0.999…. and the Debate that Repeats Forever

Adrian led a pack of disbelievers in the claim that 0.999… = 1. “You’re crazy, Orlin,” he said. “You’ve lost your grip on reality. 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.

Fistfuls of Sand (or, Why It Pays to Be a Stubborn Teacher)

This is a story about one small compromise that I refused to make, a stubborn act that paid off, though I didn’t expect it to. The setting is a Calculus classroom, but I hope the story will resonate with anyone who spies something dubious in the rigid and widespread assumption that learning can be endlessly itemized, carefully quantized, and instantaneously measured.