Making Sense of Ramanujan's Infinite Sum for General Audience.

In this video we will try to Intuitively understand why the weird sum 1+2+3 and so on till infinity or the famous Ramanujan sum. Which seems very counter intuitive at first sight!
The Numberphile video- • ASTOUNDING: 1 + 2 + 3 ...
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[@mathOgenius]

In this video my goal was not to prove weather this is true or not but to give an intuitive sense to laymen people that this can be true when we handle infinities in creative ways ! Have fun playing around with infinities! For a proof of this you can watch this video (If I did it, I will just repeat this proof)- kzbin.info/www/bejne/j6asep2Cp5upi6Msi=oqNokKAJSxnhUE-Z In the Video I say beta function regularization but wanted to say zeta function regularization sorry for that!

[@Things270]

No ProbleZ

[@damayantiroypramanik9555]

Sir please create a vdo on tetration..

[@nagyandras8857]

@@mathOgenius Andrew's number is the counter proof to all of it. Its defined as 0.999...

[@lyriclabyrinth-og]

Bro explains everything so calmly. I love it.

[@mridulacharya8250]

The logical proof of " 0.999..=1" is that there exists no number between 1 and 0.999...and hence these two are exactly same

[@BreadVanVleet]

An example would be that 1/3 = 0.333… that x 3 would be .9999… but 1/3 x 3 should be 3/3

[@adam-denis]

but if you do the same think for 0,888...=1 its the same but we fond that 0,999...=1 so how can 0,888...=0,999...=1 ?

[@mathOgenius]

this wont work for 0.88888

[@mridulacharya8250]

@@adam-denis This won't work cuz I can say 0.9 exists between 0.88888 and 1 na

[@karanwagh565]

​​@@mridulacharya8250There exists infinite real number between two distinct real numbers..then how did you concluded there is no real number between 0.999999.... and 1 ??

[@priyank5161]

I discovered ur channel today... Glad I did it Finally few more intuitive math guys in my list

[@mathOgenius]

Welcome aboard!

[@ajaychhikara8450]

me 2 lol

[@Hemish12]

Me too

[@arjyamitradeysarkar48]

same with me

[@risingtech7375]

YOUR LIST PLEASE

[@BabySisZ_VR]

I love your videos! thank you for making this one

[@wasteoftime8750]

The way you explain, the accect , the simple example is magnificent

[@HansBezemer]

Brilliant explanation! Kudos, man!

[@mrsnoopypants]

Thank you so much. I've been trying to understand this for ages.

[@legendparshwa1298]

Very brilliantly explained brother!!!! HATSS OFFFF

[@Eliana_1212-m9y]

i remember i used to talk to you when there was a whatsup group...you are still the best person whom i could talk to abt maths and astrophysics. Keep going! im proud of you!

[@mathOgenius]

you can still join the discord server

[@igoranisimov6549]

-1/12 is the true result under WRONG assumption. The proof is based on the assumption that THE series converges to a number, but it is NOT. End of story.

[@AbhiShek-k5q7g]

What type of assumption should be?

[@igoranisimov6549]

First, one need to prove that the series converges to a number, but the series of natural numbers diverges that is infinite as it should be

[@Tyson23576]

Thats what is microlevel physics Things are not defined there!

[@Mr_AWP]

Been following your channel for i think 2 years now when you had less than 50k subscribers. Thanks for the quality content you provide! Learned something new today.

[@mathOgenius]

Beacuse of support from people like you this channel is thriving

[@leibnix5643]

Amazing! Really eye-opening to see! Before, I was wondering how this divergent series could converge in such a peculiar way, but now I understand the general idea! I would love to see your version of a simplified mathematical proof in a future video. Once again, great explanation!

[@dimitrinotfound]

Another great thought process to prove infinity is not a number that I approached in my way from numberphile video is 1-1+1-1+1-.....∞ is equal to 1/2. How? The intuitive way is when we add 1 and -1 we get 0. Then next we add 1 and 0 we get +1 then we add -1 we get 0 the cycle repeats till infinity. The output we get from each step is 1 or 0. The mean value of this is 1/2 if and only if we add till infinity. Or else the result is not the same.

[@surangavithanage4232]

This is one of a way for developing and giving a relative mathematical value for the summation of infinitely many terms. Your explanation is very appreciated 👍

[@ernestogemperle803]

absolutely fantastic video

[@quranjadeed]

I pay big bucks to have your accent! Even though considered heavy by English natives it’s clear yet extremely captivating. When you speak I learn!

[@11gugugaga11]

Problem in handling infinity is that since it's a concept and can never itself be reached, it must be handled by considering the rate of approach to infinity... Infinity x 1 = infinity Infinity x 2 = infinity still but it's rate of approach is now 2x faster.

[@MiguelMendoncadaConceicao]

you are one of the best math explainers i've ever seem (I'm majoring in mathematics)

[@BrijBihariPrashad]

Question: How is it that the infinite sum of this series diverges only upto -1/12 and not other possibilities if we may have the freedom to handle the sum by the concept of infinity ?

[@ChrisCatlin-u9l]

My thoughts exactly

[@BritishBeachcomber]

Thank you, my South Asian brother. Your explanation makes so much sense. Far better than the Western rubbish that most YT videos say. Ramanujan would love you.

[@siddharthrana9216]

"Physics is the medium to perceive the Universe; Mathematics is the language to communicate with the Universe." - Universe is always speaking, humans only have to listened in the right direction, and with the right tools (mathematics).

[@mathOgenius]

Absolutely correct

[@sr6424]

The best explanation I have seen. Here are couple of things - take the 1 + 2 + 3 infinite series and add 1 to it. Is this allowed? If allowed will the answer be 11/12? What’s the sum of other infinite series - 1 + 4 + 9 + 16 etc.

[@AbhijitDeka-u4f]

Sir your explanation is 100% correct lekin, The series S= 1+2+3+4+5...∞ Is considered "divergent" We can understand it by this example Imagine you have a piggy bank, and on the first day, you put in ₹1, on the second day you put in ₹2, on the third day you put in ₹3, and so on. Every day, the amount you put in gets bigger. If you keep doing this forever, the amount of money in your piggy bank will just keep growing and growing without ever stopping. There is no limit to how much money you'll end up with. Means kabhi ye series khtm hi nhi hogi kyunki hum har din piggy bank me paise daal rhe hain. Same will happen in the series , and it won't give a finite value because it will just grow bigger and bigger without ever stopping and issi ko hum "Divergent" kehte hain. So, jab hum kehte hain ki ye series -1/12 ke equal hai ye iss principle ke hisab se fit nhi hoti hai jo ki hai "Divergent series"

[@prmishra1]

1+2+2^2+2^3+...=-1. It's true in some sense and people are using it.

[@dipankarhowladar9949]

reimann zeta function also proves it zeta(-1)=-1/12

[@frankoconnor806]

Yes great description very clearly explained and at an easy to digest pace too. Peace and love from Australia

[@Strangevqwedudvrudbak]

This is the best work in 2024 that I have done by subscribing ur channel brother

[@dongho1561]

Bravo!!!! you explained very well and I appreciate it very much.

[@prasadshenwai6118]

Very simple and easy to understand explanation! Please make follow-up video to explain how it's intelligently handled by infinity concept/beta function and its implications in the real world.

[@mdanayetullah8702]

Thank you very much. Your explanation is very simple to understand.

[@jima4513]

This is the best video ive seen about this summation, subscribed

[@mathOgenius]

Thank you

[@anamaymishra3269]

Watching this interesting video , during my online political science class .

[@asjadrazakhanquadri.9722]

This guy is a Maths genius 🏅 I like his videos very much He really deserves millions of likes and Subscriptions 👍👍

[@patpat5135]

With infinity, you can prove that anything is equal to anything

[@chintandesai2236]

yes, 5*0 = 6*0, then 5=6

[@Anonymous._.03.]

Thats nonsense..

[@Mikrinajumbo1988]

So what i understand is - “ Infinity is not physical ; it is spiritual “

[@themartian7121]

Thanks - very well explained!

[@jayaram2u]

This video really made sense. Great explanation 👍🏻👍🏻

[@sureshkrishna3787]

I thought you where gonna tell the same proof for infinite sum bro.... you didn't do that but you are make me realize that infinite is a concept..... Tq bro

[@parameswarantk2634]

Just like division by zero is not allowed, addition, subtraction, multiplication and division involving infinity is not allowed in maths Because infinity+infinity is again infinity and not 2 infinity

[@fauzanree1983]

Infinity is not a number

[@Param_Hayaran]

​@@fauzanree1983that's what he is saying.. infinity isn't distributive or associative

[@DikyVb]

@@fauzanree1983 I think Infinite is higher dimension of Numbers

[@sormu16]

A guy playing with math, breaking all well-agreed definitions and common sense. No, you can not add positive numbers and get anything negative. There are definitions for convergence. What you can do is use math in your own way and get absurd results. Ramanujan turns in his grave being mentioned in this.

[@thorstambaugh1520]

@@Param_Hayaran Infinity can be handled as a group or set and yes it does have distributive and associative properties but ONLY as a group. These do not translate when infinity is used as a number in an equation

[@vishwa1767]

Please make a proof video for this as well sharing insights of Sri Ramanujan.

[@MoharDutta]

Since 0.99999... is a rational number this real number can be written in decimal form 0.9+0.09+0.009+... In enumerable order Also any interval is non enumerable so (0.99999...,1] is non enumerable therefore there exists infinitely many real numbers between here. But by density property of Rational in R There exists rational r€R , irrational s€R st. 0.999...

[@JeeAsp-U-5000]

goat of math only one human not prove mind of RAMA

[@gihansampath917]

This is what teaching is about....explaining why it happens....not how it happens.... 👏👏👏

[@Aditya-tt2jz]

Well explained 👍 Keep going.......

[@chocoice4519]

brilliantly explained.. salute.. ❤

[@Tanish.1200]

Doing great! Keep it up brother👍

[@Someone-vg8fk]

Could this alternatively mean that we are not handling infinity well, we dont understand its concept fully, and we are manipulating it randomly ?

[@talatdhk]

The Following will give you a little bit of insight into what it is all about. 1/3 is a rational number that we can express as 0.3+0.1/3 =0.33+0.01/3 =0.333+0.001/3 =0.3333+0.0001/3 and so on infinitely. Each of above expression is an absolute number (1/3) without use of infinity. But abstract concept of infinity enters scene when you express it as 0.333.. It's only in case of absolute value 1/3 that you can go on adding infinite number of 3's. We know that Numerator/Denominator =Quotient+(Remainder/Denominator) 12/10=1+(2/10) In the same way, 10/10=1+(0/10), but we can also express it like 10/10=0.9+(1/10)=0.99+(0.1/10)=0.999+(0.01/10)=0.9999+(0.001/10)=0.99999+(0.0001/10). So 10/10=1=0.99999.. Remember that adding 9's at the end infinite number of times is only possible because of left remainders 0.1, 0.01, 0.001, 0.0001 and so on.

[@gohkianhui3997]

Thanks for clarification. So that means the equal sign in 1=0.99999.... to infinite is only valid when you add the term +0.0000......1 behind the expression right? Otherwise we should not say 0.9999.... = 1, rather stick to its conventional mathemathical expression: limit n to infinite for 0.9999n approaches 1.

[@ameerahmed6623]

0:04 Gauss equation n(n+1)/2 is sum of numbers from 1 to n. Assume n=infinity. Then n(n+1)/2=-1/12 So infinity= -1/2+square root of 1/12 and -1/2 -square root of 1/12

[@AbhiShek-k5q7g]

U should solve quadratic in order to get the value of n n²+n=-1/6 n²+n+1/6=0 Now by Sridharacharya formula n= (-1+- rootunder 1/3)/2

[@kartikdd8678]

Absurd.

[@syther836]

​@@kartikdd8678 😂 Might be an absurd solution but it makes a lil amount of sense

[@kartikdd8678]

@@syther836 ∞^2+∞-1/6=0 even worse

[@snowop8809]

Bro combined the divergent series to coverage 😂

[@victoriamacarthur8906]

*my teacher talking about adding apples to teach us addition* me: “what about negative apples?” teacher: “well you can’t have negative apples” *starts exponentially mass producing apples*

[@sunandasengupta8113]

Negative apples must b the rotting apples added in the beginning... 😅

[@timirbiswas3834]

Moral of the story is you must not try sum up a divergent series upto infinity. Even if you find the sum of a divergent series in terms of 'n' then don't try to evaluate that sum with the limit 'n' tends to infinity !!!

[@ind6337]

Thank you!!

[@flyingfox8072]

Start watching at 3:00😁😁

[@oscope11]

Feels like he proves that infinities bring out mathematical superpositions

[@kazedcat]

Infinity is weird and you should not expect that infinity will behave like a normal finite number. Infinity is not a number it can be a number but using it like a number will give you weird results.

[@OneAmongBillions]

Thank you for the thoughtful explanation.

[@pias-04]

He explained it like he doesn't like the smell of this equcation.

[@User2008_s]

Amazing 🔥🔥

[@smitaacharya4085]

Too good a video for mathematics . Math fellow forever !

[@hasush]

Very good job on bridging the gap between the intuitive impossibility of adding apples and never getting -1/12 and how that intution is wrong since we truely have no intuition for infinity.

[@Naveenkumar-kx9uu]

Thanks Sir , How to visualize the Methods like Beta-Regualization , Ramanujan's Summation to make sense

[@ansh47]

Very well explained brother 💚

[@nishantkumarrobin7388]

Handling infinity is a trick in mathematics. Like rabbit out of a hat. No matter how you perform the trick, the end should be surprising enough so the general audience is awestruck and no one cares about the actual way the trick is performed. Logically it makes no sense. How can rabbit appear out of nowhere? If S = 0.99999….. and 10S = 9.9999…. and we conclude that 9S = 9, then infinity - 1 = infinity and -1 = 0 which is a logical error, but hey we got the rabbit. That’s good enough. This is one thing I learnt in mathematics. Sometimes it’s good to be the audience and be awestruck by the trick.

[@3dgaming263]

Simple and easy explained. Thanks sir

[@sir_albaxious1909]

You just now earned a sub

[@Joysarkar-f3w]

Love you bro ❤❤❤

[@Tanish.1200]

Can u please explain solution of this equation ?!

[@scarbo2229]

What I derive from this is that since infinity has no relation to reality, any equation containing it is also devoid of reality, as a natural extension. I would also suppose that, in this case the result could be pretty much anything. I assume -1/12 just stands in as an example of this.

[@Malaydrip8]

what is the reason to multiply s with 10 can we multiply with any other number?

[@staticz_drago8530]

We multiply it with 10 becus the first decimal is repeating if suppose we have 0.1212121212......... we will multiply that by 100 beacause 2 decimals are repeating

[@sadanandbhat2617]

Well explained.

[@ankitkumar-eg8gq]

At 3:43 you subtracted 9.9999... -0.9999... --------------- 9.0000...... So here after decimal .9999... are non terminating recurring number right? So at 4:39 9.990 -0.999 ------------ 8.991 Why you subtract with 9.990 instead with 9.999 because even removing infinity, the number after decimal should be recurring number just like done at 3:43 since we are following same procedure after removing infinity. Plz make me understand this.😮

[@RobGeorge-l9v]

Because the first equation had an infinite number of nines after the decimal point,while the second one had a finite number of nines(three),which are not recurring.

[@mathOgenius]

second example was for non reoccurring one, to show what happens when we remove infinity

[@gohkianhui3997]

I still find the explanation quite confusing 😕 I don't think you can operate on infinity like normal arithmetic since the last digit is not accountable. Like S=0.9999to infinite case. The thing is you assume all the point beyond decimals for 10S-S just subtract out perfectly, but how do you know the decimal points at infinity point for 10S is a 9 or a 0 since you multiply a 10? There is a danger in blindly believing everything authority say. String theory in my opinion just make the leap of faith to solve their infinity dilemma in their equation using this equation. The field has claimed many young bright mind to dedicate their entire life looking for way to force the nature to fit with their mathematics without much success.

[@ASHKETCHUM-Sneha]

Wow, you gave the feel to me to understand that which i really can't understand 😊

[@ravindrasalunke693]

You can simply say that, in the 's series' the last digit is TRUNCATED. Like this - 10s - s = 9.99 - 0.999 By Truncating the last digit (a kind of approximation) the equation will be - 10s - s = 9.99 - 0.99 Now s = 1 is ACHIEVED. Such type of approximations are perfectly alright in Engineering, but not in Science or Mathematics.

[@nabarunghoshal560]

When something is not defined, anyone suggesting anything about that cannot be taken for granted, even if the person is Ramanujan.

[@YourAstrophysicistV]

Amazing this video makes so much sense

[@emaad1111]

Sir please do a topic on linear equations graph

[@thecarman3693]

OK, infinity is not a number. But then we treat it exactly like a number when we multiply 0.99999 ---> by 10 to get 9.99999 -->. And then we go and perform subtraction on it. It seems we get to pick and choose when and when not to treat infinity as a number.

[@SnigdhaMedha]

The video starts at 3:01

[@mridulacharya8250]

After seeing all comments...I concluded... Series of natural number is closely linked to -1/12 but the conventional sum is not that connection

[@slantingclock9679]

Thanks for the videos welcome back sir🙏. Can you please make a video on how to excel in maths like a genius would

[@MeetShrivastavaLWCS]

I am OBC category person. Can i watch this?

[@9e20sagniknandi7]

Hein😂

[@Tahazif_TheCool22]

Wtf?

[@harishchalwadi]

😂??

[@ExistingPriyanshu]

No you already have 27% reservation

[@sarcasticboi1566]

Exactly ​@@ExistingPriyanshu

[@narangfamily7668]

beautifully covered

[@sridharannarasimhan4916]

While writing, his nervous hand would have shaken a little, resulting in the minus sign

[@tajshoosh1196]

Good video. I swear most advanced mathematicians don’t understand infinity 😂 Infinity is nonending (c) - 🤣 But to accomplish these types of math tricks, they start by treating infinity as ending. Still, like a child, I love the magic tricks.

[@kuriakosekjoseph6253]

Sir to be very frank...... Your video although informative in its own right raises more questions than it answers. You should have also tackled the how it happens/the proof behind the expression also along with the why it happens in maths. And you can see those questions in your comments. Please make a video tackling those.

[@madly1nl0v3]

1) First, you said you tried to make sense of Ramanujan summation, then you did for 1 = 0.999... And 2) 1 and 0.999... are not infinite as ζ(-1), both of them have upper limit as 1.

[@mathOgenius]

yes you are right! for people who do not want to go into too much detail I took this simple example where infinity lets us prove something which is not totally true, 0.999999.. has an upper limit one, but does this mean it is equal to one?

[@mead3634]

very helpful thanks

[@fAmoNeY7286]

Can you tell us about more new and informative mathematical concepts and tricks?

[@LawD14]

Great video

[@brettr7970]

...and all delivered while still wearing your pyjamas. Kudos.

[@akshaychebathini713]

Sir If I take S=0.9999...infty and 10S=9.999...infty , the value changes as you have did in 2 derivation.

[@bububuububu2025]

Thank u for explain 😊

[@rahilaminlaskar6140]

my dear brother if put two mirrors front of each other then the infinite mirrors will appear ?? eheather it can be said as imaginary

[@nointerference11]

Bro's teeth are brighter than my math's career😂😂😂

[@shubhamchandra9258]

0.999... = 1 because you can make the number arbitrarily close to 1.

[@sie_khoentjoeng4886]

The equation only valids if you believe that oo + 1 > oo.. ( oo is not an exact number) As long as you don't believe it (oo + 1 > oo), it means the equation (1+2+..+oo =1/12 is logically wrong...

[@mikeburns6603]

Many times people say things that are absurd to try to seem profound. If you try to add up an infinite series that never converges then it's one example. If you assume something false (that this series converges) then you can prove anything.

[@Theworldismystage-k9t]

This is a theoretical sum only. It’s not consistent with one of the fundamental principles of general relativity and quantum physics which is that the universe is expanding unbounded. If the universe was indeed expanding infinitely, the infinite series would sum to infinity or an undefined value.

[@sarvindersingh7490]

But u didn't explain how 1+2+3+4+... Inifite= -1/12

[@aakash5288]

Congratulations for future 500k

[@omeryehezkely3096]

I give you 2 numbers: One number is 0.999 till infinity and the other number is exactly the same with only one random digit not being 9. I don't tell you which one is which and I ask to identify which one of them is equal to 1 and which one isn't. Can you solve it?

[@mathOgenius]

I would need the location of the changed digit otherwise its uncertain.

[@paparmar]

What is the significance of the result that if one extends the partial sum formula (S(n) = n(n+1)/2) to real numbers, i.e., S(x) = x(x+1)/2, the integral from -1 to zero (the only domain in which the function is negative) is precisely -1/12 ?

[@ahmadwuhaib579]

Hello. What is the Ramanujan summation?