11 Mathematical Induction 12

Before presenting the details of the principle of mathematical induction let’s understand the situations to which it applies. We’ve seen that to prove a universal assertion, we start by setting up the scenario that represents the hypothesis of the assertion. This scenario involves certain hypothetical objects, and certain assumptions. We then use the information of the scenario to work towards the desired conclusion. The principle of mathematical induction says that in certain common situations there is an additional assumption, called the induction assumption or induction hypothesis, that you are permitted to add to your list of assumptions. We’ll state this assumption below. As with any assumption you are not required to use it, but may use it if it is helpful. The principle of mathematical induction is often useful when proving universal assertions when the universe of the assertion is: