Proof that if $\displaystyle S$ is any finite set and $\displaystyle T$ is any infinite set then $\displaystyle |S|<|T|$. In mathematical words prove that there exists a surjection $\displaystyle \phi:S\to T$ which is not one-to-one.

What I am trying to get to is perhaps there exists a set that cannot be placed with ono-to-one correspondence with a proper subset and is greater then an infinite set! I doubt that but I am trying to connect this to my other post on "the set of all finite sets".