# Definition:Space of Convergent Sequences

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## 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:

- $c_\infty$

## Also see

- Definition:Convergent Sequence
- Definition:Space of Zero-Limit Sequences
- Definition:Space of Almost-Zero Sequences

## Sources

- 2017: Amol Sasane:
*A Friendly Approach to Functional Analysis*... (previous) ... (next): Chapter $1.1$: Normed and Banach spaces. Vector Spaces