I just heard a radio ad for Harper College that was…surprising.

The ad lists off a bunch of pairs of things where one is greater than the other and eventually suggests that I’d be greater with a Harper education than without one. What caught my attention, however, was the very first pair of things listed, which went something like this:

“x to the n is greater than x to the n minus one.”

I suppose that you could read that a couple of ways, but if they mean

x^{n}> x^{(n-1)}

then I think they haven’t checked enough cases.

**In case you forgot**, *x ^{n}* means

*x*times

*x*times

*x*and so on until x has been multiplied by itself

*n*times. For example, if

*x = 2*and

*n = 4*, we have

*2*x

^{4}= 2*2*x

*2*x

*2 = 16*. In this case, the ad’s assertion is true, because

*x*x

^{(n-1)}= 2^{(4-1)}= 2^{3}= 2*2*x

*2 = 8*.

The problem is that for a mathematical statement to be true it has to work for all possible assignments of variables, and that’s not the case here. For example, if *x* is a fraction between *0* and *1*, then the opposite is true:

x^{n}< x^{(n-1)}for

0 < x < 1

The ends of that range are bad too: The number 1 multiplied by itself any number of times is always *1*, so if we set *x = 1* then both sides of the equation are equal to *1*, meaning neither side can be greater than the other. The same thing is true for *x = 0*. And if *x* is a negative number, the sign changes every time you multiply it by itself, so one side of the equation is negative, depending on the value of *n*.

**I don’t normally** expect mathematical rigor from advertising, but when there’s a formula, and it’s an educational institution…

(I tried to email the Harper math department, but the first two people on the department web page bounced. I think I may have found the address of someone who teaches Quantitative Literacy at Harper. I’ll update this if I hear anything back.)

**Update**: I got a friendly reply from Gary Schmidt thanking me for the contact and telling me (with just a hint of concern) that this doesn’t represent Harper’s mathematics program.

I knew that. Actually, it brought on a pang of sympathy. I spent a lot of time as a student and staff member at the Illinois Institute of Technology, and I can remember some things coming out of our marketing department that made us cringe a bit.

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