#injective $INJ @Injective

An injective function, also called a one-to-one function, is a mapping in which every element of the domain is sent to a unique element in the codomain. This means no two distinct inputs can share the same output. Injectivity is important because it preserves distinctness and allows functions to be reversed on their images. To prove a function is injective, one typically shows that if , then . Injective functions appear throughout algebra, calculus, and computer science, ensuring structure, preventing loss of information, and enabling well-defined inverses on their ranges.