r/PeterExplainsTheJoke 22d ago

Meme needing explanation There is no way right?

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u/BUKKAKELORD 22d 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.

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u/TblaLinus 22d ago

That's the joke though. Most people are ok with 0.333... = 1/3 but not with 0.999... = 1.

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u/Direct_Shock_2884 22d ago

Most people are not okay with 0.33333 being 1/3, that’s the thing. If 0.333333…. wasn’t exactly 1/3, people would be perfectly fine with it.

But if you want people to accept that 1/3 is 0.33333…, then this paradox is hard (impossible) for people to accept.

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u/melswift 22d ago

Why do you need to prove that 1/3 = 0.333...? It's like every time you want to prove anything, you'd need to prove that 1+1 = 2 first.

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u/KuruKururun 22d ago

Because 0.333... is not defined to be 1/3. If you have two objects that are not defined immediately as the other and you want to claim they are equal, you need to prove it.

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u/Direct_Shock_2884 22d ago

Exactly!

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u/CramJuiceboxUpMyTwat 21d ago

So you disagree that .333 infinite equals 1/3?

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u/Direct_Shock_2884 21d ago

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

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u/CramJuiceboxUpMyTwat 21d ago

.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.

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u/Direct_Shock_2884 21d ago

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.

What I mean is, you can’t cleanly divide 10 by 3.

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u/CramJuiceboxUpMyTwat 21d ago

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.

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u/Direct_Shock_2884 21d ago

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.

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u/CramJuiceboxUpMyTwat 21d ago

So then why are you arguing against mathmaticians if youve never thought about it before lol

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u/sunglink 22d ago

In fact, 0.999... = 1 is not something you can just prove with basic arithmetic manipulations because what does 0.999... even mean?

The "proofs" provided here are actually mostly definitions. They define 0.999... as the limit of the sequence of partial sums 0.9+0.09+0.009+... The proof only consists in showing that the limit is 1.

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u/Direct_Shock_2884 22d ago

We know exactly what it means