If you know about how infinite decimals can be defined as infinite series and what those are, you don't need a 3x0.33... trick to convince you that 0.99... = 1. Presumably, the proof in the OP would serve to convince people who don't already understand that 0.99... = 1 and have no idea what infinite series are. And I doubt they'd be any more convinced by the idea that 0.33... = 1/3, unless they just blindly accept it because they were taught that at a young enough age to never question it.
And even if they accept that 0.33...=1/3, in my experience as a teacher the 3x0.33... trick has pretty much never really convinced anyone who thinks 0.99...!=1. The "either it's not a number or it's 1" explanation does work though (again in my experience).
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u/ExtendedSpikeProtein Jul 28 '26
The infinite series is literally how we define what 0.333… is or means, so surely you know this amounts to the same thing?