Injective and Surjective Functions

Injective functions

A function is injective if every element of the domain maps to a unique element of the codomain. This means that if a function is injective, no two elements from the domain can map to the same element in the codomain. For example, if we consider $f: A\to B$ to be an injective function, then by definition, for any two elements $a,b$ from $A$ such that $a\ne b$, we have $f(a) \ne f(b)$. An injective function is also called a one-to-one function. To define an injective function, the codomain must have at least as many elements as are there in the domain.

Examples

Take the following sets:

Using these sets, we can define the following injective function:

The function ...