# Mathematical Induction for Seven Year Olds

The Barenaked Ladies’ “Snacktime” is on very heavy rotation in my house these days. It’s officially an album for children (which explains the heavy rotation, because if kids like something once, they like it for approximately the next billion times). However, a lot of it is laugh-out-loud funny for adults. For example, from the alternate alphabet song:

D is for djinn, E for Euphrates,

F is for fohn, but not like when I call the ladies.

But I digress.

The first song on the album is “789”, about the nefarious dealings of the number 7.

1, 2, 3, 4 and more makes 7

Why is six afraid of 7?

Cause 7 ate 9

Recently the eldest kid piped up: “Seven eats all the numbers. There are no more numbers after 8.” I asked why. “Well, seven ate nine, so it’s 7-8-10, so then seven ate ten, so it’s 7-8-11, so then seven ate 11, and then it just keeps going.”

So, the Barenaked Ladies just inspired my seven-year old to discover the principle of mathematical induction, which is one of the first techniques you learn when you venture into the land of advanced mathematics. The idea is that if you can prove that something is true for some integer *n*, and that it is also true for *n+1*, then it has to be true for all integers greater than *n*. So, for a simple (and somewhat silly) example, if you can first prove that if *n>0* then *n+1>0*, and then you also prove that *1>0*, then all positive integers are greater than zero. I remember having a hard time wrapping my head around this idea when I first bumped into it in high school (though I got over it in college after enough algebra classes with Michael Artin). I just find it pretty nifty that you can get the idea from a kid’s song.

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