I am having a bit of trouble with what should be a simple proof:

Let (an) be a convergent sequence of real numers, an >= 0 for all n in the natural number set. If the limit of an is a (an->a) show that a >= 0.

I understand that I need to use an epsilon neighbourhood to show a contradiction when a is < 0 but am having a hard time finding an epislon that produces a contradiction.

Thanks for the help