# Category:Definitions/Limits of Sequences

This category contains definitions related to Limits of Sequences.

Related results can be found in Category:Limits of Sequences.

### 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 $\left \langle {x_n} \right \rangle$ 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**.

## Pages in category "Definitions/Limits of Sequences"

The following 12 pages are in this category, out of 12 total.

### L

- Definition:Limit of Complex Sequence
- Definition:Limit of Rational Sequence
- Definition:Limit of Real Sequence
- Definition:Limit of Sequence
- Definition:Limit of Sequence in Normed Vector Space
- Definition:Limit of Sequence/Complex Numbers
- Definition:Limit of Sequence/Metric Space
- Definition:Limit of Sequence/Rational Numbers
- Definition:Limit of Sequence/Real Numbers
- Definition:Limit Point/Normed Vector Space/Sequence
- Definition:Limit Point/Topology/Sequence