Ramanujan Paradox | 1+2+3+4+....... = -1/12 | Aman Sir Maths

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BHANNAT MATHS

3 жыл бұрын

Ramanujan Paradox | 1+2+3+4+....... = -1/12 || Bhannat Maths | Aman Sir Maths
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Пікірлер: 2 698
@abhishekkhulbe3905
@abhishekkhulbe3905 3 жыл бұрын
I just shocked to see that how the sum of all natural numbers is -1/12 . A humble salute to the one and only S. Ramanujan
@dipikaghosh6224
@dipikaghosh6224 3 жыл бұрын
It's a paradox
@silverfangg45
@silverfangg45 3 жыл бұрын
@@dipikaghosh6224 string theory me lagta hai
@Amit1994-g9i
@Amit1994-g9i 3 жыл бұрын
@@silverfangg45 nope
@jayantsingh3078
@jayantsingh3078 3 жыл бұрын
@@Amit1994-g9i In String theory it uses
@binodtharu8348
@binodtharu8348 2 жыл бұрын
@@silverfangg45 agr string theory mei lgta hai to hm kya kre string theory is just a "theory" and i think u should google the meaning of "theory".......(i mean string theory is not like it could be 100 percent true)
@techmaster6587
@techmaster6587 2 жыл бұрын
"An equation for me has no meaning unless it expresses a thought of God!!" ~ *S. Ramanujan* ♥ *JAI NAMAGIRI THAYAR DEVI* 🚩♥
@IIT24Aspirant
@IIT24Aspirant 2 жыл бұрын
So that's why he was so much interested in infinity equations?
@techmaster6587
@techmaster6587 2 жыл бұрын
@@IIT24Aspirant yepp!
@cassianperera2426
@cassianperera2426 2 жыл бұрын
Ramanujan is a true genius in Mathematics, according to this statement mentioned by him.
@jod5783
@jod5783 Жыл бұрын
Aa gaye gawar
@cassianperera2426
@cassianperera2426 Жыл бұрын
It is exactly true that the Ramanujan's statement.
@SagarsAudioHub
@SagarsAudioHub 2 жыл бұрын
"Mathematicians होते ही साफ दिल के" 😀❤️🙏 Sir Ramanujan was the hero , is the hero and will be the hero 🙏 Big salute to him. And, your teaching is fabulous sir ji 💞
@theharo4084
@theharo4084 2 жыл бұрын
Mathematician bolke illogical baat bhi bolrhe ho
@hridayjoshi7247
@hridayjoshi7247 Жыл бұрын
Meri bhua to nahi hai
@cheapdealskabanda7709
@cheapdealskabanda7709 Жыл бұрын
F
@thegames4499
@thegames4499 5 ай бұрын
kyu bhai tumhara knowledge jayada ho gaya hai kya kya tum ramanujan se zayada gyani ho
@sudhirkumar-kp5lc
@sudhirkumar-kp5lc Жыл бұрын
Ramanujan in one of his papers also dropped hints to form the equation of a black hole in one of his letters. It's crazy how much he would have contributed to mathematics had he been introduced to it earlier.
@vinaykumarsingh6223
@vinaykumarsingh6223 Жыл бұрын
The line " fat gyi thi .....aankhe logo ki"is just OP 😂😂😂😂😂
@Southmovies509
@Southmovies509 Жыл бұрын
😂
@DeepakKumar-iy1ck
@DeepakKumar-iy1ck 8 ай бұрын
😂😂😂😂😂
@goldandsilver415
@goldandsilver415 2 жыл бұрын
A Mathematitians who breaks the law of Mathematics 😵 Salute to the legend Proud to be an indian
@primelemma
@primelemma Жыл бұрын
Laws of mathematics are never break they are generlize
@O-Kyklop
@O-Kyklop Жыл бұрын
He didn't brake any law. he just didn't know what the Infinite really is.
@BorutoOtsutsuki__
@BorutoOtsutsuki__ 9 ай бұрын
​@@O-Kyklopfr there are many loopholes in the term infinite itself , smart mathematicians can make more equations like this
@O-Kyklop
@O-Kyklop 9 ай бұрын
@@BorutoOtsutsuki__ The loopholes are in the mind of the ignorant. Basically, the Infinite has no numbers. So, there are not much equations a mathematician can make and this for a simple reason: the equations may have no end but have always a beginning whereas the Infinite has none. Basic school stuff.
@dhrubaganguly7758
@dhrubaganguly7758 7 ай бұрын
Why are you breaking english grammar rules?​@@O-Kyklop
@shouryashukla5817
@shouryashukla5817 2 жыл бұрын
Well it was destined to be paradox, as the very first series 'A' is a paradox itself, as the sum of 1-1+1-1+1-1+1-1+...... Can be either 1 or 0 depending on the last quantity of the series, as it's till infinity it's unclear what is the last numeral, so the answer should be either 1 or 0, but, by solving this series i.e. by taking common we got 1/2, it's actually impossible, I think it's the average of 1 and 0, and we can't solve maths by taking a contradictory value and further assigning it, hence sum of all natural numbers was destined to be a paradox.
@Supriyobiswas649
@Supriyobiswas649 Жыл бұрын
Finally, someone who actually knows how math works.
@neeraj540-w7s
@neeraj540-w7s Жыл бұрын
kzbin.infoGfBXmTDz15E?feature=share
@samarthgupta5981
@samarthgupta5981 Жыл бұрын
Exactly, well that's the beauty of infinity in such problems, we know something is there which is distorting the true value but we can never find it coz it's ♾️😂
@indmh20shreyas42
@indmh20shreyas42 Жыл бұрын
Yeah,if th no. of terms,if are even ,then the sum is 0 and if odd,then 1😊 well said ,bro!
@ETM247
@ETM247 Жыл бұрын
Exactly
@gaurangagarwal6508
@gaurangagarwal6508 2 жыл бұрын
Just 1 word Salute to Mr. Ramanujan ji
@pulsar2977
@pulsar2977 2 жыл бұрын
that's 5 words...
@Yashchoudhari00
@Yashchoudhari00 Жыл бұрын
@@pulsar2977 lmao bro .but Ramanujan sir 🙏.
@DakshJee-xx7bj
@DakshJee-xx7bj 6 ай бұрын
Thats 5 words
@swapnilsinghrathore9846
@swapnilsinghrathore9846 Жыл бұрын
Sir,मेने पहले भी महान आदरणीय श्री रामानुजन जी की paradox के बारे में देखा और समझा था,परंतु आपने बड़े ही सरल तरीके से इसको समझाया और रामानुजन जी के बारे में बताया इसके लिऐ आपका बहुत बहुत आभार 🙏🏻🙏🏻🙂🙂
@OmPrakash-nw4ip
@OmPrakash-nw4ip Жыл бұрын
Proud to be an Indian. Huge respect for S. Ramanujan 🙏🙏🙏🙏
@animeshkumar8396
@animeshkumar8396 2 жыл бұрын
I feel very proud of a teacher like u who remembers the contribution of legends and make us aware of their story..A BIG SALUTE TO U SIR...And ur way of teaching is just intresting and ADDICTIVE..THANKS for sharing their stories
@MrDrgdf
@MrDrgdf 2 жыл бұрын
भगवान कसम इससे चूतिया intro आज तक नही देखा
@Rhythmraj009
@Rhythmraj009 2 жыл бұрын
ye sirf paper par proof ho sakta h na ki physically agar hum dhyan se dekhe to numbers ke sath ki bhi khel sakta h par ramanujan was great.......... par hume ye nahi bhulna chaiye ki agar ye equation humne use ki to hum physics ke rules ko tod rahe honge
@UdaySingh-pp6ee
@UdaySingh-pp6ee 2 жыл бұрын
Tum chutiye ho..math smjh m aata to tumhe pta chalta ki kya shi hai kya glat... Aise hi upar upar s log kisi pdf s koi problem solve krk tumhe dikhayega aur tumhe lgta h ki bhut shi ..wah wah.. Bhai..ku6 Janna hai to jakr books pdhi..aur smjho.. Tum jaise logo ki wjh s koi bhi teacher bn jata h.. koi bhi Paisa kama rha h.. Aise hi science experiments krne wale channel hai jin salo ko ku6 pta nhi hai kya hota hai reaction m..kyu ho rha h..bs idhr udhr ki copy krk experiment kr denge aur tumhare jaise chutiyo ki line hai hi unko subscribe krne k liye,,
@madhabimandal2280
@madhabimandal2280 2 жыл бұрын
@@Rhythmraj009 bro no,this series is used to prove string theory.Aye phy banate hain,thodta nahi hai.
@madhabimandal2280
@madhabimandal2280 2 жыл бұрын
@@Rhythmraj009 if you don't believe me you can read online materials
@macbcheesy
@macbcheesy 2 жыл бұрын
I swear, one of my favorite things about math is that we don't need to speak the same language to understand it. He's taught me more in this video than I learned watching the others.
@badriiyengar
@badriiyengar 2 жыл бұрын
But, certainly that is not the evidence to prove here your teacher ( author of the Upload ) is correct here. Everybody knows that 1 = 2 would be cirrect when 0 can be accepted to be denominator as well as Numerator!
@morbius9537
@morbius9537 2 жыл бұрын
@@badriiyengar what crack you smokin?
@xyyzxg
@xyyzxg Жыл бұрын
​@@badriiyengar I think you skipped simple math. You can't divide a number by a number which doesn't exist that is 0. If divided by 0+ then it tends to infinity.
@badriiyengar
@badriiyengar Жыл бұрын
@@xyyzxg I have not come here to enter into a debate. My post implied that Zero can not operate as a Denominator, for it would lead to ubsurdity, like producing a number from nothing. Sad part is that you have not understood what I meant( implied). By the way "X" to the power of Zero is 1 only when "X" is any thing but Zero.
@zebt7477
@zebt7477 Жыл бұрын
Tu galat Sikh rha hai
@amaanalrashid8273
@amaanalrashid8273 3 жыл бұрын
The best channel to fall in love for mathematics
@silverfangg45
@silverfangg45 3 жыл бұрын
The proof is wrong
@amaanalrashid8273
@amaanalrashid8273 3 жыл бұрын
@@silverfangg45in which class are u studying now
@silverfangg45
@silverfangg45 3 жыл бұрын
@@amaanalrashid8273 12 see this kzbin.info/www/bejne/j6asep2Cp5upi6M Ye mathlogger ka video jisne numberphile bolke ek channel usme ek bande ne same proof kia tha ye sir jaisa usko galat bataya hai prove itna simple nahi hai Numberphile video 👉 kzbin.info/www/bejne/rV6sZ4uKi7-Lrdk Ye sir jee ke lia sahi hai lekin general higher topics ke lia nahi pata .
@konceptmathematics
@konceptmathematics 2 жыл бұрын
Maine Ramanujan summation par atleast isse better video banaya hai
@konceptmathematics
@konceptmathematics 2 жыл бұрын
And please do subscribe the channel
@rohitkachare3498
@rohitkachare3498 Жыл бұрын
Mai ek Arts ka student hu. History padh raha tha. S. Ramanujan ji ke bare me padha to shock ho gaya. Etne mahan Ganitdnya the. Salute for his invention in maths..
@KSJGaming
@KSJGaming Жыл бұрын
imagine a number n such that 1+2+3+...+n=-1/12 we get n and then u see 1+2+3+...+infinity=-1/12 dont u think infinity will be defined then?
@shiveshkumar3694
@shiveshkumar3694 2 ай бұрын
For their sum be -1/12 n must be infinity which we cannot imagine
@abhisehrawat5831
@abhisehrawat5831 16 күн бұрын
Can't imagine n without this paradox
@sidindian1982
@sidindian1982 2 жыл бұрын
While preparing for data science mathematics ( linear algebra CALCULUS, STATS & discrete mathematics )..i truly think of Sri Ramanujan sir 🙏❤️❤️🙏🇮🇳
@samiullahk7223
@samiullahk7223 Жыл бұрын
Y not god?
@aadityagururani7519
@aadityagururani7519 Жыл бұрын
​@@samiullahk7223 why not ramanujan?
@cxnaruto4931
@cxnaruto4931 Жыл бұрын
Maths God= ramanujan hence proved
@cxnaruto4931
@cxnaruto4931 Жыл бұрын
@@IsaacNewton818 sir pliz laws vapas lelo apne 🙏
@justmath331
@justmath331 2 жыл бұрын
Finally someone made me understand this series without calculus Thank you very much sir
@ankurgupta9106
@ankurgupta9106 2 жыл бұрын
This video is wrong in so many levels. He is fooling you
@anubhabmondal5342
@anubhabmondal5342 2 жыл бұрын
It is not the real proof...this proof is proposed by numberphile youtube channel then everyone copied it....this proof does not exist because of divergent series...the actual proof is coming from complex field...
@ankurgupta9106
@ankurgupta9106 2 жыл бұрын
@@anubhabmondal5342 yeah mathaloger made a 40 minutes long video explaining why this proof was wrong.
@gauranshkapur8977
@gauranshkapur8977 2 жыл бұрын
@@ankurgupta9106 yes that video explains everything very clearly
@shashwatINDIAN
@shashwatINDIAN 2 жыл бұрын
Basic mathematical operations (+-÷×) can only be applied to convergent series. But 1+2+3+4+6+......... is a Divergent series, so mistake starts from the point we assume the value of this series to be a constant just by doing addition substracting. By the way Mathematically applying the basic operations, even 1=2 can be proved and according to that any two given distinct numbers can be proved equal to each other but that's not true. 1≠2, 2≠3, 3≠4,..... But very easily it can be proved that 1=2, 2=3, 3=4,.....
@saranathantg
@saranathantg 2 жыл бұрын
While my great admiration is for Ramanujan, I am grateful to you for bringing to light in simple way his greatness. Thank you Sir
@blacklegend2438
@blacklegend2438 Жыл бұрын
0 was found by aryabhatta who was Indian and infinity was found by ramanujan sir the first number and last number both were found in india
@abhishankpaul
@abhishankpaul 11 ай бұрын
Except for the last one. Infinity was known more or less to all mathematicians across all civilizations. Any sane person will say that numbers have no end
@subramaniams6091
@subramaniams6091 Жыл бұрын
Humble Pranams to Ramanujan Sir. Besides, the tutor’s narration is exceptionally brilliant.🎉
@chaitanyatale4666
@chaitanyatale4666 3 жыл бұрын
SALUTE TO THE GREATEST MATHEMATICIAN OF ALL TIMES RAMANUJAN SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
@tango1980Mwj
@tango1980Mwj 2 жыл бұрын
sadly we live ina country where people like Salman, SRK, Dhoni, Kohli..... (infinite series)... get more importance then people like Ramanujan... I live 4 kms from Ramanujans house in chennai... Love u bhai from chennai..
@ankhi6604
@ankhi6604 Жыл бұрын
Why are you even mentioning them? They are expert in their fields. I know that Ramanujun doesn't get that much importance but you can compliment him without mocking others who are genius in their profession.
@akshitrawat82
@akshitrawat82 Жыл бұрын
@@ankhi6604 yess! Every body is perfect in their own field.. I pay huge Respect towards Ramanujan sir 😄😃
@gautamgupta6029
@gautamgupta6029 3 жыл бұрын
THIS VIDEO IS WORTH #1 TRENDING!! 👍👍👍 JUST AMAZING SIR !! SALUTE TO AMAN SIR .. AND COUNTRY'S PROUD SRI.RAMANUJAN SIR 🙏🙏
@silverfangg45
@silverfangg45 3 жыл бұрын
The proof is wrong bro
@Rahul.G.Paikaray27
@Rahul.G.Paikaray27 3 жыл бұрын
Sahi bate de
@silverfangg45
@silverfangg45 3 жыл бұрын
@@Rahul.G.Paikaray27 First of all the prove is wrong A and B are divergent series . And its copied from numberphile video kzbin.info/www/bejne/rV6sZ4uKi7-Lrdk which is itself wrong which was rectified by mathlogger video 👉 kzbin.info/www/bejne/j6asep2Cp5upi6M The actual proof is not so simple he is proofing like 1=2
@Rahul.G.Paikaray27
@Rahul.G.Paikaray27 3 жыл бұрын
@@silverfangg45 thanks brother
@binodtharu8348
@binodtharu8348 2 жыл бұрын
@@silverfangg45 i agree that this proof is wrong because its divergent series but this proof is not like proof of 1=2, in that proof we use the thing that (2-1)^2=(1-2)^2 type things......
@kamallumar
@kamallumar Жыл бұрын
How are we adding in A- B where's the + sign coming from , I'm basic at maths but help me understand how's A= 1-1+1-1+1-1 And B= 1-2+3-4+5-6+7-8+9-10 A-B (1-1+1-1+1-1+1-1...) -(1-2+3-4+5-6...) How's it (1-1)+(-1+2)+.. why are we adding it
@subhashpatil2833
@subhashpatil2833 Жыл бұрын
Salute to Ramanujam. Sir you explained in excellent manner. You are real maths master.🙏🙏
@jitendramohan7500
@jitendramohan7500 2 жыл бұрын
B series can be grouped as (1-2)+(3-4)+++ and sum tends to - infinity so it is divergent series so sub or add of series B to other series as divergent with convergent leads to indeterminate form results in paradix
@tanmaynayak2250
@tanmaynayak2250 2 жыл бұрын
Bhai kya keh raha samaj ma nahi aa raha
@Siddharth_Mauryaa
@Siddharth_Mauryaa 2 жыл бұрын
@@tanmaynayak2250 BSC kro tb smj me ayega
@Mr.Ak.2608
@Mr.Ak.2608 2 жыл бұрын
Its divergent series, so can't be converge to any real no. 😂😂 Maths hons karo tab samjh ayega
@soumyajitsarkar507
@soumyajitsarkar507 2 жыл бұрын
​@@Mr.Ak.2608 the actual proof is by remmans zeta function
@Mr.Ak.2608
@Mr.Ak.2608 2 жыл бұрын
@@soumyajitsarkar507 by both reimann zeta and direchlet eta functions
@ayyasuddin3394
@ayyasuddin3394 2 жыл бұрын
The Man Who Knew Infinity (Srinivasa Ramanujan)🙏🏻🙏🏻🙏🏻
@lohitadityanaik8144
@lohitadityanaik8144 2 жыл бұрын
India is blessed with legends like Ramanujan sir
@sbssarma3517
@sbssarma3517 Жыл бұрын
Ramanujan is not a mere hero. He is a Mega Star of Mathematics who radiated super brilliantly such that his contemporaries were blindendened by his scintillating lustre of wisdom.
@O-Kyklop
@O-Kyklop Жыл бұрын
Ramanujan didn't understand the concept of Infinity and made gross mistakes because of that, as the so called Paradox in this video. And the guy in this video, "explaining" the Paradox seems not to understand much better the question of Infinity.
@someone-jl4sj
@someone-jl4sj Жыл бұрын
​@@O-KyklopRamanujan was correct it is the video that is wrong
@O-Kyklop
@O-Kyklop Жыл бұрын
@@someone-jl4sj No fellow, he wasn't. There is no way Infinity being -1/12. First off, because these sums he uses to demonstrate it are not Infinite. There are some more reasons but this one is sufficient to refute it.
@someone-jl4sj
@someone-jl4sj Жыл бұрын
@@O-Kyklop Ramanujan never said that -1/12 represents this sum. What Ramanujan showed was that this was analytical continuation of Riemann Zeta function. And this is the value of Zeta(-1). For more information search Riemann Zeta function.
@O-Kyklop
@O-Kyklop Жыл бұрын
@@someone-jl4sj It xdoesn't change anything. If the result is oo=-1/12, is wrong.
@deshbhktA
@deshbhktA Жыл бұрын
Genius Ramanujan ji 🙏 Thanks Aman ji for presenting it nicely, and praising the hero of Maths from India. 🇮🇳✌️
@KedarAhire411007
@KedarAhire411007 2 жыл бұрын
This is the great way of giving tribute to Ramanujan ji...Thank you Aman sir...🙏👏
@princeladdha65
@princeladdha65 2 жыл бұрын
A huge salute to ramanujan , such a great mathamatician who born in india 🙏🙏 Proud to be an indian🇮🇳❤
@aadityasharma5948
@aadityasharma5948 2 жыл бұрын
The man who knew infinity ♾️♾️♾️
@zarapkarajinkya4034
@zarapkarajinkya4034 Жыл бұрын
I think the paradox happened because series A was supposed to be 0 but became 1/2
@praveenkumarsingh1436
@praveenkumarsingh1436 Жыл бұрын
Not always zero. It depends on the number of terms in the series, whether it is odd or even if it is even sum is 0 if odd, sum is 1.
@shivamkumarrai8598
@shivamkumarrai8598 Жыл бұрын
​@@praveenkumarsingh1436but in no situation it can be 1/2
@nitinmaharana3706
@nitinmaharana3706 11 ай бұрын
@@shivamkumarrai8598 They used average because we really cant if the last digit of infinity is odd or even ,so we are forced to take 1/2 but its not accurate we say it as the closest sum of all natural numbers.
@abhishankpaul
@abhishankpaul 11 ай бұрын
You don't know whether infinity is odd or even. If you consider the partial sums, if the series contains even terms, sum is 0 else 1. There is no way you can have 1/2. You cannot take averages as well
@paurusshukl4892
@paurusshukl4892 10 ай бұрын
Rules of finite maths don't apply to infinite series.
@gss-motivation4903
@gss-motivation4903 2 ай бұрын
True.
@nirajkhare3915
@nirajkhare3915 2 жыл бұрын
Also you cannot rearrange terms in an infinite series without changing the sum (if it's defined) unless it converges absolutely. Please teach convergence first and then see the work of Ramanujan using extension of complex analytical function by
@biplabmahato119
@biplabmahato119 2 жыл бұрын
Yes, with out absolutely convergent we cannot rearrange the terms. This prove is wrong.
@Ramu-bw4ub
@Ramu-bw4ub 9 ай бұрын
Without Taylor series expansion?? I think Taylor series should be best applicable here.
@AvnishKumar-bt1pd
@AvnishKumar-bt1pd 3 жыл бұрын
Series A is discussed by Mohit Tyagi in maths for fun
@krushnachandrarath3652
@krushnachandrarath3652 2 жыл бұрын
Thanks for the post. May I add that this paradox is used in string theory. Casimir's effect in physics on existence of attraction between two charged particles in vacuum is explained by him using this paradox.
@soumiksaha8484
@soumiksaha8484 Жыл бұрын
Thanks for fyi
@zebt7477
@zebt7477 Жыл бұрын
We use a made up value to prove a made up theory doesn't mean your made up value is true
@alien3200
@alien3200 7 ай бұрын
This prove is wrong. I can prove it to be -1/8. Bhai its a divergent series and divergent series ka sum infinite hota hai. Kisi finite value pe converge nai hota. Its Like using infinite GP wala formula when the common ratio is more than 1
@RS_Official07
@RS_Official07 3 ай бұрын
7:32 the first step is itself wrong because if a series is going upto infinity then how can you take something equal to infinity when it's value is not defined Also if u are just naming the series with A how did u take the series EQUAL to A. Similar case with S and B series as well. Hope you understand
@bibeksubedi2909
@bibeksubedi2909 Жыл бұрын
My reaction was Oh My God after he proved it😂😂❤ Hats off to Ramanajun and Aman sir🙏
@harshbhushanpathak2392
@harshbhushanpathak2392 3 жыл бұрын
You are really doing a good work and this needs to be continue sir. The moment you found the value of A I was shocked this is really the magic of maths . Salute to the legend S. Ramanujan 🙏🙏
@ankurgupta9106
@ankurgupta9106 2 жыл бұрын
This video is wrong
@AdityaRaj-yu2ir
@AdityaRaj-yu2ir 2 жыл бұрын
@@ankurgupta9106 Yess
@yagami1130
@yagami1130 Жыл бұрын
This video is 100 percent wrong, since distribution law isn't correct in infinite series
@harshbhushanpathak2392
@harshbhushanpathak2392 Жыл бұрын
@Ankur Gupta @Aditya Raj @yagami this is a paradox which actually is used for calculation of electric forces between two uncharged plate in vacuum , and also in string theory in real time. So it is definitely correct .
@yagami1130
@yagami1130 Жыл бұрын
@@harshbhushanpathak2392 yes its indeed true but the way its proved in this video is totally wrong, he must prove it using zeta function...that's what Ramanuja did.
@techmaster6587
@techmaster6587 2 жыл бұрын
The Man Who Knew Infinity *JAI NAMAGIRI DEVI* 🙏🙏
@Crackdsssbtgt
@Crackdsssbtgt 2 жыл бұрын
I started to like each and every videos of yours... Your way of explanation is incredible... I also want to be a teacher like you are!
@ferdousbhuiya
@ferdousbhuiya 9 ай бұрын
I could not hold my tears. How it is possible. Real hero of Math. Salute you Boss.
@sopusuryawanshi6934
@sopusuryawanshi6934 7 ай бұрын
Wrong hai bhai paradox
@CD10ANIL
@CD10ANIL Жыл бұрын
The key of infinity in math (Still not known rule) , like of BODMASS rule, is that nothing can be removed from infinity once it added to it, though can be rearranged and add more but can not remove, this is what is missing above and causes such paradox. Sometimes simplicity avoids big mistake. This is like a black hole , one is talking about taking back something from blackhole. So the statement that the sum of the infinite series 1+2+3+...infinity is equal to -1/12 this result is based on the assumption that division by zero is allowed. but division by zero is undefined, so the sum of the series is also undefined. There is a mathematical theorem that states that the sum of an infinite geometric series is equal to a / (1-r), where a is the first term of the series and r is the common ratio between the terms of the series. In the case of the series 1+2+3+...infinity, the first term is a=1 and the common ratio is r=1. So, the sum of the series would be: S = 1 / (1-1) = 1 / 0 However, as I mentioned before, division by zero is undefined. So, the sum of the series is also undefined.
@HRajMNNIT
@HRajMNNIT 3 жыл бұрын
The explanation just blown my mind 🤯🤯🤯🤯
@kamleshdevi-fg2br
@kamleshdevi-fg2br 3 жыл бұрын
Sir, Please make a video on NIKOLA TESLA SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🇮🇳
@silverfangg45
@silverfangg45 3 жыл бұрын
@Abhay Pandey naam batana to Zara indian scientist Google search mat karna
@kamleshdevi-fg2br
@kamleshdevi-fg2br 3 жыл бұрын
@Abhay Pandey Bhai, INDIAN SCIENTISTS भी महान थे पर ,NIKOLA TESLA ki kahani सुन लेना sir से एक बार ,आप चोक जाओगे 🙏🏻
@harshjais369
@harshjais369 2 жыл бұрын
@@kamleshdevi-fg2br @kamlesh devi Yes Tesla was a genius. He's father of our today's modern world. He always thinks for mankind. We humans should credit all the great persons for their work instead of arguing who is indian or ..., who is great than ..., etc.
@abhishekbhuyan3576
@abhishekbhuyan3576 2 жыл бұрын
@@silverfangg45 abe Bengali tu apni aaurate bechne me focus kar. india pe already kai saare mathematicians, philosophers or academics hai.
@ritasagar77
@ritasagar77 3 жыл бұрын
hamare desh ko AAP jese teacher ki jarurat hai jo hume en mahan vidyano se rubaru karaye pata nahi aaj kal ke sabhi log en mahan logo ki baat hi nahi karte
@jsk5549
@jsk5549 3 жыл бұрын
@@AnmolSah27 Tere bap se jayada Knowledge hai sir ka
@Ankitkumar-fi4rc
@Ankitkumar-fi4rc 3 жыл бұрын
@@AnmolSah27 Tera Pura family sale inka mukbla nahi kar sakta h , aur tu to abhi bachcha h 🤣🤣🤣
@Ankitkumar-fi4rc
@Ankitkumar-fi4rc 3 жыл бұрын
@@jsk5549 ha bro uska baap ka baaap ka baap ka baap ......... Infinite time tak koi utna nahi janta jitna aman sir ,🤣🤣🤣
@ankurgupta9106
@ankurgupta9106 2 жыл бұрын
The proof presented in the video is completely wrong
@Ankitkumar-fi4rc
@Ankitkumar-fi4rc 2 жыл бұрын
@@ankurgupta9106 are yaar dekho thik se
@DVFacts
@DVFacts Жыл бұрын
Why not we subtract S from A (A-S) why only we choose B to minus from S
@APSAHAYMP
@APSAHAYMP 8 ай бұрын
Rearrangement and distributive law is not allowed in infinite series...only in absolutely convergent series it can be done...... Even the proof using riemann zeta function would be wrong because -1 is not in the domain of zeta function. Before teaching for jee it is absolutely essential to do graduation in the subject.....so that such videos do not end abruptly without any disclaimer.
@ankur20010
@ankur20010 2 жыл бұрын
This problem is covered in the first basic real analysis course. And there are a lot more such examples in the real analysis book by terry tao The reason for this paradox is that you can't do operations as mentioned in the video , on an infinite series. You need to prove the convergence first and then justify the regrouping etc.
@yashrajchouhan82
@yashrajchouhan82 2 жыл бұрын
Bro, sir Ramanujan was much more beyond than our thinking, he would have thought about that before
@AdityaRaj-yu2ir
@AdityaRaj-yu2ir 2 жыл бұрын
@@yashrajchouhan82 Bhai tune kitni maths padhi hai. Ramanujan was a genius but not a god he can be wrong.
@todten1476
@todten1476 2 жыл бұрын
@@AdityaRaj-yu2ir he could be wrong but then again all his equation were proof later years. And his given equation is used till today to study blackholes. Remember black hole was first predicted in 1916 and ramanunjan died around 1920. Now imagine if he lived more than 32 years. Without any good education background he reached G.H Hardy with his math
@yashrajchouhan82
@yashrajchouhan82 2 жыл бұрын
@@AdityaRaj-yu2ir Bhai Ramanujan ke time par ya uske baad bhi kayi mathematicians the par kabhi yeh suna ki kisine unhe wrong proof kiya ho, humne toh yeh hi suna ki jo koi naa kar paya woh Ramanujan sir ne kiya toh I think he's the mathematician God and yadi yeh baat galat hoti toh mathematicians bohot pehle hi proof kar chuke hote kyuki duniya mein tere jaise bohot log hain jo Indians ki success se jalte hain aur hn paradox ka matlab hi yeh hota hai ki dekhne par galat lage par vastavikta mein sahi ho
@AdityaRaj-yu2ir
@AdityaRaj-yu2ir 2 жыл бұрын
@@yashrajchouhan82 tumhari knowledge kam hai
@NageshwarRTMehta
@NageshwarRTMehta 2 жыл бұрын
Sum of series of number greater than 1 is always ♾️infinite As it is solved in all steps if you think about relative elements taken from different series have so much gappings....... A And if you think answer this series is right then I have an idea that you can give me that amount of money and there is no loss of you 😄 But salute to RAMANUJAN sir 🇮🇳🇮🇳 May be people are unable to find wrong step involved in this solution.... 😇
@soujanyoghosh9174
@soujanyoghosh9174 2 жыл бұрын
♾️-♾️ is indeterminate form
@dafureveerbhadra2772
@dafureveerbhadra2772 2 жыл бұрын
Bro, this result helps in solving string thoery. No other value of sum of natural numbers solve string theory
@dafureveerbhadra2772
@dafureveerbhadra2772 2 жыл бұрын
Also this proof is not actual, the actual one is given by using gamma function
@shibanjanmukherjee3706
@shibanjanmukherjee3706 2 жыл бұрын
Yes this proof is wrong,actual proof requires gamma function and complex analysis
@yashrajchouhan82
@yashrajchouhan82 2 жыл бұрын
What!!! You people are saying that Ramanujan has done wrong
@nishantverma2966
@nishantverma2966 2 жыл бұрын
It's pure imagination and can't be thought by ordinary mind Ramanujan Sir was inhuman
@HoshangGovil
@HoshangGovil Жыл бұрын
By ChatGPT: The Ramanujan Paradox is a mathematical result that appears to contradict common sense, as well as some basic principles of calculus. It is named after the Indian mathematician Srinivasa Ramanujan, who discovered the paradox in the early 20th century. The paradox involves a sum of an infinite series, similar to the divergent series mentioned in the previous question. Specifically, the paradoxical result arises from considering the sum of all positive integers and the sum of their squares: 1 + 2 + 3 + 4 + ... = -1/12 1^2 + 2^2 + 3^2 + 4^2 + ... = 0 These results may seem surprising or counterintuitive, as it appears that we are summing an infinite number of positive terms to obtain a negative value in the first equation. However, it is important to note that these results do not represent actual sums in the usual sense. Instead, they are examples of a more general concept in mathematics called analytic continuation, which involves extending a function beyond its original domain in a way that preserves certain properties. The Ramanujan Paradox has been a topic of much debate and controversy over the years, with some arguing that the paradoxical results are simply mathematical artifacts with no physical significance, while others suggest that they may have applications in areas such as quantum field theory and string theory.
@AdityaKumar-ji8dk
@AdityaKumar-ji8dk Жыл бұрын
Ramanujan proved his theorems when he was dying...those were the last 2-3 years of his life when he prepared all the proves of his theorems...he worked in very poor health conditions...blood coming out of his mouth with cough, but still writing...you can see such scenes in the movie 'the man who knew infinity'. He devoted his whole life to to bring out his theorems and formulae so that all the theorems will be preserved. He worked for giving the world something great, not for his own wants. He is a true legend...a mathematician which will be remembered forever.
@Amit1994-g9i
@Amit1994-g9i 3 жыл бұрын
These things work only if the series converge, else there exists a countability of infinity which states that every infinity is not equal.
@ayushsinha1298
@ayushsinha1298 2 жыл бұрын
Yep I'm a jee aspirant and was thinking the same that when he replaced and take common minus and say it A ,I myself thought that how "that" infinity in which +1 was included and how "that" infinity in which 1 was not included can be same????
@rohanmishra23
@rohanmishra23 2 жыл бұрын
@@ayushsinha1298 because if we add 1 in infinity it is also an infinity
@lalitchoudhary3540
@lalitchoudhary3540 2 жыл бұрын
Exactly, what I want to say
@theseeker9591
@theseeker9591 2 жыл бұрын
I understand what u say but do u have a reason to say that algebra don't work if series is divergent.
@ashishj2358
@ashishj2358 2 жыл бұрын
kzbin.info/www/bejne/j6asep2Cp5upi6M
@ajslive334
@ajslive334 2 жыл бұрын
Sum of all natural numbers is -1/12 Which is impossible but the way he proved is amazing But it also shows that if we take another series of a and b of a different type then a different answer would also come But the truth is that sum of all natural numbers will never be negative and cannot be solved by anyone in the universe
@inquisitiveindian36
@inquisitiveindian36 2 жыл бұрын
Yes. That's what paradox is defined as.
@krishnkantshridhar664
@krishnkantshridhar664 2 жыл бұрын
Sir I am very curious and wants to study about more such equations by you please start a Ramanujan Series where you teach us these type equations .Its my humble request .🙏🙏🙏🙏
@Aakashmahto17
@Aakashmahto17 Жыл бұрын
Next shri Ramanujan of Indian Aman sir 💓
@samirpyakurel8059
@samirpyakurel8059 Жыл бұрын
mistakes 1. A=1-1+1-1+1..... from here he take 1 out and take minus common i.e, A=1-(1-1+1-1+1-1+.....) now he says all the things in bracket is equal to A which is completely wrong first A is different than the second A because one 1 is taken out if A is n then second A is obviously n-1. since we are taking about infinity we take it as granted that every infinity is same which is actually not true. i cant include everything in this comment but thats my major point. ramanujan is a legend mathematician but he was a human too. if someone will say 2+2=5 would you believe it? no but we have lots of proofs that supports it. there are lots of mistake in above proof but the first step is mistake itself.
@gss-motivation4903
@gss-motivation4903 2 ай бұрын
True..Ramanujan applied the rule of convergent series to divergent or oscillating series and hence obtained the erroneous result.
@plasma-xp2rq
@plasma-xp2rq 2 жыл бұрын
wait, is this not wrong? for a divergent series, we cant perform all those operation. Although there can be a connection between zeta(-1) and this series but they wont be equal.
@surajv1986
@surajv1986 2 жыл бұрын
Thanks a lot Sir for taking the efforts to explain lucidly the works of our great Mathematician Shri Ramanujan!!!
@Yuvrajsingh-3ub
@Yuvrajsingh-3ub 2 жыл бұрын
Greatest mathematician... Ever on the earth. 🌎🌎
@anmolavhad1118
@anmolavhad1118 Жыл бұрын
Sir jab hum iss equation se -1 common nikalenge to +♾️ bhi -♾️ ho jayega to vo equal kaise ayenge A=1(-1+1-1+1-1+........♾️) A=1-(1-1+1-1+1-1+......--♾️) So, A is not equals to (1-1+1-1+......--♾️)
@INDUDWIVEDI-jr8rp
@INDUDWIVEDI-jr8rp 4 ай бұрын
भाई तुमको कॉमन कैसे लिया जाता है ये नहीं पता इसलिए तुम ऐसा कह रहे हो पहले मुझे भी नहीं पता था तब मुझे भी ये समझ में नहीं आया था।
@harisankargadnaik5207
@harisankargadnaik5207 Жыл бұрын
Ramanujan doing misuse of infinity chain . A = 1 - A likhne main galti hui hai. A not equal to 1 - A . Kiun ki 1 bahar hai aur ek term kam ho rha hai andar wale ko A assume karna sahi lag rha hai but ye sahi nhi hai . Example :- we say mass of sea remain same after taking one balti of water from sea but actually the mass of the sea changes. This is my point of view 🤗❤️
@satveersingh2664
@satveersingh2664 2 жыл бұрын
Although I m not from Mathematics ,I can understand u' r teaching ,u r best teacher in Maths .
@sudiptasamajdar9156
@sudiptasamajdar9156 2 жыл бұрын
{n} is a divergent sequence, so sum of all natural number canot be a finite quantity. {(-1) ^n+1. n} is also not convergent it is undefined oscillation. So we can't assume any real quantity A or B as a sum of this series.
@soumyaghosh8823
@soumyaghosh8823 2 жыл бұрын
Only Absolutely convergent series can make rearrangement and sum remains unaltered by Riemanns theorem
@rudradansena6298
@rudradansena6298 2 жыл бұрын
Yes that's true but who will teach this kind of bhakt where real analysis not exist for this kind of teachers , and I think ramanujan had no idea about the convergence so that he has did such type of blunder .
@curiosityandlearningforciv662
@curiosityandlearningforciv662 2 жыл бұрын
Hello Mr. Aman, Captain XYZ( Indian armed forces) this side, I donot have a formal background of maths but I gave a thought on this series and found out following assumption flow in your calculations : You assumed 1+2+3+4........= S Now by assuming the series sum to be a finite variable S, you have forced the certainty on infinity(because only after that you were able to solve B =-4S +S =-3S but actually what you are solving is - -4* infinity + infinity). And due to this we see such an absurd answer!!
@animasharma2650
@animasharma2650 2 жыл бұрын
Shut up until u know infinity
@sarfaraz660661
@sarfaraz660661 2 жыл бұрын
A blind person perceive all hole is same.
@bjhonusa
@bjhonusa 2 жыл бұрын
Term Infinity means some number you can not imagine. It does not means it's beyond calculation. Read the maths carefully.
@dhruvchaudhary4684
@dhruvchaudhary4684 Жыл бұрын
​@@animasharma2650😂 ok wait
@aadilansari5997
@aadilansari5997 Жыл бұрын
Sir you have the mind to question and query. Please read up quora especially Alon Amit.. You are right, when dignify infinity with the title of a number, you are inadvertently playing fast and loose with the concept of a number. For example in a normal number system if a+b = a+ c then b=c. But if you add infinity to the normal number set then Inf + b = Inf+c doe not allow us to infer that b= c.
@rfsplayer162
@rfsplayer162 Жыл бұрын
-1/12= reciprocal - 12 divide by -1 = -12=-12/1=-12 multiply 1 = -12+0=-12=-12 divided by 0=0 Hence infinity =0 Amaan
@p.h.gaming9319
@p.h.gaming9319 Жыл бұрын
Perfect
@-SARTHAKSHARMA
@-SARTHAKSHARMA 9 ай бұрын
Ramanujan sir was uncontrolled nuclear rxn salute to such personality in just of 32 age 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥
@rajeshmalviya1968
@rajeshmalviya1968 2 жыл бұрын
Thank you brother.....I am maths lover....and while watching this clip, many times my eyes got wet in love with The Great and genius Poojya Ramanujan Sir........your way of explanation is beautiful........❤❤❤❤❤🙏🙏🙏🙏🙏
@Sumit_memer.
@Sumit_memer. 2 жыл бұрын
RAMANUJAN JI MAHARAJ KI JAI PURE DUNIYA ME JAIJAIKAR HO AAP MAHAN HA (RAMANUJAN JI AAP MAHAN HO)
@nihal7771
@nihal7771 3 жыл бұрын
😶kamse kam 5-6 mahino se dimag kharab ho gaya tha yeh jaan ke ki sum of natural number till infinity -1/12 hota hai but aaj finally proof mil gaya tho accha lag raha hai Thanks for this video sir ji
@sauravsutar2125
@sauravsutar2125 4 ай бұрын
Bhai iska proof toh 2014 se youtube channel PE hai... Nd still it is a illogical proof
@Pw_insider07
@Pw_insider07 7 ай бұрын
if you take A = 0 then you write A= A-1 ....does it makes any sense ??????
@user-bunny_01
@user-bunny_01 Жыл бұрын
We can also prove A = ½ ..in this method :- 1-1+1-1+1-1+1..... Its like infinite G.P whose common ratio is -1 and first term is 1 " sum of infinite G.P = first term / 1-common ratio " => 1/1-(-1) = 1/2
@ritxve
@ritxve 2 жыл бұрын
Isme problem isliye aa rhi h kyuki ∞ terms h aur ∞ koi bhi ek specific number nhi h wo khud hi thik se defined nhi For example, let's say X = ∞ Also we know that ∞ + 1 is also ∞ » X + 1 = X » 1= X - X » 1 = 0 (LOL) As it's not true reason is that ∞-∞ is simply inderminate and not zero.
@MrRaghavann
@MrRaghavann Жыл бұрын
Correct yar something is wrong here.
@parteek_bhamania
@parteek_bhamania 2 жыл бұрын
Apne physics wallah kuchh kisi karn se hi chhoda hoga ya jo time alakh sir ka tha wo aap ko soot nahi kar raha hoga. Lekin sir ek baat bataun apse badhiya maths teacher maine aaj tak nahi dekha aur sayad na hi age kabhi dekhoon ga. Logo ka kya hai wo to ease hi hate felate hain but sir jab main bada hokar kuchh ban jaunga na to alakh sir se to kya hi pata lekin apse jaroor milonga. Thanks sir for giving me this type of mathematics knowledge jab main apse maths padhta hoon to sach batun maza hi aa jata hai. Once more thank so much 😊😊🙏🙏
@deltechdiaries5907
@deltechdiaries5907 2 жыл бұрын
the greatest mathematician ever
@joydebnath2111
@joydebnath2111 Жыл бұрын
Sir you are great. I tried it in finite case 🙂 B=1-2+3-4+5-6+.........n=-1-1-1-1-........n/2=-n/2 S=1+2+3+4+........n Now, S+B=2(1+3+5+.......n/2)=2×n^2/4=n^2/2 Or,S=n^2/2-B=n^2/2+n/2=n(n+1)/2 And S-B=2(2+4+6+........n/2)=2×n/2×(n/2+1)=n(n+2)/2 Or,S=n(n+2)/2+B=n(n+2)/2-n/2=n(n+1)/2 In both case sum of n natural number is n(n+1)/2 which is true.🙏
@goldy7141
@goldy7141 Жыл бұрын
Sir A series mai tha 1-1+1-1...infinity Suppose isme n terms hai Toh jab isko modify kiya 1-(1-1+1...) Toh apne jisko A mana usme number of terms toh alag hojayenge n-1 terms honge as 1 ko pehle bhar leke - common liya toh usko A kaise mana? Even if infinite tak ho tab bhi toh kuch no. Of terms rahe honge?
@GursewakSinghOfficial
@GursewakSinghOfficial 3 жыл бұрын
GAJAB SIRJI 🔥🔥🔥🔥 WE WANT MORE VIDEOS LIKE THIS ❤
@learningpoint060
@learningpoint060 2 жыл бұрын
You can add anything and subtract anything from infinity so that's make no sense if we write A=1-A..., If this makes sense we can prove anything because we don't have proper algebra of infinity... And maths don't run on assumptions... So it should just be considered as paradox as per my opinion.. as I am a Maths teacher too.. 🙌🏻
@jay1735
@jay1735 2 жыл бұрын
Where is the assumption? It is just a paradox... And Ramanujan gave the proof..
@SwayamSrivastava-D
@SwayamSrivastava-D Жыл бұрын
@@jay1735 he had never given that prove . He had just gave the result and from then people are trying to prove that but not one had proved it yet . This prove is also not right prove it have some mathematical errors
@cyphex9809
@cyphex9809 2 жыл бұрын
The problem in this proof lies in the very first step. The sum of the given AP is very clearly positive infinity (due to it diverging off from any finite value) which has been assumed as S and then you have used that variable in solving equations which results in such an absurd answer.
@mohammadshamim3065
@mohammadshamim3065 2 жыл бұрын
Agreed with you ...
@md.nahidrezashovo4147
@md.nahidrezashovo4147 Жыл бұрын
X = 1+1+1+1+1+...... => X = 1+(1+1+1+1+......) => X = 1+X => X-X = 1 => 0 = 1 See paradox is paradox, it seems to be real but not real.😃
@yourenglishtour
@yourenglishtour Жыл бұрын
Ramanujan's story is mind blowing. Eyes tear when I hear about his magical mind of maths...😍
@utuberaj60
@utuberaj60 2 жыл бұрын
One more point Sir. Can we not also prove the sum of infinite natural nos in an Arithmetic series to be infinity using the basic formula S= n(n+1)/2, and ser n= infinity?
@siddharthreddy9461
@siddharthreddy9461 Жыл бұрын
​​@itzaadi4627o it isn't Infact, the above sum is tending or diverging to infinity under regular mathematical axioms for finite real numbers
@narpendersingh6511
@narpendersingh6511 2 жыл бұрын
Dear sir thanks for registration of paradox but you didn't mention why this paradox occurs. You forgot to mention the paradoxical outcomes generated by manipulation of a divergent series i.e here in this case both series A and B are divergent which can be proved by limit theorem and in an attempt to manipulate divergent series the resultant is a paradox which also originates from riemann zetta function.
@bhavanarushiandey4101
@bhavanarushiandey4101 Жыл бұрын
My heart full thanks to you sir. The reason is a teacher must need to the cause .
@abhishankpaul
@abhishankpaul 11 ай бұрын
True
@AshishSinha-x6c
@AshishSinha-x6c Жыл бұрын
Series A Converges to 0 or 1 Series B is divergent meaning its sum shall not converge to a number which means sum of B is not a number and the value 1/4 is obtained by mathematical operation between number and a non number. Series S is also a divergent series meaning sum of S is not a number and using mathematical operations between number and non number is done..... So this derivation from starting assumed S as a number which it is not and found it out.
@rayxxee1826
@rayxxee1826 Жыл бұрын
Looks like the teacher doesn't understands the concept of infinity he most probably thinks that 1/0 is equal to infinity
@vishalyadav0099
@vishalyadav0099 9 ай бұрын
India is blessed with legends like Ramanujan Sir.. ..
@ramanjeet1111
@ramanjeet1111 2 жыл бұрын
What does Ramanujan’s infinity concept mean? Does it mean that our universe has an end point, or does infinity have an end also?
@adarshraina137
@adarshraina137 2 жыл бұрын
Yes
@ramanjeet1111
@ramanjeet1111 2 жыл бұрын
@@adarshraina137 wat yes
@shlokjadhav8253
@shlokjadhav8253 3 жыл бұрын
Sir please also make one on Aryabhatt sir, bhaskaracharya sir, Dr.C.V.Raman sir.
@chandansharma4258
@chandansharma4258 2 жыл бұрын
Practically and generally it's impossible to find sum of infinite natural numbers is negative. Through questions it can be find all that .
@productionmillionviewsz5338
@productionmillionviewsz5338 Жыл бұрын
Great ji and He always said that Mata is telling me maths and he is great
@rrawatsachin93
@rrawatsachin93 Жыл бұрын
Jab jab me The great mathematician Ramanujan ke baare me sunta sach me etana proud hota ki aankho me aashu aa jaate hai, proud to be an indian. Jai hind
@adarsh659
@adarsh659 3 жыл бұрын
Ye sumation conventional summation nhi h.. This is a technique assigned to provide a numerical value to a divergent summation..
@kartiknayak8380
@kartiknayak8380 3 жыл бұрын
Sir aise hi bhut maza aata bhut ache ❤️
@karanpvsa9853
@karanpvsa9853 3 жыл бұрын
Bhannat sir ramanujan sir ji ki jay
@saquibmohammad2860
@saquibmohammad2860 Жыл бұрын
For the sake of students, the series 1+2+3+.... does not REALLY equate to -1/12. What's actually happening is actually a consequence of a result called Riemann Rearrangement Theorem. The theorem states (very loosely I'm not going in to detail) that if the order of terms in a particular series are shuffled, or rearranged, an infinite series can be used to give any number of any choice. For example, let us take 1-1+1-1+..... Now if I want to rearrange this sequence, I can choose to write it like this. 1+1-1+ 1+1-1+.... Since both positive 1's and -1's are infinite, I can write this indefinitely but by earlier logic as presented in the video, the sum is tending towards 2/3. Now which one is correct? The answer is both. Depending on how you write the series, the sum changes. So in a way, the answer depends on the way the series is written. So, if you see this equation again, understand that this answer comes out to be -1/12 only when this series is written in this particular fashion. And it can be made to be anything. If we write it in some other way.
@bhausahebkunjir
@bhausahebkunjir Жыл бұрын
The series is Divergent . You cannot perform these oerations. Here a mistake is being glorified for publicity. If done for fun, the should have been clrified.
@saquibmohammad2860
@saquibmohammad2860 Жыл бұрын
@@bhausahebkunjir it's Divergent but not absolutely Divergent. That's why I said the sum is not really equal to -1/12 when written as a sum of natural numbers. That's Riemann's rearrangement theorem, essentially stating that series that are Divergent but not absolutely can be rearranged to give any sum.
@prabhassen7287
@prabhassen7287 4 ай бұрын
This is about popular mathematics and about a genius who did not have any formal mathematical training. I think it is unfair to bring in modern day mathematical rigors into it. Hardy understood this and took this unassuming genius under his wings and presented him to the modern world of mathematical rigors d further research. We can only wonder how his intuitive thoughts are now used in modern Era mathematics and physics.
@headshotgaming7652
@headshotgaming7652 6 ай бұрын
Jay shree ramanujan ji ❤❤❤❤
@methleshkoshle7643
@methleshkoshle7643 Жыл бұрын
What a gift to the world Ramanujan sir. You are great teacher sir 👍.
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