Injection

Definition

A function $f:X \rightarrow Y$ is injective (also referred to as one-to-one) if $x_{1} \neq x_{2}$ in $X$ implies that $f\left. \left( x_{1} \right) \right. \neq f\left. \left( x_{2} \right) \right.$ in $Y$. Rather, $f\left. \left( x_{1} \right) \right. = f\left. \left( x_{2} \right) \right.$ implies that $x_{1} = x_{2}$.

In other words, the property of being injective means that no two elements of $X$ correspond to the same element of $Y$.