Let f be a 1-1 function from A into B with B finite. Show that A is finite.

I was thinking along the lines of since $\displaystyle A \stackrel{1-1}{\mapsto} B $ and since $\displaystyle B=\{b_1, \ b_2,\ ..., \ b_n\}$, then A can have the same number of element as B, or slightly less, given that it's 1-1. Now since we can arrange all the elements of B, we should be able to do the same for A... but I'm not too sure on how to show this.