Injective function

Definition · applies to functions · also called injection, one-to-one

High school

A function $f$ is injective if every two different inputs $x$ and $y$ give different outputs: $f(x) \neq f(y)$.

Undergraduate

Consider a function $f : X \to Y$. The function $f$ is injective if, for all $x_1, x_2 \in X$,

\[f(x_1) = f(x_2) \implies x_1 = x_2.\]

Notes

“One-to-one” (injective) is easily confused with “one-to-one correspondence” (bijective).

All definitions · All distinctions · All examples