#### Introduction

- Functions can be classified by how they map elements between the domain and codomain.
- Three types of mappings are:
- Injective
- Surjective
- Bijective

#### Injective Mapping

- An injective mapping is when each element in the codomain is mapped to by at most one element from the domain.
- Another way of saying this is that no two elements in the domain map to the same element in the codomain.
- Example of an injective mapping:
- This type of mapping is also called 'one-to-one'.

#### Surjective Mapping

- A surjective mapping is when each element in the codomain is mapped to by at least one element from the domain.
- Another way of saying this is that the codomain and image (range) of the function are the same.
- Example of a surjective mapping:
- This type of mapping is also called 'onto'.

#### Bijective Mapping

- A bijective mapping is when the mapping is both injective and surjective.
- Another way of saying this is that each element in the codomain is mapped to by exactly one element in the domain.
- Example of a bijective mapping:
- This type of mapping is also called a 'one-to-one correspondence'.