I need a general proof involving limit points. Like To prove that a point x is a limit point of a set A, you have two main options:

I need a general proof involving limit points.  

Like 

To prove that a point x is a limit point of a set A, you have two main options:

1) Demonstrate that for any epsilon>0, B_epsilon(x) contains a point of A (other than possibly x itself).

2) Demonstrate that there is a sequence {a_n} of points in A satisfying lim a_n = x.

I know the limit point of 1/n is 0.  It is beginning the proof I don't understand