Uncountability of surjections onto a nontrivial finite set
= Uncountability of surjections onto a nontrivial finite set
If $B$ is a <countably infinite set> and $A$ is a <finite set> with at least two elements, the set of <surjective functions> $B\to A$ is uncountable. Fix finitely many values to cover $A$, then encode an arbitrary infinite <binary sequence> using two values of $A$ on the remaining inputs.