Surjective Function: A to B Mapping

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Discussion Overview

The discussion revolves around the concept of surjective functions, specifically the mapping from set A to set B. Participants explore the implications of surjectivity on the relationships between elements in these sets.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions whether multiple elements in set B can map to the same element in set A in a surjective function.
  • Another participant asserts that if multiple elements in B pointed to the same element in A, it would not qualify as a function.
  • A third participant agrees with the previous point, emphasizing that a function cannot have two images for a single point in A.
  • A later reply clarifies the notation used in the discussion, stating that the arrow from A to B indicates that the domain is A and the range is a subset of B, correcting the spelling of "surjective." It also notes that elements in B do not point to elements in A.

Areas of Agreement / Disagreement

Participants generally agree that a surjective function cannot have multiple elements in B mapping to the same element in A, but there is some confusion regarding the terminology and notation used in the discussion.

Contextual Notes

There are limitations in the discussion regarding the definitions of functions and surjectivity, as well as potential misunderstandings about the directionality of mapping between sets.

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.
 
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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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