injective function

We say that a function $f:A\to B$ is injective or one-to-one if $f(x)=f(y)$ implies $x=y$, or equivalently, whenever $x\ne y$, then $f(x)\ne f(y)$.

Properties

1. Suppose $A,B,C$ are sets and $f:A\to B$, $g:B\to C$are injective functions. Then the composition $g\circ f$ is an injection.

2. Suppose $f:A\to B$ is an injection, and $C\subseteq A$. Thenthe restriction ${f|}_C:C\to B$ is an injection.

For a list of other ofinjective functions, see [1].