Cauchy Sequences of Complex Numbers

Recall from the Sequences of Complex Numbers page that a sequence of complex numbers $(z_n)_{n=1}^{\infty}$ is simply just an infinite order list of complex numbers.

We will now state an important type of sequence of complex numbers.

Definition: A sequence of complex numbers $(z_n)_{n=1}^{\infty}$ is a Cauchy Sequence of Complex Numbers if for all $\epsilon > 0$ there exists an $N \in \mathbb{N}$ such that if $m, n \geq N$ then $\mid z_m - z_n \mid < \epsilon$.