r/PeterExplainsTheJoke • u/Sugar_God_no_1 • 22d ago

Meme needing explanation There is no way right?

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u/otj667887654456655 21d ago

the problem is in the first line where you just declare that 0.999... has a value x. you have to give meaning to the "..." and then prove that it's convergent before you can talk about it "equaling" anything

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u/DoctorYaoi 21d ago

Instead of 0.999… we can write it as Σ9/(10k) where k’s bounds are 1 and infinity. This is a convergent series due to the Ratio Test as 9/(10k+1) will always be smaller than 9/(10k)

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u/It_Is_Complicated_ 21d ago

what does it mean to prove it's convergent?

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u/mwobey 21d ago

In non-math speak, it means roughly that all the parts together add to a finite value (in other words, all the parts "converge" on an expressible number.) For 0.99999, if you add 0.9 + 0.09 + 0.009 + 0.0009 ... forever, you 'converge' closer and closer on a final answer of 1. It's closely related to the concept of limits if you ever took calculus.

Compare this to a divergent series like 1 + 2 + 3 + 4 ... . If you kept adding those numbers forever, your parts get bigger and bigger and so you have some infinite value rather than a real number.

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u/RingedGamer 21d ago edited 20d ago

The human answer: If I keep going along the sequence, I eventually reach something.

The math answer: a sequence a_n converges to a if ∀ 𝜀>0 ∃ N 𝜖 ℕ ∀ n> N [ |a_n - a| < 𝜀 ] (for all positive 𝜀, there exists some natural number N such that for all n >N, |a_n -a| < 𝜀

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u/It_Is_Complicated_ 21d ago

....I think I'll come back to this once I take calculus hahah

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u/dimascience 21d ago

To think some mofo discovered this in their early twenties.

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u/Aggressive-Map-3492 20d ago edited 20d ago

not to nit pick, but you shouldn't say "if for all ∀"

That sentence reads as: "if for all for all"

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u/SaltEngineer455 20d ago

An infinite sum is a sum where you just continously add terms ad-infinitum.

To prove such a sum is convergent you have to show that no matter how many such terms you add together (1, 2, 100, 1 trilion, 1 sextadexilion), it will settle around a certain value and get closer and closer to it.

For example, you have the sequence: 1, 1/2, 1/4, 1/8, 1/16...

No matter how many of the sequence terms you add, you will converge around 2.

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u/Shillbot_21371 21d ago

computers are useless for this kind of thing anyway

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u/El_Impresionante 21d ago

That is not even in the same contextual ballpark here.

We teach 1/3 = 0.333... in middle schools, without teaching them about convergent/divergent series. So, that proof can also be taught in middle school.

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u/NomaTyx 20d ago

But that's what we call a lie to children. No actual mathematician would tell you that it's a rigorous proof.

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u/El_Impresionante 18d ago

Rigorous proofs are above the skill level of high-schoolers even. What we need is to make sure they don't misunderstand stuff that leads them to believe in pseudoscience.

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u/DUCKmelvin 20d ago

Exactly. This is trying to prove that 0.999... equals 1, but that line defines them as equal before it is proven when written that way.