Definition:Pointwise Difference of Real-Valued Functions

Definition

Let $S$ be a non-empty set.

Let $f, g: S \to \R$ be real-valued functions.

Then the pointwise difference of $f$ and $g$ is defined as:

$f - g: S \to \R:$

$\forall s \in S: \map {\paren {f - g} } s := \map f s - \map g s$

where the $-$ on the right hand side is real-number subtraction.

Thus pointwise difference is seen to be an instance of a pointwise operation on real-valued functions.

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