Category:Definitions/Convergent Complex Sequences

This category contains definitions related to Convergent Complex Sequences.
Related results can be found in Category:Convergent Complex Sequences.

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

$\sequence {z_k}$ converges to the limit $c \in \C$ if and only if:

$\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \cmod {z_n - c} < \epsilon$

where $\cmod z$ denotes the modulus of $z$.