# Definition:Space of Almost-Zero Sequences

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## Contents

## Definition

The **space of almost-zero sequences**, denoted $c_{00}$ is defined as:

- $\displaystyle c_{00} := \set{\sequence{z_n}_{n \in \N} \in \C^\N : \exists N \in \R_{> 0}: n > N \implies z_n =0}$

As such, $c_{00}$ is a subspace of $\C^\N$, the space of all complex sequences.

## Also denoted as

The **space of almost-zero sequences**

- $c_{00}$

can be seen written as:

- $c_c$.

## Also see

## Sources

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