injection

An injective function (aka injection, or one-to-one function) is a function $f$ that maps distinct elements of its domain to distinct elements of its codomain.

For each element $y$ of the function's codomain, there exists at most one element $x$ in the function's domain such that $f(x)=y$.

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 $a=b$,
or equivalently,
if $a\ne b$, then $f(a)\ne f(b)$.
in the contrapositive.

Symbolically,

Which is logically equivalent to the contrapositive

Proving that a function is injective amounts to showing that whenever $f(b)=f(a)$ for some $a,b$ in the domain, that $a=b$ necessarily.

See also: surjection, bijection