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For a surjective function from A--> B, I was just wondering if more than one elements in B can point to the same element in A if the function is surjective.
A surjective function, also known as an onto function, is a type of mapping between two sets, A and B, where every element in set B has at least one corresponding element in set A. In other words, the function covers or maps to the entire range of the codomain, B.
In order for a function to be surjective, every element in the codomain, B, must have at least one corresponding element in the domain, A. This means that for every y in B, there must exist an x in A such that f(x) = y. To determine if a function is surjective, you can check if every element in B is mapped to by at least one element in A.
A surjective function maps to the entire range of the codomain, B, while an injective function maps to unique elements in the codomain, B. In other words, a surjective function covers the entire range, while an injective function maps to distinct elements. A function can be both surjective and injective, in which case it is called a bijective function.
No, a function cannot be both surjective and not surjective at the same time. A function is either surjective or not surjective, depending on whether it maps to the entire range of the codomain, B. However, a function can be both surjective and injective at the same time, in which case it is called a bijective function.
Surjective functions are important in mathematics and science because they allow us to map elements from one set to another in a way that covers the entire range of the codomain. This is useful in many applications, such as data analysis, graph theory, and cryptography. Surjective functions also help us understand the relationship between different sets and their elements, and can be used to prove the existence of solutions in various mathematical problems.