# Definition:Root of Mapping

(Redirected from Definition:Zero of Function)

## Contents

## Definition

Let $f: R \to R$ be a mapping on a ring $R$.

Let $x \in R$.

Then the values of $x$ for which $f \left({x}\right) = 0_R$ are known as the **roots of the mapping $f$**.

## Also known as

The ring $R$ is often the field of real numbers $\R$ or field of complex numbers $\C$.

In this case, for a given function $f$, the **roots** are usually known as the **zeroes of the function $f$**.

## Also see

- Definition:Root of Polynomial, of which this definition is a generalization.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3.14$: Problem $7$ - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): $\S 2.1$: Functions