Math Help - Need a hint.

1. Need a hint.

So I am trying to prove that if we have a sequence an, and it has a subsequence that converges to p, then (e=epsilon), p-e<an<p+e happens frequently. How do you prove that something happens frequently, generaly speaking.

Thank you.

2. Re: Need a hint.

Maybe I can negate the expression, and try to prove that the expression that I got after negating happens almost always and find a contradiction??