“You’re saying if we agree with Adrian, then calculus goes away?” “You see, Adrian? If there were a ‘smallest’ number, the concept of a limit wouldn’t make any sense. It was a teacher’s sweetest dream: an oddball digression that winds up shedding new light on the central themes of the course. “But can’t any number be divided by two? Isn’t there always a smaller number?” “That’s why you shouldn’t divide it,” Adrian said. “What if you take your little number, and divide it by two? Dividing it by two should make it smaller. “And this second-smallest number,” I said, “what happens if you divide it in half?”Īdrian shook his head. ![]() “There you go again, with your crazy talk,” Adrian scolded. “It’s a tiny little number, of course,” Adrian replied. “So what’s the distance between 1 and 0.999…?” It’s the biggest number that’s still smaller than 1.” “It’s so close to 1 that there’s no number in between. “If 0.999… isn’t equal to 1, then what is it?” It was probably time to steer the lesson out of the wilderness and back onto dry pavement.īut the Socratic in me (I grew up with a family cat named Socrates) couldn’t resist another attempt. I could have left it there – Adrian had delivered his performance, landed some good-one liners (even Kevin was cracking smiles), and instigated a debate that led to a cool proof. “He must have clicked a YouTube video about 9/11 being an inside job,” Angel suggested. “Well, consider this,” I said, and quickly offered an alternative justification – not quite a proof – of the same fact, one to highlight the absurdity of Adrian’s stance:īy now, the other students had begun to turn on Adrian, who still held firm. Besides,” Adrian huffed, folding his arms, “you don’t tell me what I want.” “Ah,” I said, “but you wouldn’t want your definition to lead to inconsistencies, would you?” “Give me a proof that they’re different.” Some surrendered to my argument, but Adrian held firm. With my sanity under challenge (for neither the first nor the last time), I pushed back by offering the standard proof of the fact:Īt this point, dissent began to flow among Adrian’s ranks. “You’ve lost your grip on reality, Orlin. (By 0.999…, I mean the decimal number in which the 9’s go on forever and ever.) “You’re crazy,” Adrian said. (Well, at least it had to do with math.) The students got curious about repeating decimals.Īdrian led a pack of disbelievers in the claim that 0.999… = 1. ![]() I’m surprised we got anything done.īut one day’s digression stayed surprisingly on-topic. We swapped movie suggestions, debated Beatles albums. I’d taught those kids for four years, and there was too much fondness built up between us. In Calculus class, it was often hard to resist distractions.
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