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.