# Definition:Space of Convergent Sequences

## Definition

The space of convergent sequences, denoted $c$ is defined as:

$\displaystyle c := \set{\sequence{z_n}_{n \in \N} \in \C^\N : \exists L \in \C : \forall \epsilon \in \R_{>0} : \exists N \in \R: n > N \implies \cmod {z_n - L} < \epsilon}$

As such, $c$ is a subspace of $\C^\N$, the space of all complex sequences.

## Also denoted as

The space of convergent sequences

$c$

can be seen written as:

$c_\infty$