📂Functions

Including Functions

Definition

Let’s denote $X \subset Y$. A function that satisfies the following is called an inclusion function.

$$i : X \to Y, \quad \text{and} \quad i(x) = x,\quad \forall x\in X$$

Explanation

Simply put, it’s an identity function whose codomain could be larger than its domain.

$i : X \hookrightarrow Y$¹ or $i : X \subset Y$² notation is also used.