Definition:Sequence with Finite Support

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 :


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

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