What is the context of this problem? Is this a set theory course? What is the definition of < ? What kind of proofs you are looking for: the ones that strictly follow from ZF axioms or proofs in naive set theory?
At first I apologize my horrible English; it's not my native language.
I need little help with these exercises:
1. Let m and n be natural numbers such that m < n. Show that there exists natural number p, that n =m + p+
2. Let n be a natural number and let f:n+ -> w (omega) be function. Prove that set ran(f) has the largest member.
(p+ means the follower of the number p; n+ means the follower of the number n)