Definition:Limit of Sequence/Rational Numbers

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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 $x_n$.