1. The problem statement, all variables and given/known data Prove that every nonempty set of positive integers contains a smallest member. This is called the well-ordering principle. 3. The attempt at a solution I'm just starting out with analysis, so I'm not too sure about the format of proofs. Here goes: Proof. First suppose the set S of positive integers is finite. Then assume S contains no smallest member. It follows that for every x in S, there exists an infinite number of members of S less than x. This contradicts our assumption that S is finite. Thus every finite set of integers contains a smallest member. Any help/critique is appreciated.