Well Ordering Proofs and Counterexamples
In the Prime Products example, we proved that every integer greater than 1 is a product of primes by showing the set of counterexamples is _____.
A Well Ordering Proof starts with the assumption that the set of counterexamples is not empty. It then follows that this set must have a smallest element, by the Well Ordering Principle. Much of the math focuses on showing that the set is empty or that there is another element in the set of counterexamples that is even smaller than the smallest element.