What is Divergence to infinity?

The sequence $(u_n)$ tends to $+\infty$ if for every $A \in \R$, there exists $N \in \N$ such that $u_n \geq A$ for all $n \geq N$. We write $\lim\limits_{n\to+\infty} u_n = +\infty$; the definition of $\lim u_n = -\infty$ is analogous. A sequence that does not converge is said to diverge.