4.1 Injection

A function is an injection iff $\forall (a, b), (c, d) \in L: (b = d) \Rightarrow (a = c)$ . Injection is also called ``one-to-one''.

In English this means that each value in the domain is mapped to a unique value in the range. In other words, no two values in the domain map to the same value in the range. If we consider the domain and range both as $\mathbb{R}$ (real numbers), and define $L = \{(x,y)\vert x,y \in \mathbb{R}, y = x + 1\}$ , then $L$ is an injection.

The function $L = \{(x,y)\vert x, y \in \mathbb{R}, y = x^2\}$ is not an injection because we can find the counter example of $(2,4), (-2,4) \in L$ .