**Lemma** $\lim_{ n \to \infty } \frac{1}{n} = 0$. Example of a [[Convergence]]. **Proof** Given $\epsilon>0$, by [[Archimedean Property of Real Numbers]] $\exists N \in \mathbb{N}$ such that $\frac{1}{N}<\epsilon$. So for all $n \geq N$, $|\frac{1}{n}| \leq |\frac{1}{N}| < \epsilon \; \square$.