Definition:Space of Almost-Zero Sequences

Definition

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

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

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:

$c_c$