Sequence Limit

The Epsilon-N Definition of a Limit

The limit of a sequence $\{a_n\}$ as $n$ approaches infinity is a number $L$, written as $\lim_{n \to \infty} a_n = L$, if for every number $\epsilon > 0$, there exists a natural number $N$ such that for all $n > N$, we have $|a_n - L| < \epsilon$.