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d_b
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For a sirjective 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.
d_b said:For a sirjective 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 mathematical function where every element in the range of the function is mapped to by at least one element in the domain. In other words, every element in the codomain has at least one pre-image in the domain.
The main difference between a surjective function and an injective function is that a surjective function may have multiple elements in the domain that map to the same element in the codomain, while an injective function ensures that each element in the domain maps to a unique element in the codomain.
In order to prove that a function is surjective, you must show that for every element in the codomain, there exists at least one element in the domain that maps to it. This can be done by either using the definition of a surjective function or by using a proof by contradiction.
Yes, a function can be both surjective and injective. This type of function is called a bijective function and it means that every element in the domain has a unique pre-image in the codomain and every element in the codomain has at least one pre-image in the domain.
A surjective function can be represented graphically by a line or curve that passes through every point in the codomain, indicating that each element in the codomain has at least one pre-image in the domain. This type of function is also known as a "one-to-one onto" function.