $\displaystyle U(x_0, \epsilon) $, of xo, the set $\displaystyle U(x_0, \epsilon) $ is an infinite set."

Well, the definition I know is: $\displaystyle x_0$ is a limit point of a set A if every deleted neighborhood of $\displaystyle x_0$ 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

thanx