Definition:Unbounded Divergent Sequence/Complex Sequence
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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 $n \to \infty$.