Notes by Lex Toumbourou

A function $f(x)$ is said to be injective or one-to-one, if every element in the domain has a unique image.

In other words, every unique input to $f(x)$ must have a unique output.

Formally, we can say either:

• for all, $a, b \in A, \text{ if } a \ne b \text{ then } f(a) \ne f(b)$
• or, for all $a, b \in A, \text{ if } a = b \text{ then } f(a) = f(b)$