[math]\begin{align}y &= \sum_{i=0}^\infty 2^i \\y &= 1 + 2\times\left(\sum_{i=0}^\infty 2^i \right) \\y &= 1 + 2y \\y &= -1 \\\sum_{i=0}^\infty 2^i &= 1 + 2 + 4 + 8 + ... = -1\end{align}[/math]
>>16879802it be that way with operators
Consider a lamp with a toggle switch. Flicking the switch once turns the lamp on. Another flick will turn the lamp off. Now suppose that there is a being who is able to perform the following task: starting a timer, he turns the lamp on. At the end of one minute, he turns it off. At the end of another half minute, he turns it on again. At the end of another quarter of a minute, he turns it off. At the next eighth of a minute, he turns it on again, and he continues thus, flicking the switch each time after waiting exactly one-half the time he waited before flicking it previously. The sum of this infinite series of time intervals is exactly two minutes.Is the lamp on or off at two minutes?
>>16879802Its like Schrodinger's Cat.It was created to demonstrate the absurdity of an idea. Basically taking the self contained postulates of a concept and logically extrapolating them to end up with a result that is obviously pants on head retarded. Its not an actual argumentative refutation as such but rather a way of saying "I say Chaps, there is obviously something seriously fucked up here, let's step back and have another look and then consider all the possibilities outside the box". Their intentions are good and motivated by a love of pure logic and knowledge.But trolls and brainlets get hold of the idea and spread it around the peasants who take it literally. Lol. Many laughs were had. Think of it being among the highest forms of trolling achieved by Mankind.
>>16879863Retinal persistence implies that the lamp is on for human eyes.
>>16879863As with anything, it depends on your choice of ultrafilter.
is the limit of a weighted sum
>>16879802It's what happens when you tell jeets they're smart and let them do math. Just ignore it and it goes away.
>>16879863it doesn't matter
>>16879802*sigh*https://www.youtube.com/watch?v=beakj767uG4
>>16879802Anything is trivially true in a contradictory system.As a free bonus, this divergent sequence converges to any complex value.1 + i being my personal favorite.
>>16879863I swear to god if you don't stop fucking with the lights I will break all of your fingers.
>>16880084at least it ain't the thermostat...
>>16879863For the uninitiated, this is a variation of the grim reaper paradox and is echoed by pseuds. For these types of switches there is a gate voltage and a smooth transition where there is no current to some current. At increasingly small time scales the current will not have enough time to stop flowing through the bulb. To make matters worse, in order to quickly toggle the switch at higher and higher frequencies, larger and larger forces must be applied. The switch would eventually mechanically break before your scenario could be fulfilled, rendering the circuit broken and turning the lamp off. >REEEEEE but muh heckin grim reapersNot realistic, kys.
>>16879863Flicking the lights on and off so quickly caused a malfunction, so it's off. But if you are talking about there's no such thing as infinitely getting too small, it's correct. Space on the smallest scale has walls of waves that slope around particles.Anyway, being locked in a cube, you can die from time erosion. From memory..
>>16879828Good morning saar.
>>16879802The slippery slope of infinite sums. If you can define 'sum' to mean the limit of partial sums, you can also define it to mean Ramanujan summation. Neither one has anything to do with actually summing up all the elements one by one as the word 'sum' implies to normal people.
>>16879863>Is the lamp on or off at two minutes?This is a nonsensical question because he will have to flick it infinitely fast before that happens.
>>16879832corollary:y = 1 + myy = -1/(m-1)m=13 implies y = -1/12[math]1+2+3+4+5+6+... = 1+12+144+1728+... = -\frac{1}{12}[/math]
>>16879863>I define a function f mapping [0,2) to the quasihyperoctosurreals.>What is f(2)?Seriously?
>>16880358But only for an infinitesimal moment.Ezpz, boss
>>16880356It even easier. Assume the divergent series converges. That is assume P and ~P are both True. Guess what?So is Q. For any Q you want.Even if Q is the statement, "The divergent series converges to -0.08333...".Logic is amazing!
>>16880404You're a mouth-breathing mongoloid.
>>16880413Hardly a refutation.Your silver tongue was tarnished when mommy handed you her iPad to shut you the fuck up.
>>16880419Ramanujan summation doesn't assume that a divergent series converges, you inbred mongoloid.
>>16880428Maybe you need to review the thread so far, you illiterate undertrained Pakistani LLM.You do not need to use any bullshit other than logic to show this is bullshit.You can use the most finely tuned bullshit sculpting method you like. But you do not need anything more powerful than (P ^ ~P) => Q.
>>16880437i do not need to acknowledge you are a woman (social category). i can assign you the value of faggot (social category). this does not mean i assuming you are both a woman and a faggot.
>>16880437>mentally ill retard starts devolving into incoherenceI know I hurt you. :^)
>>16880440>>16880441You failures have nothing but gender-based insults based on even more incorrect assumptions.You could have discussed the zeta-function and analytic continuation but you can't so you don't.Failed failures fail again.
>>16880428Ramanujan summation assume values for the areas were the function is otherwise infinite.So, feel free to assume -0.08333... if it makes you feel better.But it's still just (P ^ ~P). "The undefined function takes on this specific finite value."Wow, look at our Q.It's exactly -0.08333... .
>>16880442nothing in my comment was about gender, fag
>>16880444>I know I hurt you. :^)Such a big strong man. So many wrong assumptions. Please mansplain again how you can assume any value you want in the analytic continuation.Just please don't hurt little me ever again.
>>16880442>>16880443>>16880445>mentally ill retard keeps seething incoherentlyI know I hurt you. :^)
>>16880455Like I said, "You got nothing but your precious contradictory assumptions which you clutch as pearls and tell yourself they're magic.". So you hurl insults into the æther and pretend you've expanded.Whatever that may mean to you; there's your Q, toodle-doo.
>>16880502>You got nothing but your precious contradictory assumptionsProve you're not psychotic by quoting two assumptions actually made in my posts. Protip: you literally can't.
>>16880513Take your pick:A) The divergent series converge.B) When extending the domain of the function to sets were the function was not defined due to singularities (aka, infinities) we are free to use any finite value we choose, because.Pay up.
>>16880525Notice how I correctly predicted your inability to quote any assumptions, contradictory or otherwise.>b-b-but what about the psychotic episode i had where i heard voices saying things
>>16880530> {0|0}List your posts then. Otherwise your empty game is empty.Pro-tip: you won't.
>>16880538>mentally ill cretin can't keep track of the exchange
>>16880544Exactly as I predicted.I won.
>>16879863>muh what's the last number in an infinite sequence This is just nonsense for the confusion of midwits.
>>16879832This is obviously wrong though.
>>16881382You can make up any solution you like in this way so yes, when that happens that means is wrong or that there are no solutions
>>16881382>obviouslyis it now?
>>16881388At what iteration do you get anything but a larger positive integer from the previous one?Are there any cases of sums of positive integers adding to create a negative?
>>16881391yes. see>>16879802and>>168803621 + 2 + 3 + 4 + ... = 1 + 12 + 144 + 1728...
>>16881394Right, but none of those actually disprove what I said.
>>16879863Off. If there’s any time limit even an infinite sequence of paired actions will end with the second action. Kind of question Alphabet uses to weed idiots out of the applicant pool.
>>16881402>if there is no end to the sequence, the sequence will end with..There is no time limit because time is being stretched to infinity.
>>16879863On. At the two minute mark I would be able to read by the light of that lamp and it wouldn't even give me a headache.
(x(x+1))/2 crosses the y axis at x = 0 therefore the sum of all natural numbers is 0.Gib phd pls.
>>16881394>1 + 2 + 3 + 4 + ... = 1 + 12 + 144 + 1728...Now show where this turns into a negative.
>>16881419see>>16880362>>16879832>>16879802
>>16881420>show this>reposts things that don't show the thing to be shownIs this some lazy bait or are you 'tarded?
>>16881421op image shows how 1 + 2 + 3 + ... = negative. do you not understand the proof?the quoted post shows how 1 + 2 + 4 + 8 + ... = negative. do you not understand the proof?the quoted post generalizes the above series. do you not understand the proof? i think you're the one trolling. the posts are very clear to anyone who has seen series before
>>16881423>show WHERE the negative emerges Is it a reading comprehension issue?
>>16879802>>16879828>>16879832Ah yes. The contradictions that arise from assuming you can do an infinite number of things. I don't even have to work to debunk ZFCucks. They do it to themselves for me.
>>16881424on your end i believe it is, yes. are you not able to solve y = 1 + 2y?
>>16881434The math describes the whole, yet results in a nonsensical conclusion. I understand the proof here but it's quite clear that there's a problem with it if there's no place the negative could possibly emerge.
>>16881425someone tell wildeburger that limits are just function arguments of some function that’s calculating the summation
>>16881439the negative emerges with perfectly fine mathematical operations. if you do not like infinity, then perhaps you should consider becoming a finitist.
>>16881418x = -1 too, moron.
>>16881439>there's no place the negative could possibly emerge.Sometimes infinity minus infinity is still infinity, Anon. Just think about that.You really can not do normal arithmetic with them. Asshole infinities.It's best to exclude them from the start.
>>16881444>each iteration results in a positive>the sum of this infinite series of positives is a negative Putting the proof aside for a moment, does this makes sense to you?
>>16881448Yes, I think that's the issue here. An infinity is a different category of entities than numbers are.
>>16881450A whole different sort of animal entirely.Big. Obnoxiously so.I like the infinitesimals more. They're cute and squishy.But you can't have one without the other.
>>16881449are you trying to tell me you don't believe in infinity? so you're a finitist?
>>16881453I'm not a math guy, but I always find it inexplicable and bizarre when I see infinities treated as if they were numbers. And then people will make arguments based on proofs involving these kinds of conflations, resulting in obvious nonsense.
>>16881457Are you trying to "win an argument" here?
>>16881457I like littles.
>>16881445Reread my post and read it carefully, bozo.
>>16881463Reread mine too, ho-ho.
>>16881443Functions is something Norman also questions. Norman is quite skeptical of the entire scheme.
>>16881459>where is the proof?>there is no proof.>i understand the proof.>the proof doesn't make sense.>does it make sense to you?^you are here
>>16881468I only see two proofs ever offered. Both are flawed.
>>16881468Let me know if you understand the difference between these two:>show that this equals a negativevs>show where the negative emerges Hint: there are actually two completely different questions.
>>16881465Done. It only reinforces my initial assessment that you're a goofus.
>>16881510You missed that other root. Negative numbers often confuse people like you.Pro-tip: Quadratics always have two roots. Sometimes, you can only imagine them.
>>16881382That is how negative integers work in computers. -1 is the same as the highest unsigned number, all bits set to 1, a sum of powers of 2 up to the maximum.
>>16881522Look kids, a pedant. It's OK to throw rocks at it.
>>16881517Which axis did I say the function crossed at x=0 anon?
at least it's not 0.(9) again
>>16881533Which root did you miss, Anon?
>>16879832Why is there 1+ 2x() in the second line?
>>16881548None. Or maybe all of them. Because that's not what I was describing.Somehow you managed to be even lower IQ than my low IQ joke.
>>16881574Pro-tip: In the xy-plane, there is a y-axis for every value of x. Think about that.>my low IQ jokePro-tip: Keep your day job.
>>16881468Anon?
>>16881475They appear to be two separate questions at first glance, but as you look deeper, they have the same cause.I give you the evens, then take away the naturals. You owe me the odds.Remember the original equation, subtract infinity from both sides. On the left, keep the original since subtracting infinity from it removes nothing. On the right, keep -0.08333... because Riemann and his gf Zeta like it.It just be like that.
>>16881919On the other hand, the summation of naturals is conceptually very simple. You can conceptually "see" the entire process all at once since its infinite repetition of the same thing over and over. You can also look at any individual operation along the way to infinity and examine it. Given that you can do this, and given that at no point along the process, is it possible for a negative to emerge, where does the negative actually come from?>subtracting infinity from infinityDo these kinds of operations even make sense for infinites without some sort of mental gymnastics to hide that they don't?
>>16881948We just covered this. It emerges from the misapplication of finite arithmetic to transfinites. Practically every line in the "simple" proof is an abuse of finite arithmetic.The core error though is assuming that the sum is finite in the first place. If it was, you'd be fine, but it's not.All one ever proves is that if the sum is finite, then it is -0.08333... . They never show the sum to be finite though. It is not.(P ^ ~P) => Q, every single time.
>>16881993Oh my mistake, I though I was talking to someone who accepted the "proof" given in this thread.
>>16881861By your logic, the function crosses the y axis everywhere so your reply was even more meaningless.
>>16882069Origins and constants of integration are completely arbitrary or set by the specified boundary condictions.And boy, our shared idiocy knows no bounds.
>>16882068Show me the "proof" presented in the thread and I'll comment on that too.Pro-tip: You still won't.
okay i'll throw a bone to the ones seething itt. the reals extend to infinity. the reals can also be bent into a circle, such that +infty = -infty. whenever you get a diverging sum to +infty, you can equivalently interpret that +infty as -infty. this -infty can also be tuned such that it cancels out the (in limiting case) +infty of terms, leaving a negative residue. this is how 1+2+3+4+...+infty = negative, because the +infty is equivalent to -infty.
>>16882077What do you mean? Is this not a (faulty) "proof" presented in this thread?>>16879832
>>16882081There is no negative infinity here, only a positive one.
>>16882082The substitution in (2) provides an extra infinity to subtract in step (4).Finite arithmetic does not apply to transfinites. You have shown that if the series converges, it converges to this particular value.It does not converge. So you cannot perform finite arithmetic on it like you want to do.(P ^ ~P) => Q, every single time.
>>16881434Is it really okay to take out part of the series "in front" without increasing the lower "i=..." beneath the sigma to 2?Please be gentle, I'm just a depressed dropout that has suffered from low self esteem my entire life.
>>16882092Yea that makes sense actually. What does >(P ^ ~P) => Q,mean?
>>16881434You are subtracting y (which is defined as a provable divergent sum, aka infinity) from both sides.You can't. At least not without introducing a negative infinity.
>>16882097The extra 2 was distributed out and the index was adjusted accordingly.
>>16882098From a contradiction (the divergent series converges) all things follow (and it converges to -0.08333...).Logic is all you need for this one.
>>16881522Thank you for the laugh, Anon. Good on you.
>>16882097Idk how to write in pretty equation text but:>sum(2^i | i = 0 to inf)>1 + sum(2^i | i = 1 to inf)>1 + 2/2*sum(2^i | i = 1 to inf)>1 + 2*sum(2^(i-1) | i = 1 to inf)>Let u=i-1>1 + 2*sum(2^(u) | u = 0 to inf)>Uhhh let i = u, I guess>1 + 2*sum(2^(i) | i = 0 to inf)
>>16882097[math]\begin{align}\sum_{i=0}^\infty 2^i &= 1 + 2 + 4 + 8 + ... \\& = 1 + 2\left(1 + 2 + 4 + ...\right) \\& = 1 + 2\times \sum_{i=0}^\infty 2^i\end{align}[/math]
>>16882125Why did you keep >i=0 below the summation symbol if you're not starting at 0?
>>168821352^0 = 1
>>16882136>if you don't multiply a number, you get 1Not doing anything to 2 leaves you with 2.
>>16882156This.
this is the equivalent of[math]a = b\\a^2 = ab\\a^2 - b^2 = ab - b^2\\(a+b)(a-b) = b(a-b)\\a+b = b\\b+b = b\\2b = b\\2 = 1[/math]the limits of the operation just arent properly defined
>>16882221not even close.[math]0\neq\infty[/math]
>>16882125Oh, now I seeWhat a strange thingThanks for the effort
yeah that's not true, but pic rel is true
>>16882278[math]\zeta(s) = 2^s \pi^{s-1}\sin\left(\frac{\pi s}{2}\right)\Gamma(1-s)\zeta(1-s)[/math]We will use the following facts.[math]\begin{align}\sin\left(-\frac{\pi}{2}\right) &= -1 \\\Gamma(2) &= 1! = 1 \\\zeta(2) &= \frac{\pi^2}{6}\end{align}[/math]And thus[math]\zeta(-1) = 2^{-1}\cdot \pi^{-2}\cdot(-1)\cdot(1)\cdot\left(\frac{\pi^2}{6}\right) = -\frac{1}{12}[/math]But observe[math]\zeta(-1) := \sum_{i=1}^\infty \frac{1}{i^{-1}} = 1 + 2 + 3 + ... = -\frac{1}{12}[/math]Q.E.D.
>>16882434How about if you understand that adding positive numbers can never give you a negative number?How about if you understand that adding integers can never give you a fraction?
>>16882501If you accept that adding rational numbers can give you irrational numbers, andIf you accept that adding algebraic numbers can give you transcendental numbers, thenYou can accept that adding integers can give you rational numbers, andYour can accept that adding positive integers can give you negative answers.Any further questions?
>>16882504So lets see.> Adding rational numbers can give you irrational numbers.In the context of an infinite sum that is perfectly possible. Many examples.> Adding algebraic numbers can give you trascendental numbers.Again, yes. Some infinite series that add to pi are examples of this and the above.> Adding integers can give you rational numbers.Funny because integers are actually rational numbers. No wonder there.> Adding positive integers can give you negative answers.Nope. A positive integer sum is always a positve integer. You sound like you just want to babble pretending to make sense.
>>16882504All statements follow from a contradiction. son.All of them.
>>16881573Because the series expands to S = 1 + 2 + 4 + ...If you multiply it by 2 it becomes2S = 2 + 4 + 8 + ...If you add 1 at the start it becomes equal to the first series.1 + (2S) = 1 + (2 + 4 + 8 + ...)
>>16882562>All of them.Even the ones that don't?
>>16882632Especially those ones.
>>16882632Particularly those.(P ^ ~P) => Q, for every single Q.
>>16882599S = ∞2S = 2•∞ = ∞ = 3.14159265•S1+2S = 4+7SThis is fun.
>>16882641>for every single QEven for ~Q?
A mathematician and an engineer are at a party and they are both sitting 10m from a table with a nice cake on it. The engineer decides to place a bet. He claims he can get to the cake, by first walking 5m, then half of that, then half of that and so on. The mathematician knows this is impossible, he will never get there, so he accepts it prompty. The engineer than walks 5m, then 2.5m, then 1.25m, then 0.625m and then he simply stretches his arms and reaches for the cake, winning the bet.
>>16882656Exactly that one.
>>16882659>and then he simply stretches his arms and reaches for the cake,finding only a tortoise with cake breath.The mathematician laughs hysterically as blood gushes from what used to be the engineers hand."Laboratory skill issue" mocks the tortoise.
>>16882434Yes that function equals that, but then we need to understand that the continuation is analytic and thus required analyticity (probably) every where, so for divergent s where Re{s} < 1.the sum of natural is not -1/12, but the solution to this equation which satisfies convergence and is analytic everywhere does have an answer at -1.so you're abusing the equality sign by abusing the zeta symbol.That's not a proof dumbass.In fact the proof is trivial using weierstrass approximation theorem.
>>16882664Marvelous.
>>16882705Odin made the Counting numbers.Everything after that is man's hallucination.
>>16881382actually, putting yourself in a setting where that infinite sum does converge (2-adics) it's a valid proof and the sum really will converge to -1
>>16882221Actually there's a critical mistake on the 3rd to 5th lines. Since [math] a=b [/math], [math] a^2 = b^2 [/math], so in [math] a^2 - b^2 = ab -b^2 [/math] the LHS reduces to 0 and the RHS reduces to 0 resulting in [math] 0 = 0 [/math]Morever the step[math] (a+b)(a-b) = b(a-b) [/math][math] a+b = b [/math]neglects that such an operation can only be performed if [math] a\not= b [/math]. The uniqueness of the distributive property requires that the term being distributed is non-zero. If [math] a = b[/math] then [math] a + b \not = b [/math] is a possibility. Moreover the conclusion [math] 2= 1[/math] demonstrates that the assumption [math] a + b = b [/math] is false since it leads to a contradiction and hence we of course verify that [math] a + b \not= b [/math].What [math] \sum 2^n = -1 [/math] and its calculation is simply a demonstration that extended addition and multiplication to a divergent series is not well defined. In order for the typical operations of arithmetic on series to well defined, the series must be at least absolutely convergent. There are similar results to that series that are convergent but not absolutely convergent.
does this actually have any practical aplication? can i use -1/12 for a hedge fund?
let A(x) = 1/(1-x)^2 = 1 + 2x + 3x^2 + 4x^3 + ...thenA(x) - 4xA(x^2) = 1/(1+x)^2A(1) - 4A(1) = 1/4A(1) = -1/12so1+2+3+4+... = -1/12
>>16882943Once again, someone has shown that "if the sum converges, then it converges to -0.08333...".Unfortunately, the series diverges.
>>16882952Once again someone has shown their ignorance by declaring that the only possible definition of "convergence" is the one he learned in freshman calculus.
>>16882958> ∞ - 4•∞ = 0.25Dear god, it's retarded.
>>16882943A(1) = ∞ = 7•∞ - 6,so -6•∞ = -6 and ∞ = 1.Obviously, ∞, I mean A(1), is the magic Euler number.
>Hey, so I was just reading about the sum of the series (1 + 2x + 3x^2 + 4x^3 + dots), right? Turns out, it converges to **-0.08333...** at (x = 1). Pretty cool, huh(Sips coffee, raising an eyebrow) Okay, so, first off—**no**. That series doesn't converge at (x = 1). You can’t just plug (x = 1) in and expect a value. The series diverges! It goes to infinity!>Nah, man, that’s just what they want you to think. If you look at the series for **long enough**, you can totally "sum" it to something. Like, you know, that thing with **Ramanujan summation** or something? It's actually **-0.08333...**, trust me.(Leans forward, tilting his head)Oh, yeah? You “trust” me? You just quoted some random fact without understanding the whole context. That’s like me quoting Shakespeare just because I heard it on a TikTok. Doesn't mean I get the play.>No, no, I’ve read it online! It’s like some **zeta function** thing. You can totally get it. People **do** it all the time. It’s just, like, a different way to look at it. Like, it's **regularized** or something. I’m telling you, it's **real**.(Shrugs and puts his coffee cup down) So, let me get this straight. You’re telling me that you’re gonna take a series that doesn’t even **converge**, and you’re gonna "regularize" it into something that makes sense? That’s like trying to sell me a car that doesn’t even have wheels, and then you’re like, "Nah, bro, it’s still **street legal**.">(Smiling smugly) Well, you don’t know everything, do you? Some of these math nerds just "accept" it, and they use it all the time. So why not me, right?(Squints, considering) You want to quote stuff without understanding it, huh? Alright, you want some real fun facts? You ever heard of **Bessel functions**? I bet you’ve never even *seen* one outside a Wikipedia article.
>>16882974(Grabs a napkin, draws something messy) You’re just doing mental gymnastics to make yourself look like you know what you're talking about. What you’re doing is **not** math. It’s like you took a look at a complex proof, and then threw a bunch of random symbols in the air. Then you say, "Hey, look, it’s true!" It’s not.>(Defensive) No, man, you’re just stuck in the old way of thinking. I know about **analytic continuation** and how it’s used. Some of these things don’t have to “converge” in the traditional sense. It’s all about how you “interpret” them.(Smiling, leaning back)Yeah, but that’s the point, right? You can’t just “interpret” math however you feel. It’s like a car having four wheels **if you don't care about the car even being able to drive**. You’re taking the whole thing out of context, cherry-picking what fits your narrative, and ignoring the fact that **math doesn’t work that way**.>(Starting to get frustrated) But the **fact** is, people **use** it in **advanced** mathematics all the time! You know, like the **Zeta function** regularization stuff, right? They don’t care that it’s “divergent.” They just accept the result.(Grinning)You know what? You’re right. People **do** use regularization in some advanced ways, but here’s the kicker: **you** don’t get to just slap those results around without understanding **why** or **how**. You can’t just pretend you’re some kind of "math wizard" because you’ve read a few things. That's like me quoting lines from Shakespeare and saying I’ve “figured it out” after watching a movie once.
>>16882977>(Seething) You’re just jealous because you don’t know the “cool” advanced math stuff. Everyone’s so behind, and I’m ahead of the curve.(Laughs)No, I’m not jealous. I’m just **not pretending** that I understand something I don’t. You’re trying to play around with things you only half-understand. I’ve spent years studying this stuff. You can’t just brush it off because you found a Wikipedia article and a cool-sounding fact.(Shrugs)You want to quote infinity and say it’s a number? Go ahead. But the minute you try to use that in a real proof, you’re gonna get called out. And then you’ll just end up looking like a kid who read a magic trick and thought they knew how it worked.
>>16882943>letYou deserve what you tolerate.
>>16882092ramanujan summation works even under paraconsistent logic, you mentally ill baboon
>>16882109also it diverges under certain types of summations, and it converges under others, so on top of metally ill, you are also retarded and the embodyment of the Dunning-Kruger effect
>>16882974>—lol, lmao
>>16883066>>16883073As it's literally spelled out here >>16882974.Step-by-step.
>>16883073Storm, do you know what they call a series that converges to multiple values?Divergent.
>>16883066(Smiling, leaning back)Yeah, but that’s the point, right? You can’t just “interpret” math however you feel. It’s like a car having four wheels **if you don't care about the car even being able to drive**. You’re taking the whole thing out of context, cherry-picking what fits your narrative, and ignoring the fact that **math doesn’t work that way**.
**(Verse 1)**I want to talk about a sum,That seems to drive some people dumb,A series that just won't behave,Yet it gets a number from the grave.It’s 1 plus 2 plus 3 plus 4,You add and add, but it’s a bore!It’s divergent, it’s no joke,Yet they say it sums to—*wait, what?*—"Negative one twelfth," they provoke.**(Chorus)***But it’s not real!*That’s not the way sums are meant to feel,The terms don’t just "add" in some surreal appeal,It diverges, it explodes, but they still make it appeal,With Ramanujan and Zeta—oh, what a deal!**(Verse 2)**You know the story: Ramanujan, wise,Told the world some strange disguise,With series that seem wild and obscene,And now they claim ( A(1) ) can be *clean*.But trust me, mate, there’s no clean slate,The math just doesn't tolerate—That infinite sum, it won’t be tamed,No matter how much your Zeta’s named.**(Bridge)**Oh, the sum's been "redefined,"By theorems that have been combined,But deep down, we must agree,It’s a mess with no guarantee.It's a series, it’s not *real*—And no, it's not your magic meal,Just because you *summed* it "through"Doesn't mean it's *accurate* too.**(Chorus)***But it’s not real!*They try to prove with passion and zeal,That sums can be warped with some clever appeal,Using Zeta, or Ramanujan’s seal,But let’s stay grounded in what's ideal!**(Outro)**So take your "summation" and take your "proof,"But let’s not jump to the hoaxy roof,In math, there's beauty and truth that shows,Even when the infinite sum just *blows*.Just because a formula's famous and neat,Doesn't mean that *all* results can be sweet.
>>16883435god i hope ai kills the music industry. this is excellent
>>16883441>this is excellentAll in the prompt, but thnx.>god i hope ai kills the music industryI still need inspiration. My best unaided was a Jay-Z "99 Problems" rewrite as a BOfH.>so you gots login problems>i feels bad for you, son>i gots 99 password>and bitch, yours ain't oneHit me.
>>16883456All you niggers can't you see, can't you seeHow your crime's affecting our societyEvery time you errYou will blame the whitesThat makes you a waste of life!
>>16882646Except the point of that post was it assigned a finite value to an infinite sum. It isn't arbitrary like what you are suggesting.
>>16883499>It isn't arbitraryIt literally is. Do you really need me to show you the "proof" that not only is the sum -0.08333... , but also 0.08333... and thus 0 as well? Or can you figure out how stupid you you are acting without being made to look the fool?Again, probably.
>>16883510Nothing you wrote made any sense
>>16879802it came to him in a dream yet 99% os sci believe this lol>>/x
>158 posts>100 of them are from some retard who doesn't understand Ramanujan summation has exactly defined limits on its applicability and rules for manipulating the sum, which prevent different people assigning different values to the same infinite sum, let alone him understanding how they're tied to the mathematical meaning behind such a sum
>>16883517>Nothing you wrote made any senseTo you.
>>16883625>(Seething) You’re just jealous because you don’t know the “cool” advanced math stuff. Everyone’s so behind, and I’m ahead of the curve. (Laughs)No, I’m not jealous. I’m just **not pretending** that I understand something I don’t. You’re trying to play around with things you only half-understand. I’ve spent years studying this stuff. You can’t just brush it off because you found a Wikipedia article and a cool-sounding fact. (Shrugs)You want to quote infinity and say it’s a number? Go ahead. But the minute you try to use that in a real proof, you’re gonna get called out. And then you’ll just end up looking like a kid who read a magic trick and thought they knew how it worked.
>>16883625he's a retard that skimmed over some reddit thread explaining the principle of explosion and now believes himself to be a genius beyond all mortals, or some shit, the nigger likely doesn't even know about paraconsistent logic
Math version of Emperor's new clothes
>>16883952The person you think is the emperor is not the emperor.
>>16883966Doesn't matter, I've seen his willy.
>>16883972but have you sucked it?
>>16883936Neither do you. You almost read about it, once. But you didn't.Did you, Storm?
>>16883936>paraconsistent logicThe divergent sum will sometimes almost possibly sort of converge, maybe.Classic cope.
>>16883936[Narrator]: The Anon is using a rare form of the many worlds interpretation of barely-consistent logic where he hopes for the possibility there could be a universe where he might have a chance of not being completely wrong for once.
>>16880084This is the objectively correct answer.
>>16882666> feverish cope hallucinationRemember guys.If your kids try to become mathematicians it is imperative that you beat them until they come back to their senses.
>>168798021. Go to Google2. Look up "Riemann zeta function and divergent series"
"...." is not real.Hello, I would like to have "....." apples.
>>16882125But are those two even the same operation?for n = 2, and i = 2, n^i = 4, but once the operation has been performed you can't know whether or not n was +2 or -2, and so therefore the substitution isn't reversible in all instances of an infinite sequence and therefore isn't a universal solution.
>>16884789I don;t want to
>>168847893. Read the results to the illiterate (YOU).
>>16879802The Numberline is an Ouroboros eating it's own tail. That's why it circles back to the negatives.
>>16879863It's fucking off dude because you've turned it on and off infinite times so you burnt it the fuck out. Moron.
Sci... Sci is defeated.
>>16886004It's actually on because, just prior to the 2-minute mark the switch will have been flicked back and forth so many times that the friction generated, to say nothing of the amount of energy put into the system will cause the entire structure to incandescence and ultimately melt, if not outright vaporize. More likely the switch itself would break first, following by the wiring melting. However, shortly after the 2 minute mark, it will burn itself out.
>>16885756You're sort of close, but not really.https://en.wikipedia.org/wiki/Real_projective_line
>>16885756>>16886030>projective lineJust [math] S^1 [/math] in stereographic coordinates.
