:PROPERTIES: :ID: 99e654a7-b030-4e21-840a-be56ba8dc86f :mtime: 20230919170359 20230919151015 :ctime: 20230919151003 :END: #+title: injective function #+filetags: :public:math:project: * Definition An injective function maps distinct inputs to distinct outputs. * Alternation defintion A function $f$ is injective iff $f(x) = f(x) \implies x = y$ * Categorical Defintion A function is injective iff is is a monomorphism.