Definition:Limit of Sequence (Number Field)

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Definition

Real Numbers

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

Let $\left \langle {x_n} \right \rangle$ converge to a value $l \in \R$.


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


Rational Numbers

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.


Complex Numbers

Let $\sequence {z_n}$ be a sequence in $\C$.

Let $\sequence {z_n}$ converge to a value $l \in \C$.


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