Prove: The set of all counting numbers is infinite.
It is clear that $\displaystyle f:\mathbb{N} \mapsto \mathbb{N}\;,\,f(n) = 2n$ is an injection to a proper subset.
That is sufficient to prove a set is infinite.
However, I think you are working in a more structured setting.
So that should be a lesson to you.
Completely explain the setting of your question.
Ok, here is the setting:
The statement that the set A is infinite means that there is a nonempty proper subset B of A such that there is a one-to-one correspondence between A and B. By a counting number means a number in the minimal induction set, and the minimal induction set is called the set of all counting numbers and is denoted by C.Hopefully this helps; I'm not good at starting these proofs, so any help is much appreciated.