Definition:Space of Almost-Zero Sequences

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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


can be seen written as:


Also see