Injective Function

A function is injective (“one-to-one”) if

$x \neq x^{\prime} \Longrightarrow f(x) \neq f(x^{\prime})$

i.e. Given a set $X$ and a set $Y$, no two elements (say, $x$ and $x^{\prime}$) from $X$ map to the same element in $Y$.

(Note: a function can be both injective and surjective, this image is injective only)