I like logical explanations of dividing by zero, which we’ve all been told is “against the
rules.”
I was sitting there in my apartment the other day with my math club buddies. Four of us in all. We decided you could still have the fraction (0 / 0) = anything you want, just whatever you need, according to the situation. We reasoned that 0 / 0 = 4, since there were four of us. That way, we could all have a portion of whatever 0 / 0 turns out to be (following a lot of research), and we could then declare ourselves Newtonian Masters (of Universal Understanding).
Just then, the Police of Division busted the door to my apartment straight down. We were startled, but these math cops took up all our papers, and I heard one snort, “Aha, dividing by zero again! Don’t you know this behavior can become addictive?”
“But sir,” I protested, “we’ve just proved we could stop at four. No reason to get greedy, just 0 / 0 = 4!”
“Well, I’m going to have to give you a citation, dividing by zero in the third degree.”
Hmmm. The third degree. That would be 64, wouldn’t it? So I asked the officer, “Does that mean my fine is $64?”
He calculated for a minute, and looked shocked. “Why…yes, it does. How did you know that?”
“Because if I said 0 / 0 = 4, and you’re saying this “crime” is only eligible to the third degree, then 4^3 or four to the third is 4*4*4 = 64.”
Then, the clincher: I asked, “Can I get the judge to cut the fine in half?”
“Possibly,” the cop said.
“Then the clerk?”
“Maybe.”
“The cashier?”
“Usually.”
“Then, on appeal, I could get it halved again, couldn’t I?”
“Seems likely.” This cop looked bored and tired.
“Then the clerk again?”
“Yes.”
“The cashier on the way out?”
“Yes. what are you getting at?”
“Sir, by the time I get through the District Court of Appeals, The U.S. Court of appeals, and the Supreme Court of the United States of America, and all their clerks and cashiers, I’ll have cut the fine to, (hmm, let’s see, steps local, 3, appeal 3, Dist Appeal 3, US Appeal 3, then the Supremes 3). That’s 15 times I can halve my fine, so:
64 32 16 8 4 2 1 0.50 0.25 0.125 0.0625 0.03125 0.015625 0.0078125 0.00390625 0.001953125. Sir, by this fifteenth halving of my fine, I’ll be down to a point where significant digits are finally rounded down to zero. I’ll owe zero! Can you see that you’re only causing a waste of time. Sir, get back out there, to the embezzlers, the inside traders, the people working such big numbers. Bookies? Yeah, bookies! Can’t you just let bygones be bygones? We’re dividing by zero, for crying out loud.”
The officer stood for a moment, bedazzled by my fancy footwork. He closed his book, and stated, “This math cop job gets so hard, sometimes…”
And with that, he and all his buddies left the room. “We’ll send that repairman for the door.”
“Thank you,” I called out.
We never saw them again.
