## 1.2. Relations and Functions

### Definition 1.2.6: One-one, Onto, Bijection

A function

*f*from**A**to**B**is called**one to one**(or one-one) if whenever*f(a) = f(b)*then*a = b*. Such functions are also called**injections**.
A function *f* from **A** to **B** is called **onto** if for
all *b* in **B** there is an *a* in **A** such that
*f(a) = b*. Such functions are also called **surjections**.

A function *f* from **A** to **B** is called a **bijection**
if it is one to one and onto, i.e. bijections are functions that are
injective and surjective.