Definition:Unbounded Divergent Sequence/Real Sequence/Infinity

Definition
Let $\sequence {x_n}$ be a sequence in $\R$.

$\sequence {x_n}$ diverges to $\infty$ :
 * $\forall H > 0: \exists N: \forall n > N: \size {x_n} > H$

Also known as
The statement:
 * $\sequence {x_n}$ diverges to $\infty$

can also be stated:
 * $\sequence {x_n}$ tends to $\infty$
 * $\sequence {x_n}$ is unbounded.