# Definition:Limit of Sequence/Rational Numbers

## Definition

Let $\sequence {x_n}$ be a sequence in $\Q$.

Let $\sequence {x_n}$ converge to a value $l \in \R$, where $\R$ denotes the set of real numbers.

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

This is usually written:

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

## 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 $x_n$.