𧡠Untitled Thread
Anonymous at Sun, 26 May 2024 09:39:12 UTC No. 16193819
Is this based on any reality? Why would someone claim that the result is -1/12?
Anonymous at Sun, 26 May 2024 10:37:34 UTC No. 16193932
>>16193819
Ramanujan was nothing special
Anonymous at Sun, 26 May 2024 10:59:34 UTC No. 16193957
let
f(x) = 1/(1-x)^2
= d/dx 1/(1-x)
= d/dx (1+x+x^2+x^3+...)
= 1+2x+3x^2+...
then
f(x) - f(-x) = 1/(1-x)^2 - 1/(1+x)^2
= 4x/(1-x^2)^2
= 4xf(x^2)
f(1) - f(-1) = 4*1*f(1^2)
f(1) = -1/3 * f(-1)
= -1/3 * 1/(1-(-1))^2
= -1/12
but also
f(1) = 1+2*1+3*1^2+... = 1+2+3+...
Anonymous at Sun, 26 May 2024 14:51:46 UTC No. 16194210
>>16193819
> this series fluctuates between 0 and 1 while never converging
> that must mean it's equal to 0.5
Anonymous at Sun, 26 May 2024 15:06:41 UTC No. 16194222
>>16193819
There's an anecdote about this series I've been trying to find. Some famous professor or lecturer puts this expression on the board and says something like "Of course, as anyone knows..."
Anonymous at Sun, 26 May 2024 15:10:13 UTC No. 16194224
>>16193819
This is the power of so called "analytic continuation". It's what happens when people unironically believe in "complex numbers". From "i is the square root of -1" you go to "1+2+3+... = -1/12". Ex falso quodlibet.
Anonymous at Sun, 26 May 2024 15:12:21 UTC No. 16194230
>>16193819
Thereβs a great numberphile vid on this. Terence Tao and others(?) releases a paper, and demonstrates a connection on WHY this happens. Turns out, the answer is based on regulators, where in this case the regulator is very βabruptβ, but if u use a different regulator, the -1/12 pops right out.
Anonymous at Sun, 26 May 2024 15:13:21 UTC No. 16194231
>>16194230
A fairly recent discovery too
Anonymous at Sun, 26 May 2024 15:14:34 UTC No. 16194236
>>16194230
What's a regulator, anon?
Anonymous at Sun, 26 May 2024 15:23:56 UTC No. 16194255
>>16193819
the -1/12 result is interesting but as far as I know those results use the equals sign with a far looser interpretation. This series clearly isn't directly equal to -1/12 and would diverge into infinity.
Anonymous at Sun, 26 May 2024 16:21:52 UTC No. 16194329
>>16193819
You cannot add up an infinite amount of numbers (except 0) and sum to an objective value. This is based on a fictional reality called "mathematicians making shit up because they got bored".
Anonymous at Sun, 26 May 2024 16:58:28 UTC No. 16194374
>>16194236
A device that sets and limits voltage in a system
Anonymous at Sun, 26 May 2024 17:07:05 UTC No. 16194383
>>16193819
this is what happens when mix non-numbers (i, β) in with math formulas.
>>16194230
yeah I'm sure they also have videos explaining that a woman is a man who demands different pronouns. doesn't make it anything more than what it is: deliberate obfuscation of reality.
Anonymous at Sun, 26 May 2024 17:35:55 UTC No. 16194435
>>16194236
It's something similar to a weight function (but doesn't add up to 1). So you do part of the series right? 1+2+3+4+5+...+N, where you stop at n. Stopping at N, it looks like the series should tend to infinity. That sum to n is basically the same as the ininite series, but with each term is multiplied by 1, except for all numbers after N are multiplied by 0, so the series is 1*1 + 2*2 + 3*1 + ... n*1 + (n+1)*0 + (n+2)*0 +...
So that regulator function of just 1's and then suddenly 0's is very abrupt. But suppose you use a different function that is much smoother, but will tend to approach this abrupt step function when you take a limit.
Now, do the infinite sum with the regulator, then result is something like A - 1/12, where the value of A depends on the regulator you choose. If you do the limit part, you see that A equals 0.
Really crazy they seem to have tamed the infinity
Anonymous at Sun, 26 May 2024 19:08:43 UTC No. 16194567
>>16193819
Rules for addition which work for finite numbers do not usually translate to something sensible when you're talking about an infinite series. The exception is sometimes when the series is convergent, and more often when it's absolutely convergent.
Anonymous at Sun, 26 May 2024 21:03:05 UTC No. 16194716
Anonymous at Sun, 26 May 2024 21:06:18 UTC No. 16194722
>>16193819
This is the math equivalent of dark matter. Some pajeet decided "move over" numbers during the addition process to get the answer of -1/12.
Retarded and typical of their kind.
Anonymous at Sun, 26 May 2024 21:31:06 UTC No. 16194774
Imagine that you're summing integers in order and the sum gets bigger and bigger. Then suddenly when you reach infinity you somehow subtract all the previous numbers you added, and also 1/12 extra. This is some wild stuff.
Anonymous at Sun, 26 May 2024 21:41:29 UTC No. 16194788
>>16193819
https://www.youtube.com/watch?v=bea
Anonymous at Sun, 26 May 2024 21:44:54 UTC No. 16194791
>>16194716
>>>/reddit/
https://arxiv.org/abs/2401.10981
Anonymous at Mon, 27 May 2024 03:43:06 UTC No. 16195216
>>16194791
>>16194788
>>16194774
Marvelous. I was just studying QED these past few days and got to the part where every caculation spits out infinities so physicists cope and say they only want differences above a ground level, which is infinite.
Then we got to calculate probabilities, and probabilities where also infinite so they said we only measure probability differences, as these can be less than 100%
Anonymous at Mon, 27 May 2024 06:52:34 UTC No. 16195379
>>16193819
Basically if the sum was convergent in the traditional sense (it's not), then the value it would converge to is -1/12.
Anonymous at Mon, 27 May 2024 09:35:35 UTC No. 16195514
>let's take this infinite sum
>well,actually let's take up to N instead
>but if you take enough shrooms you can pretend to multiply by 1 to N and 0 beyond!
>lmao let's just random completely unrelated calculations
>The regulator's swinging pendulum
https://www.youtube.com/watch?v=qij
Anonymous at Mon, 27 May 2024 09:45:27 UTC No. 16195531
>>16193819
>Is this based on any reality? Why would someone claim that the result is -1/12?
It's based on real mathematical relationships that are implicit in that series. It makes people seethe because the conclusion is incongruent with the regular understanding of addition, but the sum of an infinite series is something completely abstract, anyway.
Anonymous at Mon, 27 May 2024 09:50:25 UTC No. 16195537
>>16193819
Filtered by a high-IQ social reductio ad absurdum. Ramanujan knew how to rock the Westoid boat while seeming to be the victim of a rocking boat.
Anonymous at Mon, 27 May 2024 10:02:01 UTC No. 16195554
>>16193819
Why do schizophrenic get so triggered about a function that takes as an input an infinite series and spits out a number? Do you also freak about about SHA256?
Anonymous at Mon, 27 May 2024 10:05:18 UTC No. 16195561
>>16195554
Only certified midwits don't get "triggered" by something so blatantly violating intuition, common sense and the normal understanding of something as basic as a sum.
Anonymous at Mon, 27 May 2024 10:05:26 UTC No. 16195562
>>16195216
aren't those "infinities" purely the product of calling the electron a point charge?
Anonymous at Mon, 27 May 2024 10:07:09 UTC No. 16195566
>>16195554
>Do you also freak about about SHA256?
Hashes make perfect logical sense.
You can view the code and see how it generates a unique hash from file binary data.
The ramanujan claim on the other hand is nonsensical.
Anonymous at Mon, 27 May 2024 10:10:13 UTC No. 16195567
>>16195562
>aren't those "infinities" purely the product of calling the electron a point charge?
Yep, you're basically right. So the guy you're replying to is wrong.
Electrons have size and mass. They aren't volume-less points. Point modelling is just an approximation. Same with probability clouds for modelling electron orbits.
Anonymous at Mon, 27 May 2024 10:10:40 UTC No. 16195568
>>16195566
His point went way over your head.
Anonymous at Mon, 27 May 2024 10:14:54 UTC No. 16195570
>>16195568
>His point went way over your head.
No it didn't anon...
Please explain how it did.
Anonymous at Mon, 27 May 2024 10:15:28 UTC No. 16195571
>>16195570
>No it didn't anon...
Then explain what you think it was.
Anonymous at Mon, 27 May 2024 10:16:30 UTC No. 16195573
>>16195571
>Then explain what you think it was.
>>16195566
Now explain yourself anon.
Anonymous at Mon, 27 May 2024 10:17:15 UTC No. 16195574
>>16195573
Men, most people on nu-chan are barely sentient...
Anonymous at Mon, 27 May 2024 10:27:55 UTC No. 16195586
>>16195574
That's not an argument anon.
Hash codes actually make sense because they aren't doing what ramanujan is doing.
They aren't adding an infinite number of positive integers and claiming it is equal in value to minus one twelfth.
Also you're equivalencing and equation with an algorithm. They are very different things.
An equation isn't a
Anonymous at Mon, 27 May 2024 10:31:35 UTC No. 16195592
>>16195586
An equation isn't an algorithm.
An equation is asserting that two expressions are equal. Those expressions can involve infinite operations.
An algorithm is a finite number of steps in order to achieve some effect or goal.
Anonymous at Mon, 27 May 2024 10:50:53 UTC No. 16195603
>>16195586
>>16195592
Ok, retard. Good luck.
Anonymous at Mon, 27 May 2024 11:02:10 UTC No. 16195612
>>16195603
Lol, that's not a valid argument "retard" anon.
Do you have one?
Nope.
You have provided absolutely no argument for your position.
Anonymous at Mon, 27 May 2024 11:04:38 UTC No. 16195614
>>16195612
Every single thing you spouted is nonsense. Arguing with a thumb-sucking moron who makes irrational grunting noises seems counter-productive.
Anonymous at Mon, 27 May 2024 11:11:31 UTC No. 16195626
>>16195614
>Every single thing you spouted is nonsense.
Such nonsense that you can't even explain why it's nonsense...
>Arguing with a thumb-sucking moron who makes irrational grunting noises seems counter-producti
Or, you're the thumb-sucking Dunning-Kruger moron with no argument.
Where's your argument anon?
Oh, you have none.
Anonymous at Mon, 27 May 2024 11:12:20 UTC No. 16195627
>>16195626
https://en.wikipedia.org/wiki/Hash_
>A hash function is any function that can be used to map data of arbitrary size to fixed-size values
Anonymous at Mon, 27 May 2024 11:15:11 UTC No. 16195633
>>16195561
>violating intuition
The mark of the self absorbed brainlet with God complex
Anonymous at Mon, 27 May 2024 11:15:17 UTC No. 16195635
>>16195627
Aha, and how does that disprove anything I've said anon?
Anonymous at Mon, 27 May 2024 11:16:11 UTC No. 16195637
>>16193819
Because the error result is common in math and they assume that this is important and not just a mathematical error and a limitation of the symbolic language used.
Renaissance mathematicians would laugh at this shit.
Anonymous at Mon, 27 May 2024 11:19:37 UTC No. 16195641
>>16195635
The Ramanujan summation for that series can be framed as a hash function in accordance with the definition I just quoted. This contradicts your irrelevant and incoherent screeching about muh algorithms and muh equations and muh finite number of steps.
Anonymous at Mon, 27 May 2024 11:20:31 UTC No. 16195642
>>16195633
>>violating intuition
>The mark of the self absorbed brainlet with God complex
Check out my new equation anon.
((2x2+2)/2)+((3x3+3)/3)+((3x3+3)/3)
It makes sense because ramanujan said it makes sense.
Just because.
Anonymous at Mon, 27 May 2024 11:22:21 UTC No. 16195644
>>16195633
Ramanujan would have agreed with my statement because he wasn't a dead-in-the-water midwit like you. He relied on intuition quite a bit.
Anonymous at Mon, 27 May 2024 11:22:53 UTC No. 16195645
>>16194791
>Robert Smith
Anonymous at Mon, 27 May 2024 11:26:11 UTC No. 16195651
>>16195641
>The Ramanujan summation for that series can be framed as a hash function
An equation isn't an algorithm anon lol.
>>16195641
>This contradicts your irrelevant and incoherent screeching about muh algorithms and muh equations and muh finite number of steps.
You equating two things that aren't the same anon.
Also
"An equation is a statement that two things are equal in value. A function is a mapping from one set to another such that nothing in the first set is mapped to more than one thing in the second set. The two are wholly different concepts; an equation is never a function, and vice-versa."
You're equating things that aren't the same.
That's all you're doing.
Anonymous at Mon, 27 May 2024 11:27:42 UTC No. 16195654
>>16195651
>An equation isn't an algorithm anon lol.
Why are you still talking about algorithms, mouth breather? We're talking about functions now.
>You equating two things that aren't the same anon.
It's equating the application of the function to the function's value for that argument, though. Those are equal by definition. You sure are fucking stupid.
Anonymous at Mon, 27 May 2024 11:35:24 UTC No. 16195664
>>16195654
>Why are you still talking about algorithms, mouth breather? We're talking about functions now.
Hash programs are algorithms executed as finite incremental code functions anon.
1 + 2 + 3 + β― + β = -1/12 is an equation with infinite operations...
>>16195654
>It's equating the application of the function to the function's value for that argument, though. Those are equal by definition. You sure are fucking stupid.
1 + 2 + 3 + β― + β = -1/12
An equation is never a function anon.
Has anyone used this equation to Hash data?
Nope...
Would it be of any use to Hash data?
Nope...
Anonymous at Mon, 27 May 2024 11:37:35 UTC No. 16195667
>>16195664
Ok, fucktard. I just wanted to demonstrate why it's useless to treat your likes as if they are human and capable of understanding.
Anonymous at Mon, 27 May 2024 11:45:35 UTC No. 16195673
>>16195667
>Ok, fucktard.
Calm down autistic genetic reject.
>I just wanted to demonstrate why it's useless to treat your likes as if they are human and capable of understanding.
Lol, you equivalence completely different things that aren't at all interchangeable repeatedly like an idiot.
You'll never learn.
How many decades will it take you to realize that an equation isn't an algorithm or a function?
How many decades will it take you to realize that 1 + 2 + 3 + β― + β = -1/12 can't be used to Hash data?
How many decades will it take you to realize that 1 + 2 + 3 + β― + β = -1/12 has absolutely nothing to do with reality and thus has no practical use in anything?
How many decades will it take you realize that you AREN'T intelligent?
How long anon?
Anonymous at Mon, 27 May 2024 11:46:23 UTC No. 16195674
>>16195673
Didn't read. Arguing with morons is useless. The correct course of action is to shit all over them.
Anonymous at Mon, 27 May 2024 11:47:29 UTC No. 16195676
>>16195674
You read it.
It upsets you.
You have no valid argument.
You are not smart anon.
Anonymous at Mon, 27 May 2024 11:49:13 UTC No. 16195677
>>16195676
There isn't any debate going on. I explained to you what that guy meant by his post. You still failed to grasp it. You may continue to "debate" the voices in your head now.
Anonymous at Mon, 27 May 2024 11:57:14 UTC No. 16195679
>>16195677
>There isn't any debate going on
Aha, sure anon... sure...
>I explained to you what that guy meant by his post
You are that guy anon.
>You still failed to grasp it. You may continue to "debate" the voices in your head now.
Lol. You failed to grasp that an equation isn't an algorithm or a function.
The Ramanujan Summation: 1 + 2 + 3 + β― + β = -1/12 doesn't make any sense because it is an EQUATION.
Anonymous at Mon, 27 May 2024 12:01:05 UTC No. 16195683
>>16195679
>You are that guy anon.
Mental illness.
Anonymous at Mon, 27 May 2024 12:12:44 UTC No. 16195692
>>16195683
It's sad when you're called out for your bullshit aye anon?
Anonymous at Mon, 27 May 2024 12:16:11 UTC No. 16195694
>>16195692
What's sad is that many mentally ill people don't know they're mentally ill.
Anonymous at Mon, 27 May 2024 12:29:05 UTC No. 16195706
>>16195694
>What's sad is that many mentally ill people don't know they're mentally ill.
Lol. You failed to grasp that an equation isn't an algorithm or a function.
The Ramanujan Summation: 1 + 2 + 3 + β― + β = -1/12 doesn't make any sense because it is an EQUATION.
Don't get upset at me for that.
Anonymous at Mon, 27 May 2024 12:31:14 UTC No. 16195710
>>16195642
What do the dots mean? What does the equal mean?
Mathematically illiterate people are the dumbest
Anonymous at Mon, 27 May 2024 12:42:41 UTC No. 16195721
>>16195706
I already explained to you that this equation simply equates application of a function to an argument, with the value of the function for that argument.
Anonymous at Mon, 27 May 2024 12:52:27 UTC No. 16195731
>>16195721
>>16195710
You failed to grasp that an equation isn't an algorithm or a function.
The Ramanujan Summation: 1 + 2 + 3 + β― + β = -1/12 doesn't make any sense because it is an EQUATION.
Anonymous at Mon, 27 May 2024 13:01:38 UTC No. 16195737
>>16195731
You're a meat-based language model.
Anonymous at Mon, 27 May 2024 13:02:45 UTC No. 16195739
>>16195710
Hey, look at this anon!!!
OMG
1x2x3x4x...= -89^23
Ramanujan said so!
Another cool equation that doesn't equate because it's bullshit.
Anonymous at Mon, 27 May 2024 13:04:04 UTC No. 16195741
>>16195737
5/9 = 124
Ramanujan said so!
Another cool equation that doesn't equate because it's bullshit.
Anonymous at Mon, 27 May 2024 13:12:40 UTC No. 16195752
>>16195741
S([1, 2, 3, 4, ...]) = -1/12
Where S is Ramanujan summation. Seethe.
Anonymous at Mon, 27 May 2024 13:30:35 UTC No. 16195765
>>16195752
S([2, 4, 8, 16, ...]) = -2/3
Where S is another Ramanujan summation. Seethe.
Anonymous at Mon, 27 May 2024 13:38:05 UTC No. 16195775
>that one monkey who can't into sums and just keeps sperging out
the absolute state of this board
Anonymous at Mon, 27 May 2024 13:40:41 UTC No. 16195779
>>16195775
You failed to grasp that an equation isn't an algorithm or a function.
The Ramanujan Summation: 1 + 2 + 3 + β― + β = -1/12 doesn't make any sense because it is an EQUATION..
Anonymous at Mon, 27 May 2024 13:47:07 UTC No. 16195789
>it just keeps repeating the same incoherent drivel like a bot over and over again
I think I broke it. ;^(
Anonymous at Mon, 27 May 2024 14:08:14 UTC No. 16195820
>>16195789
β+β+β+β+β.....= 99/109
Anonymous at Mon, 27 May 2024 14:44:43 UTC No. 16195889
>>16195835
>Why are they like this?
100 = -2
Why are they like this?
Anonymous at Mon, 27 May 2024 15:18:45 UTC No. 16195956
>>16195889
Why doesn't it make sense for a function taking a sequence to have a value of -1/12 for that sequence?
Anonymous at Mon, 27 May 2024 15:19:40 UTC No. 16195957
>>16195567
electrons in qed are described as points. I mean they have wavefunctions and all that but that doesnt describe their size, which is still a point.
If an electron has size it would have additional structure, such as vibrational and rotational modes
Anonymous at Mon, 27 May 2024 16:38:26 UTC No. 16196089
>>16195956
You're just arbitrarily saying that one number equals another when it doesn't lol.
>>16195957
>electrons in qed are described as points. I mean they have wavefunctions and all that but that doesnt describe their size, which is still a point.
Yep, your confusing modeling with reality anon.
And yes, every particle has a de broglie wavelength. Even macroscopic objects like bowling balls.
>If an electron has size it would have additional structure, such as vibrational and rotational modes
Electrons have spin, mass and size etc.
This has all been confirmed with collisions and particle accelerator experiments.
Anonymous at Mon, 27 May 2024 16:54:09 UTC No. 16196114
>>16196089
>your confusing modeling with reality anon.
Im not confusing anything, im literally describing what a model says.
I dont know what you are hinting at by name dropping De Broglie. Ok?
Spin and Mass are not vibrational or rotational "modes". Well, one rotational mode at best, and nothing vibrational.
There is simply nothing observed on electrons that is explained by requiring them to have a size. You introduce something superfluous that explains nothing and would likely have theoretical consequences not reflected in reality.
You'd have to answer things like the speed of sound in the electron volume, the density, the elasticity of the electron. So far no one has even succeeded at spinning an electron like it was a basketball (except for its intrinsic spin at a permanent value)
Anonymous at Mon, 27 May 2024 17:11:04 UTC No. 16196136
>>16196114
>Im not confusing anything, im literally describing what a model says.
Modelling isn't reality anon haha.
Electrons aren't volume-less points.
>Spin and Mass are not vibrational or rotational "modes". Well, one rotational mode at best, and nothing vibrational.
Electrons have spins and vibrate anon...
Just as Protons and Neutrons do.
Because...
They have mass and volume.
>I dont know what you are hinting at by name dropping De Broglie. Ok?
Collisions between all particles with mass and volume result in wave-like behavior. That's the point of mentioning it anon.
>You'd have to answer things like the speed of sound in the electron volume
Lol, You only need to answer things you can measure anon. And you can measure the mass, volume, spin, vibration and energy of an election.
Anonymous at Mon, 27 May 2024 17:26:54 UTC No. 16196152
>>16196136
>Electrons have spins and vibrate anon..
Electrons dont vibrate
>>16196136
You cant measure the vibrations nor the volume. Measuring vibrations would be akin to measuring the speed of sound, so i dont know why you deny this while saying it is possible
Anonymous at Tue, 28 May 2024 06:28:44 UTC No. 16197200
>>16196152
Electrons vibrate all the time
Anonymous at Tue, 28 May 2024 09:27:46 UTC No. 16197432
>>16193819
wasnt that just his way of showcasing the flaws of calculus?
Anonymous at Tue, 28 May 2024 09:56:18 UTC No. 16197451
>>16197432
>wasnt that just his way of showcasing the flaws of calculus?
Nope, he was actually that stupid.
DoctorGreen !DRgReeNusk at Tue, 28 May 2024 16:31:42 UTC No. 16197854
>ultraviolet catastrophe but math
holy mother of entropy, these fools never learn :v
Anonymous at Tue, 28 May 2024 17:01:00 UTC No. 16197888
>>16195562
>aren't those "infinities" purely the product of calling the electron a point charge?
Theres all kinds of infinite summation and integration in QFT.
Integrals over infinite time, over infinite space, over an infinite uncountable spectrum of states, over infinite paths. You dont get a break
>>16194435
I just saw that numberphile video. Very impressive, he found a way to sum up the infinite non-converging series and get a finite result, and the sum is an actual sum, it isnt Ramanujan summation or some funny function or perversion of the sign +.
Apparently there are different ways to do the sum and only a family of methods gives the finite results, every other method gives out infinite. The finite result is only 1 number, i hope this kills all these infinite series/integrals in QM
Anonymous at Tue, 28 May 2024 17:59:23 UTC No. 16197966
>>16195739
>1x2x3x4x...= -89^23
actually 1*2*3*4*...=root(2Ο)
Anonymous at Tue, 28 May 2024 18:01:07 UTC No. 16197969
>>16195765
>S([2, 4, 8, 16, ...]) = -2/3
actually 2+4+8+16+32+64+...=-2
Anonymous at Tue, 28 May 2024 18:04:25 UTC No. 16197974
>>16193932
He was especially FAT.
Anonymous at Tue, 28 May 2024 18:08:39 UTC No. 16197980
>>16193957
My nigga did you just replace a non-continuous function with a Taylor polynomial, without stating the necessary restrictions on the domain, then attempting to sub in values that should result in undefined range.
Good bait have a (You)
Anonymous at Tue, 28 May 2024 18:15:22 UTC No. 16197988
>>16194210
Applying calculus rates of change to mathematical fluctuations is choosing applied math, then being retarded and applying math back to math.
However, this is considered high level mathematics by some. The ideation here would be to look for patterns or anomalies in the fluctuation rate and values in comparison to the others, number position, prime distancing, etc... Using math to analyze math is an infinite bag of tools, to analyze an infinite bag of systems.
Calling it 0.5 might be lazy, but I wouldn't consider it wrong either, there are always layers of abstraction in all sciences.
Accepting that there is a layer of abstraction where this is correct, but technical layers where it is wrong, is one of the signs of being capable of higher order thought. This is the type mentality that the bulk majority of the population is unable to accomplish. Mathematics at it's core is a large stack of hypotheticals built out of logic. It seems there are vast gaps in humans for the quantity of possible stacks that they can mentally accommodate before the ability to understand the root problem is inhibited.
Low IQ individuals can handle very few of these stacks.
High IQ like Terrence Tao, may not even have an upper limit, as we can't directly study his brain at this time, but it is easily magnitudes above the average human.
Anonymous at Tue, 28 May 2024 18:17:03 UTC No. 16197990
>>16197980
tl;dr a sneaky way of doing inf-inf
Anonymous at Tue, 28 May 2024 18:26:30 UTC No. 16197999
>>16197980
Give him a slice of pi.
Man, my school almost made pi our mascot.
NGL, kinda wish they did, because they chose something way more gay. (Unicorn)
Anonymous at Tue, 28 May 2024 18:31:23 UTC No. 16198012
Can you explain this like I was five. So is it saying that if you have one apple in a basket, two apples in the next basket, three in the third and so on, the contents of all of those baskets is equal to negative 1/12 of an apple? What have you smoked? I will never understand this s*it.
Anonymous at Tue, 28 May 2024 18:38:00 UTC No. 16198017
>>16198012
If you dig through the proofs for such statements there is always an error of some kind. Usually dividing by zero or treating infinity as a constant.
Anonymous at Tue, 28 May 2024 18:41:38 UTC No. 16198025
>>16198008
they actually did a sum of the infinite series, it is a sum in every right, not some function falsely called a sum
Anonymous at Tue, 28 May 2024 18:42:37 UTC No. 16198026
https://en.wikipedia.org/wiki/Diver
https://en.wikipedia.org/wiki/CesΓ r
https://en.wikipedia.org/wiki/Borel
Anonymous at Tue, 28 May 2024 18:44:13 UTC No. 16198027
>>16198017
any examples?, not him but i would not want to just take your word for it
Anonymous at Tue, 28 May 2024 18:52:06 UTC No. 16198040
>>16198026
Theres infinite ways to do the sums, some get finite results, the others infinite. Good thing is the finite result is only one result
Anonymous at Tue, 28 May 2024 19:03:00 UTC No. 16198064
>>16198027
Sure. Here is one and one only.
The most commonly used proof of the -1/12 nonsense starts with the following as the first step.
s=1-1+1-1...
s=1-(1-1+1...)
s=1-s
2s=1
s=1/2
Of course this is totally wrong. You can't assign a series a symbol and then do algebra on it without first knowing it's a convergent result. s is not convergent (proof is left as an exercise to the reader) so if you use it this way everything you're doing afterwards is wrong and will give you only garbage results like 1+2+3...=-1/12.
Anonymous at Tue, 28 May 2024 19:19:26 UTC No. 16198102
>>16198064
its a problem with infinities that you can add or susbtract from it and its still infinity, shares with this something that zero has, anything multiplied by zero is zero, in some ways you lose information.
But these series have a unique feature and that is that the sums, when done in a way that they add up to a finite number, always give you the same finite number, its not some random finite number.
I think there will be a day when this will be seen as a trivial matter, like zero is to us, number zero must have been like magic back in the day.
Anonymous at Tue, 28 May 2024 19:30:17 UTC No. 16198119
>>16198102
>its a problem with infinities that you can add or susbtract from it and its still infinity
It's not a problem exactly. The definition of addition and subtraction do not allow for infinities, so such expressions are meaningless.
Anonymous at Tue, 28 May 2024 19:33:01 UTC No. 16198122
>>16198119
I say they are worthy objects in their own with their own properties. I think mathematics is just getting a hang of them, its unfair to compare infinities to finite numbers, they wont behave like them but still have logical rules
Anonymous at Tue, 28 May 2024 19:35:03 UTC No. 16198125
>>16198122
Sure if you want to retool the fundamentals of arithmetic to include infinity as a constant, go ahead and publish your findings. Then just wait for your Fields medal in the mail.
Anonymous at Tue, 28 May 2024 19:40:12 UTC No. 16198129
>>16198125
im not going to do shit, other people are doing the work tho
Anonymous at Wed, 29 May 2024 04:38:34 UTC No. 16198660
>>16198012
In a few hundreds years people will laugh at the stupidity of today's mathematicians
Anonymous at Wed, 29 May 2024 16:47:19 UTC No. 16199281
>>16198660
That has never happened. People always praise past mathematicians for their discoveries, being the giants and the shoulder etc.
Anonymous at Wed, 29 May 2024 18:34:10 UTC No. 16199417
>>16193957
None of that has meaning.
Anonymous at Wed, 29 May 2024 22:58:16 UTC No. 16199844
>>16195514
>>16193819
>>16194222
>>16194224
Infinity doesn't exist
-1/12 exists
Therefore 1+2+3+...=-1/12
Anonymous at Thu, 30 May 2024 06:21:47 UTC No. 16200359
>>16193819
Only the basic idea of adding one discrete thing onto another, in sequencial steps, is based on real things. However, the act of repeating it forever to reach a final result isn't anything we could ever achieve, adding to infinity would take an infinite amount of time, so in that sense, it is not real.
It's an exercise in imagination
Anonymous at Thu, 30 May 2024 15:33:24 UTC No. 16200911
>>16193819
Ramanujan is not using the equals sign the same way you do. That's why you read the entire thing not just an excerpt you find on the internet. An infinite sum is not defined the same way a finite sum is, by saying that the sum diverges you are assigning it a specific value. You've already deviated from the bog standard meaning of the equals sign. All that Ramanujan is doing is assigning another value to the infinite sum and arguably it's much more meaningful than just saying it diverges.
>>16193932
He was one of the greatest mathematicians ever born and independently rediscovered concepts that each were the magnum opus of multiple greatest-of mathematicians. If he lived a full life he likely would've dwarfed any mathematician in history. Sure, if you were familiar with Gauss, Euler and MacLaurin then the idea of a Ramanujan sum might pop up in your mind but completely out of the blue? The closest is Archimedes stumbling upon would-be integral calculus.
Anonymous at Thu, 30 May 2024 16:04:07 UTC No. 16200952
>>16200911
Hello poojeet, care to discuss his actual contributions or do you want to keep shitting up my board?
Anonymous at Fri, 31 May 2024 04:47:06 UTC No. 16202008
>>16200911
Good morning sir
Anonymous at Fri, 31 May 2024 04:55:12 UTC No. 16202022
>>16194255
>the -1/12 result is interesting but as far as I know those results use the equals sign with a far looser interpretation
>>16200911
>Ramanujan is not using the equals sign the same way you do.
This is the most bizarre interpretation of what's happening here and I see it all over the internet. Obviously it's the definition of infinite summation that's different here (from the standard limit of partial sums definition) than the definition of equality (the latter would be very confusing).
Anonymous at Fri, 31 May 2024 14:52:39 UTC No. 16202558
>>16193819
no, maths is all abstract
this just happens to be the most useful definition, if the context in which you are trying to solve a problem does not allow for this, you can happily ignore it
Anonymous at Fri, 31 May 2024 18:36:09 UTC No. 16202814
>>16194224
There's nothing magical about complex numbers anon it is just an ordered pair of real numbers.
Anonymous at Sat, 1 Jun 2024 03:10:08 UTC No. 16203498
>>16194329
sure we can
Anonymous at Sat, 1 Jun 2024 04:12:14 UTC No. 16203568
>>16193819
its a trick of the light
Anonymous at Sat, 1 Jun 2024 21:24:15 UTC No. 16205181
>>16193819
I'm a biologist who can't do math but I say it's fake and gay
Anonymous at Sat, 1 Jun 2024 21:26:18 UTC No. 16205183
>>16202558
who's the water chick
Anonymous at Sun, 2 Jun 2024 02:29:40 UTC No. 16205602
Euler was summing up divergent infinite series in the 1700
Anonymous at Sun, 2 Jun 2024 12:25:17 UTC No. 16206058
Infinite summation already stretches the idea what is ordinarily meant by the equals sign. There are multiple summation methods with different results and each has an explanation why is it so.
People here are too rigid in their thinking and caught up in the result being weird rather than reading about Ramanujan sums to learn why is that. You are looking at an orange and wondering how can there be an apple of such a peculiar colour and texture.
Anonymous at Sun, 2 Jun 2024 12:33:31 UTC No. 16206064
>>16206058
>You are looking at an orange and wondering how can there be an apple of such a peculiar colour and texture.
i mean, i had never eaten an apple with a skin so tough and bitter in my life
Anonymous at Sun, 2 Jun 2024 13:01:17 UTC No. 16206085
>>16206058
>Infinite summation already stretches the idea what is ordinarily meant by the equals sign.
It does nothing at all to stretch what is meant by the equals sign. The equals sign is what it is.
Anonymous at Sun, 2 Jun 2024 17:49:06 UTC No. 16206459
>>16206058
>Ramanujan
Euler was summing up divergent series in the 1700s
Anonymous at Sun, 2 Jun 2024 17:50:18 UTC No. 16206461
>>16200911
An indian pair of hands typed this post.
Anonymous at Sun, 2 Jun 2024 18:03:14 UTC No. 16206475
Is there a way to arrive at -1/12 without using alternating series?
It seems every method involves summing 1-2+3... and setting it equal to (4-1)*S
Anonymous at Sun, 2 Jun 2024 18:30:09 UTC No. 16206503
Anonymous at Sun, 2 Jun 2024 20:17:58 UTC No. 16206647
>>16206503
Abel, Cesaro, Borel do not give the answer.
The regulator method still requires throwing away an infinite part or introducing oscillation to get the answer.