Yesterday I Couldn’t Spell Mathematishun…

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

xⁿ > x^(n-1)

then I think they haven’t checked enough cases.

In case you forgot, xⁿ 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 2⁴ = 2 x 2 x 2 x 2 = 16. In this case, the ad’s assertion is true, because x^(n-1) = 2^(4-1) = 2³ = 2 x 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:

xⁿ < 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.