# Definition:Limit of Sequence/Rational Numbers

< Definition:Limit of Sequence(Redirected from Definition:Limit of Rational Sequence)

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## 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 see

## 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 $x_n$**.