What is an injective function for dummies?

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To elaborate, if we consider two distinct elements x1 and x2 in the domain of the function f, and if x1 is not equal to x2, then the function f maps these two distinct elements to two distinct outputs, such that f(x1) is not equal to f(x2).

Conversely, the converse of this property also holds true. If f(x1) equals f(x2), it implies that the original inputs x1 and x2 must be identical, ensuring the one-to-one nature of the function.

This property of injective functions is fundamental in understanding the relationship between the domain and range of a function. It provides a clear distinction between functions that preserve distinctiveness and those that may map multiple inputs to the same output.

Mathematics, a vast field of study, encompasses numerous intriguing concepts. One such concept is the injective function, also commonly referred to as an injection or a one-to-one function.