So, I trying to prove the following: "Show that a complex number sequence converges, iff, it is a Cauchy sequence".
Let $\{w_n\}$ be a complex number sequence. For every $\epsilon>0$,$\exists N=N(\epsilon)$, such that
$|w_n-w_m|\geq\epsilon,\forall n,m>N\Rightarrow \nexists w \in \mathscr{C}$/ $\lim_{n\to \infty}|w_n-w|=0 \therefore$ the sequence does not converge.
Is it correct? I'm not sure if the first statement implies the conclusion.