Surjective Function: A to B Mapping

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In a surjective function from A to B, each element in B must be mapped from at least one element in A, ensuring that the function covers all elements in B. However, multiple elements in B can point to the same element in A, which is permissible in surjective functions. The definition of a function prohibits any element in A from having more than one image in B. The direction of the mapping indicates that A is the domain and B is the codomain. Therefore, the discussion clarifies that while elements in B can share images from A, the function must maintain its definition.
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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.
 
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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.

if I'm not wrong it can't follow because its not a function...I just want to make sure if I got it right
 
Right. By definition, it can't be a function. It would mean that point in A would have two images, which is forbidden.
 
Just a couple of points to clarify. If you write the arrow from A to B that means the domain of f is A and the range of f is a subset of B. Elements in B don't point to elements in A. And it's spelt surjective.
 

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