1 = 2

That PEMDAS poll reminded me that math is the wrong hands can be used to prove anything:

Proof that 1 = 2:

A = B

A^2 = A * B

A^2 - B^2 = A * B - B^2

(A + B ) * (A - B ) = B * (A - B )

A + B = B

B + B = B

2 * B = B

2 = 1

QED!


I got an F in 10th grade algebra, deservedly so: I didn't learn algebra until Calculus forced me to finally learn it. But one tedious day in that 10th grade algebra class the teacher put this proof up on the chalkboard and challenged us to locate its error. No one spoke up for several minutes. Then I thought I saw what was wrong, but doubted I could possibly be right before anyone else in the room had seen the problem, so whispered my theory to Noel Becketti, who sat right behind me. He instantly raised his hand and said what I'd told him. Right! exclaimed the teacher, and Noel beamed. Noel, if you're out there, I never forgot that moment of stolen glory.

 

Back when I ran a support desk for our far flung salesreps I got more than one perplexed call about a "bug" in Lotus 123 (and later, Excel) that would return "error" whenever a formula attempted division with a zero. "Shouldn't it equal zero?" was the common complaint. Interestingly, for most of the types of elementary sales analysis we did, making a missing denominator return zero with an IF clause worked better than trying to exclude the truncated data, so in some sense our reps were right - it SHOULD equal zero. I've always thought the division operand in computer code should have an IF component of syntax so handling the empty denominators would be automatic.