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What is the difference between injective and surjective
- 小老鼠Original
- 2023-10-30 11:29:1017494browse
The difference between injective and surjective is: injective focuses on the one-to-one relationship between the input and output of the function, each output value uniquely corresponds to an input value; while surjective focuses on the function The output value can cover the entire value range, that is, each output value can be mapped to.
#In mathematics, injective and surjective properties are two properties that describe the mapping relationship of functions.
Injective: A function is called injective if different input elements (elements in the domain) map to different output elements (elements in the value domain) ). 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.
Surjective: A function is called surjective if for every element in the range, there is at least one input element corresponding to it. In other words, the value domain of the function corresponds to the domain of definition, and each output value of the function can be mapped to.
Simply put, injective focus is on the one-to-one relationship between the input and output of a function. Each output value uniquely corresponds to an input value; while surjective focus is The output value of the function can cover the entire value range, that is, each output value can be mapped to.
In addition, there is a related concept called bijection. A function is called a bijection. If it is both injective and surjective, that is, there is a one-to-one relationship between the input and output of the function. Corresponding relationship. Bijection ensures that each output value of the function has a unique corresponding input value, and the output value of the function can cover the entire value range.
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