Injective function

by Patrick Stevens Jun 14 2016 updated Jun 29 2016

A Function $~$f: X \to Y$~$ is injective if it has the property that whenever $~$f(x) = f(y)$~$, it is the case that $~$x=y$~$. Given an element in the image, it came from applying $~$f$~$ to exactly one element of the domain.

This concept is also commonly called being "one-to-one". That can be a little misleading to someone who does not already know the term, however, because many people's natural interpretation of "one-to-one" (without otherwise having learnt the term) is that every element of the domain is matched up in a one-to-one way with every element of the domain, rather than simply with some element of the domain. That is, a rather natural way of interpreting "one-to-one" is as "bijective" rather than "injective".



Joe Zeng

Why is it misleading to call injective "one-to-one"?