Converge

In mathematics, a sequence $a_{n}$ is generally said to converge to $x$ if roughly speaking as $n$ goes to infinity $a_{n}$ gets closer and closer to $x$ and stays there. Rigorously, $a_{n}$ is said to converge to $x$ if for all $\epsilon >0$ there exists N such that for all n > N we have $|a_{n}-x|<\epsilon$.

Similar definitions can be made for convergence of functions.