# Definition:Unbounded Divergent Sequence/Complex Sequence

## Definition

Let $\sequence {z_n}$ be a sequence in $\C$.

Then $\sequence {z_n}$ tends to $\infty$ or diverges to $\infty$ if and only if:

$\forall H > 0: \exists N: \forall n > N: \cmod {z_n} > H$

where $\cmod {z_n}$ denotes the modulus of $z_n$.

We write:

$x_n \to \infty$ as $n \to \infty$.