Property of [[Real sequences]]. **Definition** We write $a_{n} \to \infty$ as $n \to \infty$ if for every $R \in \mathbb{R}$, exists $N$ such that $a_{n} > R$ for every $n \geq N$. See **Property** [[Reciprocal of Terms of Properly Divergent Real Sequence Tends to Zero]]. ### Examples - $n\to \infty$ as $n \to \infty$: Given $R \in \mathbb{R}$, take $N>R$ using [[Archimedean Property of Real Numbers]]. - $\sqrt{ n } \to \infty$ as $n \to \infty$: Given $R \in \mathbb{R}$ take $N>R^{2}$ then for all $n \geq N$ we have $\sqrt{ n } \geq \sqrt{ N } \geq R$. - [[Criterion for Convergence of Geometric Sequence]]. - [[Monotone Bounded Real Sequence is Convergent]].