Definition:Support of Mapping to Algebraic Structure

General Algebraic Structure
Let $\struct {A, *}$ 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:
 * $\map {\operatorname {supp} } f = \set {s \in S : \map f s \ne e}$

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