Escaping the Monster, by induction!
Problem Set Omega
Joseph Park, Conner Hutson, Jared Tufts
Target Audience: Elementary school students
Artifact: Ladder
If you are able to reach the first step, and reach the next step from any step, then every level is reachable.
Scenario:
A stranger came up to Jimmy and asked if he wanted to come get some candy with him. Jimmy was curious at first, but he remembered what his mom said about stranger danger. So he politely declined but the creeper kept following him. To his advantage, there was a ladder leading him to the Willy Wonka factory. How does he know he will be able to climb the ladder all the way up to his destination?
Predicate (P(n)): The nth step on the ladder is reachable.
Base case:
Thankfully Jimmy is an athlete and plays recreational soccer, so he is able to step up onto the first step (rung) of the ladder. Therefore, he is on the ladder now (specifically where n = 0).
Induction step:
Because Jimmy is such a stellar athlete, he will not be tired at all from taking one step up the ladder. He knows that from one rung of the ladder, he will be able to climb up to the next rung (from rung n to rung n+1) with no difficulty.
It is one long ladder - Jimmy grew up!.
Willy Wonka factory: en route!
Now, Jimmy is comfortable knowing that he will be able to reach the top of the ladder as long as he keeps climbing and does not give up! He knows he will reach that destination because he read that it is possible and that the number of steps is countable, but just unknown. So long as he can climb the first step and can go from one step to the next, any step is reachable to Jimmy.
Conclusion
Proof by induction is like climbing a ladder!