Injection is a property of function mapping relationship. A function is said to be injective if different input elements map to different output elements. In other words, for every output element in the function, there is a unique corresponding input element. It can also be said that each output value of the function is unique.
#In mathematics, injective is a property of function mapping relationship. A function is said to be injective if different input elements (elements in the domain) map to different output elements (elements in the range). In other words, for every output element in the function, there is a unique corresponding input element. It can also be said that each output value of the function is unique.
Specifically, for function f: A → B, where A and B represent the domain and value range of the function respectively, if for any a1, a2 ∈ A, when a1 ≠ a2, there is f (a1) ≠ f(a2), then the function f is an injection.
Intuitively understood, injection can be regarded as a "non-repeating" mapping relationship, and each output value corresponds to a unique input value. In images, an injection can be understood as a mapping in which no two arrows point to the same point.
The property of injectivity has important applications in mathematics and computer science. For example, in scenarios such as encryption algorithms in cryptography and unique indexes in databases, it is necessary to ensure the property of injectivity.
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