Injective functions

An injective function, also known as a one-to-one function, is a rule that assigns each input to a unique output — no two different inputs share the same output. In other words, if you have two distinct inputs, their images under the function will always be different. This property ensures that the function doesn’t "collapse" different inputs into the same result, preserving the distinctness of the original elements. Injective functions are important in mathematics because they guarantee that information about the inputs can be uniquely recovered from the outputs.