How does proof by induction work?
In: Mathematics
First I set up 2 dominoes right next to each other and I push one over. It falls into the second domino and also knocks it over. After that I set up a long row of dominos. I could then tell you that if I push over the first domino, that eventually the last domino in that row will fall over. The proof lies in the fact that I already showed you that each domino will knock over the domino next to it.
When we do mathematical proof by induction we do the same thing. We have to show that every time we advance a step from n -> n+1 that the chain will continue until we get to whatever result we are proving (set up the row of dominos). After that we just have to show the initial case (push the first domino over).
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