1. a function from one set to another where every element in the target set is mapped to by at least one element in the domain
Usage: mathematics

Examples

• The function f(x) = x² is not a surjection from real numbers to real numbers because negative numbers have no preimage.
• To prove that a function is a surjection, you must show that every element in the codomain has at least one preimage.
• The mapping from students to grades is a surjection if every possible grade is assigned to at least one student.
• In linear algebra, we studied whether the transformation was a surjection onto the vector space.
• The professor explained that surjections are also called onto functions in some textbooks.
• A bijection is both an injection and a surjection.