# Definition:Limit of Sequence/Rational Numbers

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## Definition

Let $\left \langle {x_n} \right \rangle$ be a sequence in $\Q$.

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

Then $l$ is a **limit of $\left \langle {x_n} \right \rangle$ as $n$ tends to infinity**.

This is usually written:

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

## Also see

## Also known as

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