The Limit of a Convergent Complex Sequence

In the setting of Complex Analysis: Standing Notation, let $(z_{n})$ be a convergent sequence in $\mathbb{C}$.

(i) The limit. The limit of $(z_{n})$, written $\lim_{n\to\infty}z_{n}$, is the complex number to which $(z_{n})$ converges; it is unique by Limits of Complex Sequences: Uniqueness, Real and Imaginary Parts, Arithmetic, Real Sequences, Conjugates, Moduli, the Cauchy Criterion and the Modulus Metric (i).