0.999…. and the Debate that Repeats Forever [Math With Bad Drawings]

This is one of those infinities, and when you start working with infinity, things get weird. There’s even a whole Wikipedia article dedicated to this concept. Mind-blowing, isn’t it?

Math with Bad Drawings

In Calculus class, it was often hard to resist distractions. I’d taught those kids for four years, and there was too much fondness built up between us. We swapped movie suggestions, debated Beatles albums. I’m surprised we got anything done.

But one day’s digression stayed surprisingly on-topic. (Well, at least it had to do with math.) The students got curious about repeating decimals.

Adrian led a pack of disbelievers in the claim that 0.999… = 1. (By 0.999…, I mean the decimal number in which the 9’s go on forever and ever.) “You’re crazy,” Adrian said. “You’ve lost your grip on reality, Orlin. Snap out of it.”

With my sanity under challenge (for neither the first nor the last time), I pushed back by offering the standard proof of the fact:

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• 0.999...
• 1
• calculus
• epsilon
• infinity
• math