Funmurphys: the Blog

Isn't Math Fun?

I try to read Best Of The Web daily. Earlier this week it ran an item about Math Hysteria, sparked by a math question asked of Jeb Bush. They printed the following reader's proof that 2=1:

Let a=1

Let b=1

Therefore a=b

Multiplying both sides by a gives a²=ab

Subtract 1 from the left and b (which equals 1) from the right: a²-1=ab-b

If you remember your quadratic equations, this factors to: (a+1)(a-1)=b(a-1)

Dividing both sides by a-1, we have a+1=b, or 1+1=1

Therefore 2=1

Needless to say, there is a problem with the proof, so the next day they ran a followup under the heading Of Subs, Screens and Springs where they said that about 200 readers wrote in a pointed out the proof was no good because they had divided by zero when they divided by (a-1).

Well.

I sent them the following email:

I can't believe you got 200 emails about your proof that 2 = 1 and nobody got it right. Everybody forgot their calculus while remembering their algebra. The real answer is that you proved that 1=1. You were fine up to:

but when you divided by (a-1) you incorrected evaluated the expression.

Since you weren't just dividing by zero, but dividing zero by zero, you should have used L'Hopital's rule (in case you didn't take calculus, you can see it here: http://www.math.hmc.edu/calculus/tutorials/lhopital/).

When you evaluate (a+1)(a-1)/(a-1) as a approaches 1, you take the derivative with respect to a which is (1)(1)/(1) or 1.

When you evaluate b(a-1)/(a-1) as a approaches 1 (again with the derivative), you have b(1)/(1), or b. So when you divide

by (a-1), as a approaches 1 you have

substituting 1 for b, we have:

Oddly enough, they didn't run a correction or my email. I'm crushed, but I'll still keep reading.