Definition:Limit of Sequence (Number Field)
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Definition
Real Numbers
Let $\sequence {x_n}$ be a sequence in $\R$.
Let $\sequence {x_n}$ converge to a value $l \in \R$.
Then $l$ is a limit of $\sequence {x_n}$ as $n$ tends to infinity.
Rational Numbers
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.
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.