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.
Is 'infinity' an acceptable answer to division by zero? I still remember a...'discussion' with a stubborn teacher who insisted that anything divided by zero was zero. Anybody want to do 'black is white' next?
I'd say that if you're going to give it a value it'd be aleph 1, assuming we're working with reals... But, in truth no. It's just infinite, rather than equaling infinity.
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.
When I was in college, I saw a bumper sticker on an old Volvo parked one late night in front of the Physics building: 2 + 2 = 6* *For very large values of 2
No, it's not. That's why it is undefined. Division by zero creates ambiguity, where logic suggests differing answers for different cases. There is no good way to define it. Tom
