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I detest the algebraic "proofs" used in debates on this. Anybody who thinks that 0.999... does not equal 1 should probably also reject the idea that 1/3 is the
by the_shivers 4y ago
I detest the algebraic "proofs" used in debates on this.
Anybody who thinks that 0.999... does not equal 1 should probably also reject the idea that 1/3 is the same as 0.333... the argument for both is the identical (getting infinitely closer to some x is equivalent to x itself). You're using the thing you set out to prove as an argument in your proof.
Online debates on this subject would be a lot better if the (correct) side of 0.999... = 1 was more open about the shortcomings of these simpler proofs.
- edflsafoiewq 4y agoThat's the point of the proof, it's to show you how things you already accept are true entail something you're less certain about. But perhaps the deeper point is this is a lesson for children or students and has a level of rigor appropriate for, and not unusual in, pedagogy, not a ironclad argument for "serious" debates with internet contrarians.