# Injective function

> Let $f$ be a function whose domain is a set $X$. The function $f$ is said to be **injective** provided that for all $a$ and $b$ in $X$, if $f(a) = f(b)$, then $a = b$; that is $f(a) = f(b)$ implies $a = b$.

Let $f$ be a function whose domain is a set $X$. The function $f$ is said to be **injective** provided that for all $a$ and $b$ in $X$, if $f(a) = f(b)$, then $a = b$; that is $f(a) = f(b)$ implies $a = b$.

Symbolically, $\forall a, b \in X, f(a) = f(b) \implies a = b$.