Division by Zero

Madison, and, lately, as a result of Madison's interest, Ella, has taken to looking for ways to combine the numbers on the digital clocks on the kitchen stove and on the VCR. For example, at 11:31, she'll suddenly say: "One plus one plus one equals three!" and at 11:38, she'll say: "One plus one, cubed, equals 8! The two of them are now always alert to ways to successfully combine the numbers on the screen. I taught neither of them to do this, although I will admit that I always did it as a kid, too. (It's how I learned that if the digits in two different numbers add up to the same thing, the difference between them will always be divisible by 9. E.g., 95-77=18.)

At 2:00 this afternoon, Madison asked what it would mean to divide a number by zero. "What would be 2 divided by 0?" I explained that it was meaningless, that you can think of what it would mean to divide a number into 2 pieces or 4 pieces or 1 piece but not into 0 pieces."

"That's scary," she said.

"What's scary?" I asked.

"That it could be meaningless. I wish I hadn't asked the question. I wish I could dial back my life to before I asked the question and not ask it."

She felt a little better when, a few minutes later, David said that some people interpreted the answer to division by 0 as infinity. He took her through the reasoning: What if you divided something by 1/2? 1/4? 1/100? She saw how it got bigger and bigger the smaller fraction you divided something by, and how if you got small enough of a fraction you get such a big number that it approaches infinity.