Many-One Function

Many-One Function

## Definition / Concept

A function is many-one if at least two distinct elements of the domain have the same image.

## Formula

$$x_1\ne x_2\text{ and }f(x_1)=f(x_2)$$

for at least one pair $x_1,x_2\in A$.

## Conditions / Special Cases

A many-one function is not one-one.

## Usage

- Used when classifying functions according to their mapping behaviour.