Definition:Root of Mapping

This page is about root of mapping. For other uses, see root.

Definition

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

Let $x \in R$.

Then the values of $x$ for which $\map f x = 0_R$ 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.

• Results about roots of mappings can be found here.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.14$: Problem $7$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): zero: 3.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): root: 1. (of an equation)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): zero: 2. (of a function)
• 2008: David Joyner: Adventures in Group Theory (2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.1$: Functions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): root: 1. (of an equation)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): zero: 2. (of a function)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): zero (of a function)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): zero (of a function)