Definition:Support of Mapping to Algebraic Structure

General Algebraic Structure
Let $(A, *)$ be an algebraic structure with an identity element $e$.

Let $S$ be a set.

Let $f : S \to A$ be a mapping.

The support of $f$ is the set:
 * $\operatorname{supp}(f) = \{s \in S : f(s) \neq e\}$

Sequence
Note that by definition, a sequence is a mapping, so that the definition of support applies in particular to sequences.

Also see

 * Identity is Unique
 * Definition:Support of Continuous Mapping