# Definition:Identically Zero

## Theorem

Let $f$ be a mapping whose codomain is a subset of one of the standard number systems $\N$, $\Z$, $\Q$, $\R$ or $\C$.

Let $f$ be such that:

$\forall x \in \Dom f: \map f x = 0$

That is, $f$ is the constant mapping $f_0$.

Then $f$ is described as being identically zero on its domain.