# Definition:Space of Almost-Zero Sequences

## 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:

$c_c$.