Would someone please help me with construction of a proof that every invertible function is injection.
Thank you.
If $\displaystyle f:A\to B$ is invertible, there exists $\displaystyle g:B\to A$ such that $\displaystyle g\circ f =I_A$ . Now,
$\displaystyle f(x_1)=f(x_2)\Rightarrow g[f(x_1)]=g[f(x_2)]\Rightarrow $
$\displaystyle (g\circ f)(x_1)=(g\circ f)(x_2)\Rightarrow I_A(x_1)=I_A(x_2)\Rightarrow x_1=x_2$