Question: What is wrong with the following proof; that any order for n ≥ 10 pounds of fish can be filled with only 5-pound fish?
We use the strong form of mathematical induction. Here no = 10. Since an order for 10 pounds of fish can be filled with two 5-pound fish, the assertion is true for n = 10. Now let k > 10 be an integer and suppose that any order for f pounds of fish, 10 ≤ l ≤ k, can be filled with only 5- pound fish. We must prove that an order for k pounds can be similarly filled. But by the induction hypothesis, we can fill an order for k -5 pounds of fish, so, adding one more 5-pounder, we can fill the order for k pounds. By the Principle of Mathematical Induction, we conclude that the assertion is true for all n ≥ 10.