Definition:Sequence with Finite Support

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Definition

Let $\struct {A, *}$ be an algebraic structure with an identity element $e$.

Let $\sequence{a_n}_{n \in \N}$ be a sequence.


Then $\sequence{a_n}$ is said to have finite support if and only if:

$\set {n \in \N: a_n \ne e}$ is finite


That is, $\sequence{a_n}$ has finite support if and only if the support of $\sequence{a_n}$ as a mapping $\N \to A$ is finite.