An injective function is a type of function in mathematics where each element in the domain maps to a unique element in the codomain. This means that no two different inputs produce the same output. For example, if you have a function that assigns students to their unique student IDs, each student ID corresponds to only one student. In formal terms, a function f: A \to B is injective if for every a_1, a_2 \in A , whenever f(a_1) = f(a_2) , it must be that a_1 = a_2 . This property ensures that the function maintains distinctness among its outputs, making injective functions important in various fields, including computer science and set theory.