One-To-One

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

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

One-To-One

A Function is one to one (or injective) if for every there is at most one such that .

Remark: “One to one” is a way to talk about the uniqueness of solutions.

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Example: is not injective. We can prove this by choosing any . Solving for will give us , where has more than one solution.

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Remark: The horizontal line test is a way to visually check if a function is one to one. If you can draw a horizontal line that intersects a function at multiple points, the function is not one to one.