# Definition:Zero Mapping

Jump to navigation
Jump to search

## 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 $0: S \to R$:

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

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**zero function**