# Definition:Zero Mapping

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## Definition

Let $\mathbb A$ be one of the standard number systems $\N,\Z,\Q,\R,\C$.

Let $S$ be a set.

Let $f_0: S \to \mathbb A$ denote the constant mapping:

$\forall x \in S: \map {f_0} x = 0$

Then $f_0$ is referred to as the zero mapping.

## Also known as

The zero mapping is often encountered in the context of real analysis, where $\mathbb A = \R$, in which case $f_0$ is referred to as the zero function.

It is often denoted $0: S \to R$:

$\forall x \in S: \map 0 s = 0$