Definition:Limit of Sequence/Rational Numbers
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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 $x_n$.