Injectivity

Injectivity

A function $T:V\to W$ is called injective if $Tu=Tv$ implies $u=v$.

This could be rephrased to say that $T$ is injective if $u\ne v$ implies that $Tu\ne Tv$. Thus, $T$ is injective if and only if it maps distinctive inputs to distinctive outputs. We could also say that $T$ is one-to-one.