after the test

The test on Thursday wasn't too difficult. However, I realized that I made a mistake in the last question, of which the loop iteration is supposed to prove that the variables were natural numbers so that I could use the principle of well ordering to say that there is a lower bound to the set. Instead, I proved that the values in the loop iteration was always descending, which shows that the set is monotonic. However, I forgot that the principle of well-ordering presupposes that the set is of natural numbers. I doubt I'll forget this for the exam now... =.=