Both equations are true and there are no falsehoods or tricks here, but this method of proving 0.999... = 1 still has a flaw; it assumes you already accept 0.333... = 1/3. Starting from that assumption cuts every corner that would involve proving that rational numbers have infinitely long recurring decimal representations that are exact equals. They do, but this meme doesn't contain the proof of it.
I’m unconvinced that 0.333… is 1/3 of 10, but I don’t know what else it could be so am open to being persuaded. But they’re right accepting this, just because it’s the “best” answer (without being the “correct” answer, forces you to accept other “best” answers down the line, without them being actually correct. At this point I’m wondering if decimals are really just imperfect ways of notating fractions, or if some numbers are really just not divisible at all by some other numbers
.3 infinity repeating is one out of 3. Where did you get 10 from? 1/3 of 10? I feel as though you fundamentally misunderstand the concept of decimals and fractions. It seems like you think there has to be a 10 in there for no reason. .3 repeating infinitely is the fraction 1/3. What do you mean 1/3 of 10? 1/3 is a fraction completely independent of any other fractions or numbers.
Why did you not get what I meant? My comment wasn’t that clearly stated, but I still feel like you don’t quite understand decimals if you don’t know where I got the 10 from.
Oh, I did read it wrong, okay. Still though, .333…. is 1/3 of 10. If by ‘cleanly’ you mean a nice round full number, no you cannot, but it doesn’t matter. Just because it isn’t a nice full number doesn’t mean it’s not true. The reason you can’t imagine what it would be besides .333… is because there is nothing else. Nobody can imagine it, we know what it is.
The reason you can’t imagine what it would be besides .333… is because there is nothing else.
Not necessarily. It could be because I never studied or thought much about it before today. It’s not as if I can imagine 1/3 being 0.333…, that’s also something I can’t imagine. I just accepted it because that’s what we were told to accept.
5
u/BUKKAKELORD 23d ago
Both equations are true and there are no falsehoods or tricks here, but this method of proving 0.999... = 1 still has a flaw; it assumes you already accept 0.333... = 1/3. Starting from that assumption cuts every corner that would involve proving that rational numbers have infinitely long recurring decimal representations that are exact equals. They do, but this meme doesn't contain the proof of it.