# Definition:Limit of Sequence/Complex Numbers

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## Definition

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

Let $\sequence {z_n}$ converge to a value $l \in \C$.

Then $l$ is a **limit of $\sequence {z_n}$ as $n$ tends to infinity**.

This is usually written:

- $\displaystyle l = \lim_ {n \mathop \to \infty} x_n$

## Also known as

A **limit of $\sequence {x_n}$ as $n$ tends to infinity** can also be presented more tersely as a **limit of $\sequence {x_n}$** or even just **limit of $x_n$**.