Definition:Support of Mapping to Algebraic Structure/Real-Valued Function

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Definition

Let $S$ be a set.

Let $f: S \to \R$ be a real-valued function.


The support of $f$ is the set of elements $x$ of $S$ whose values under $f$ are non-zero.

That is:

$\map \supp f := \set {x \in S: \map f x \ne 0}$


That is, the support of a function whose codomain is the set of real numbers is generally defined to be the subset of its domain which maps to anywhere that is not $0$.