Onto

Types: Not Applicable
Examples: Not Applicable
Constructions: Not Applicable
Generalizations: Not Applicable

Properties: Not Applicable
Sufficiencies: Not Applicable
Equivalences: Not Applicable
Justifications: Not Applicable

Onto

A Function is onto (or surjective) if for every there exists such that .

Remark. is onto if there is a solution to the equation for every in the codomain. “Onto” is a way to talk about the existence of solutions.

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Remark. is onto if every element of the Codomain corresponds to at least one element of the Domain .

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Example: is not surjective because for , there is no real solution to the equation .