Into Function

Into Function

## Definition / Concept

A function is into if at least one element of the codomain is not an image of any element of the domain.

## Formula

$$\text{Range}(f)\subsetneq\text{Codomain}(f)$$

## Conditions / Special Cases

An into function is not onto.

If:

$$n(A)<n(B)$$

then every function:

$$f:A\to B$$

is necessarily into.

## Usage

- Used when classifying functions according to their range and codomain.