@@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)
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.
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 ♾️😂
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.
@@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.
"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 💞
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 🙏🏻🙏🏻🙂🙂
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..
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.
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!
@@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.
@@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.
@@amaanalrashid8273 12 see this ua-cam.com/video/YuIIjLr6vUA/v-deo.html 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 👉 ua-cam.com/video/w-I6XTVZXww/v-deo.html Ye sir jee ke lia sahi hai lekin general higher topics ke lia nahi pata .
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
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
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,,
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
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...
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,.....
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.
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 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.
@@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.
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
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.
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
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
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..
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.
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.
@@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
@@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
@@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.
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
@@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.
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
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.
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.
😶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
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 🙏🙏
@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 .
@@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.
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.
@@Rahul.G.Paikaray27 First of all the prove is wrong A and B are divergent series . And its copied from numberphile video ua-cam.com/video/w-I6XTVZXww/v-deo.html which is itself wrong which was rectified by mathlogger video 👉 ua-cam.com/video/YuIIjLr6vUA/v-deo.html The actual proof is not so simple he is proofing like 1=2
@@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......
{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.
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 .
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
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
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????
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!!
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.
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 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
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.
Hardy Sir: Ye question kisi se solve nahi hua Ramanujan Ji: Maine toh masti masti mein 2 tareeko se kar dala This line was epic. Hats off to the Greatest Mathematician Ramanujan Ji
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?
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.
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 😊😊🙏🙏
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.
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.
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.... 😇
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.
I think this person is the definition of teacher for me because once when I was a child my grandfather told me about Ramanujan paradox and I was very confused as to how it is possible, and finally my doubts were cleared and I learned new thinking in mathematics Thank you so much sir
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 .🙏🙏🙏🙏
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.
Ramanujan was a great genius , but was certainly sure that this inequality is of course not correct . You can get it by incorrect treatment of diverging sums. There are similar results for conditionally convergent series ,for which Riemann proved that you can get any number as the sum , by choosing different orders of summation.
this paradox happens because we dont know to use infinity yet..we cant subtract infinity to infinity, it wont give you zero or any positive or negative number..here in this equation this paradox happened because it took infinity substracted from infinity as ZERO which is actually not zero..but Ramanujam used this paradox to solve some divergent series..the paradox is neither true or false but just what its defined, and used for infinite series to solve equations
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
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
It's a paradox
@@dipikaghosh6224 string theory me lagta hai
@@silverfangg45 nope
@@Amit1994-g9i
In String theory it uses
@@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)
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.
Finally, someone who actually knows how math works.
ua-cam.com/users/shortsGfBXmTDz15E?feature=share
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 ♾️😂
Yeah,if th no. of terms,if are even ,then the sum is 0 and if odd,then 1😊 well said ,bro!
Exactly
Just 1 word
Salute to Mr. Ramanujan ji
that's 5 words...
@@pulsar2977 lmao bro .but Ramanujan sir 🙏.
Thats 5 words
The line " fat gyi thi .....aankhe logo ki"is just OP 😂😂😂😂😂
😂
😂😂😂😂😂
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.
A Mathematitians who breaks the law of Mathematics 😵
Salute to the legend
Proud to be an indian
Laws of mathematics are never break they are generlize
He didn't brake any law. he just didn't know what the Infinite really is.
@@O-Kyklopfr there are many loopholes in the term infinite itself , smart mathematicians can make more equations like this
@@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.
Why are you breaking english grammar rules?@@O-Kyklop
"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 💞
Mathematician bolke illogical baat bhi bolrhe ho
Meri bhua to nahi hai
F
kyu bhai tumhara knowledge jayada ho gaya hai kya kya tum ramanujan se zayada gyani ho
"An equation for me has no meaning unless it expresses a thought of God!!"
~ *S. Ramanujan* ♥
*JAI NAMAGIRI THAYAR DEVI* 🚩♥
So that's why he was so much interested in infinity equations?
@@IIT24Aspirant yepp!
Ramanujan is a true genius in Mathematics, according to this statement mentioned by him.
Aa gaye gawar
It is exactly true that the Ramanujan's statement.
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 🙏🏻🙏🏻🙂🙂
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..
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.
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!
@@badriiyengar what crack you smokin?
@@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.
@@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.
Tu galat Sikh rha hai
The best channel to fall in love for mathematics
The proof is wrong
@@silverfangg45in which class are u studying now
@@amaanalrashid8273 12 see this
ua-cam.com/video/YuIIjLr6vUA/v-deo.html 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 👉 ua-cam.com/video/w-I6XTVZXww/v-deo.html
Ye sir jee ke lia sahi hai lekin general higher topics ke lia nahi pata .
Maine Ramanujan summation par atleast isse better video banaya hai
And please do subscribe the channel
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
भगवान कसम
इससे चूतिया intro आज तक नही देखा
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
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,,
@@Rhythmraj009 bro no,this series is used to prove string theory.Aye phy banate hain,thodta nahi hai.
@@Rhythmraj009 if you don't believe me you can read online materials
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
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
Humble Pranams to Ramanujan Sir. Besides, the tutor’s narration is exceptionally brilliant.🎉
While my great admiration is for Ramanujan, I am grateful to you for bringing to light in simple way his greatness. Thank you Sir
Finally someone made me understand this series without calculus
Thank you very much sir
This video is wrong in so many levels. He is fooling you
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...
@@anubhabmondal5342 yeah mathaloger made a 40 minutes long video explaining why this proof was wrong.
@@ankurgupta9106 yes that video explains everything very clearly
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,.....
While preparing for data science mathematics ( linear algebra CALCULUS, STATS & discrete mathematics )..i truly think of Sri Ramanujan sir 🙏❤️❤️🙏🇮🇳
Y not god?
@@samiullahk7223 why not ramanujan?
Maths God= ramanujan hence proved
@@IsaacNewton818 sir pliz laws vapas lelo apne 🙏
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.
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.
@@O-KyklopRamanujan was correct it is the video that is wrong
@@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.
@@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.
@@someone-jl4sj It xdoesn't change anything. If the result is oo=-1/12, is wrong.
Rules of finite maths don't apply to infinite series.
True.
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
Yes, with out absolutely convergent we cannot rearrange the terms. This prove is wrong.
Without Taylor series expansion??
I think Taylor series should be best applicable here.
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.
Thanks for fyi
We use a made up value to prove a made up theory doesn't mean your made up value is true
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
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
Bhai kya keh raha samaj ma nahi aa raha
@@tanmaynayak2250 BSC kro tb smj me ayega
Its divergent series, so can't be converge to any real no. 😂😂
Maths hons karo tab samjh ayega
@@Mr.Ak.2608 the actual proof is by remmans zeta function
@@soumyajitsarkar507 by both reimann zeta and direchlet eta functions
Salute to Ramanujam. Sir you explained in excellent manner. You are real maths master.🙏🙏
I could not hold my tears. How it is possible. Real hero of Math. Salute you Boss.
Wrong hai bhai paradox
SALUTE TO THE GREATEST MATHEMATICIAN OF ALL TIMES RAMANUJAN SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
India is blessed with legends like Ramanujan sir
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..
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.
@@ankhi6604 yess! Every body is perfect in their own field..
I pay huge Respect towards Ramanujan sir 😄😃
My reaction was Oh My God after he proved it😂😂❤
Hats off to Ramanajun and Aman sir🙏
Proud to be an Indian. Huge respect for S. Ramanujan 🙏🙏🙏🙏
The man who knew infinity ♾️♾️♾️
The Man Who Knew Infinity (Srinivasa Ramanujan)🙏🏻🙏🏻🙏🏻
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.
Bro, sir Ramanujan was much more beyond than our thinking, he would have thought about that before
@@yashrajchouhan82 Bhai tune kitni maths padhi hai. Ramanujan was a genius but not a god he can be wrong.
@@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
@@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
@@yashrajchouhan82 tumhari knowledge kam hai
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?
For their sum be -1/12 n must be infinity which we cannot imagine
Can't imagine n without this paradox
I think the paradox happened because series A was supposed to be 0 but became 1/2
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.
@@praveenkumarsingh1436but in no situation it can be 1/2
@@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.
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
This is the great way of giving tribute to Ramanujan ji...Thank you Aman sir...🙏👏
The explanation just blown my mind 🤯🤯🤯🤯
Sir, Please make a video on NIKOLA TESLA SIR🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🇮🇳
@Abhay Pandey naam batana to Zara indian scientist
Google search mat karna
@Abhay Pandey Bhai, INDIAN SCIENTISTS भी महान थे पर ,NIKOLA TESLA ki kahani सुन लेना sir से एक बार ,आप चोक जाओगे 🙏🏻
@@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.
@@silverfangg45 abe Bengali tu apni aaurate bechne me focus kar. india pe already kai saare mathematicians, philosophers or academics hai.
दुर्भाग्य हैं हमारे देश क़े युवा का
Next shri Ramanujan of Indian Aman sir 💓
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
@@AnmolSah27 Tere bap se jayada Knowledge hai sir ka
@@AnmolSah27 Tera Pura family sale inka mukbla nahi kar sakta h , aur tu to abhi bachcha h 🤣🤣🤣
@@jsk5549 ha bro uska baap ka baaap ka baap ka baap ......... Infinite time tak koi utna nahi janta jitna aman sir ,🤣🤣🤣
The proof presented in the video is completely wrong
@@ankurgupta9106 are yaar dekho thik se
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!
Series A is discussed by Mohit Tyagi in maths for fun
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.
But this is an ap( arithmetic progression) not gp( geometric progression)
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.
😶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
Bhai iska proof toh 2014 se youtube channel PE hai... Nd still it is a illogical proof
Greatest mathematician... Ever on the earth. 🌎🌎
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 🙏🙏
This video is wrong
@@ankurgupta9106 Yess
This video is 100 percent wrong, since distribution law isn't correct in infinite series
@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 .
@@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.
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.
¡Gracias!
THIS VIDEO IS WORTH #1 TRENDING!! 👍👍👍 JUST AMAZING SIR !! SALUTE TO AMAN SIR .. AND COUNTRY'S PROUD SRI.RAMANUJAN SIR 🙏🙏
The proof is wrong bro
Sahi bate de
@@Rahul.G.Paikaray27 First of all the prove is wrong A and B are divergent series . And its copied from numberphile video ua-cam.com/video/w-I6XTVZXww/v-deo.html which is itself wrong which was rectified by mathlogger video 👉 ua-cam.com/video/YuIIjLr6vUA/v-deo.html The actual proof is not so simple he is proofing like 1=2
@@silverfangg45 thanks brother
@@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......
It's pure imagination and can't be thought by ordinary mind Ramanujan Sir was inhuman
{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.
Only Absolutely convergent series can make rearrangement and sum remains unaltered by Riemanns theorem
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 .
Ramanujan sir jaisa na koi tha aur na koi honge mera dawa hai.. ❤❤❤🎉🎉🎉
Ramanujan sir was uncontrolled nuclear rxn salute to such personality in just of 32 age 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥
A huge salute to ramanujan , such a great mathamatician who born in india 🙏🙏
Proud to be an indian🇮🇳❤
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
Yes. That's what paradox is defined as.
Although I m not from Mathematics ,I can understand u' r teaching ,u r best teacher in Maths .
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
India is blessed with legends like Ramanujan Sir.. ..
The Man Who Knew Infinity
*JAI NAMAGIRI DEVI* 🙏🙏
These things work only if the series converge, else there exists a countability of infinity which states that every infinity is not equal.
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????
@@ayushsinha1298 because if we add 1 in infinity it is also an infinity
Exactly, what I want to say
I understand what u say but do u have a reason to say that algebra don't work if series is divergent.
ua-cam.com/video/YuIIjLr6vUA/v-deo.html
the greatest mathematician ever
Genius Ramanujan ji 🙏 Thanks Aman ji for presenting it nicely, and praising the hero of Maths from India. 🇮🇳✌️
-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
Perfect
Sir aise hi bhut maza aata bhut ache ❤️
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!!
Shut up until u know infinity
A blind person perceive all hole is same.
Term Infinity means some number you can not imagine.
It does not means it's beyond calculation.
Read the maths carefully.
@@animasharma2650😂 ok wait
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.
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.. 🙌🏻
Where is the assumption? It is just a paradox... And Ramanujan gave the proof..
@@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
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.
True..Ramanujan applied the rule of convergent series to divergent or oscillating series and hence obtained the erroneous result.
Great ji and He always said that Mata is telling me maths and he is great
Thanks a lot Sir for taking the efforts to explain lucidly the works of our great Mathematician Shri Ramanujan!!!
Practically and generally it's impossible to find sum of infinite natural numbers is negative.
Through questions it can be find all that .
RAMANUJAN JI MAHARAJ KI JAI
PURE DUNIYA ME JAIJAIKAR HO AAP MAHAN HA (RAMANUJAN JI AAP MAHAN HO)
Hardy Sir: Ye question kisi se solve nahi hua
Ramanujan Ji: Maine toh masti masti mein 2 tareeko se kar dala
This line was epic.
Hats off to the Greatest Mathematician Ramanujan Ji
Unbelievable result
Ramanujan sir is greatest person ever❤❤❤❤❤
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?
@itzaadi4627o it isn't
Infact, the above sum is tending or diverging to infinity under regular mathematical axioms for finite real numbers
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.
Agreed with you ...
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 😊😊🙏🙏
Wah ,wah kitna sundar sa pyara sa solution nikla yeh theoretical question par
Really he was a Indian geñius. Really, he is Mother's gift to not only India but to the World.
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.
Ye sumation conventional summation nhi h.. This is a technique assigned to provide a numerical value to a divergent summation..
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.
Correct yar something is wrong here.
Jay shree ramanujan ji ❤❤❤❤
Sir please also make one on Aryabhatt sir, bhaskaracharya sir, Dr.C.V.Raman sir.
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.... 😇
♾️-♾️ is indeterminate form
Bro, this result helps in solving string thoery. No other value of sum of natural numbers solve string theory
Also this proof is not actual, the actual one is given by using gamma function
Yes this proof is wrong,actual proof requires gamma function and complex analysis
What!!! You people are saying that Ramanujan has done wrong
GAJAB SIRJI 🔥🔥🔥🔥
WE WANT MORE VIDEOS LIKE THIS ❤
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.
Looks like the teacher doesn't understands the concept of infinity he most probably thinks that 1/0 is equal to infinity
I think this person is the definition of teacher for me because once when I was a child my grandfather told me about Ramanujan paradox and I was very confused as to how it is possible, and finally my doubts were cleared and I learned new thinking in mathematics
Thank you so much sir
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 .🙏🙏🙏🙏
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.
My heart full thanks to you sir. The reason is a teacher must need to the cause .
True
Wanted to know the reason for quite a while ☺️
This proof is wrong bro
Sir i will give you more priority than ramanujan as he was failed to deliver his observations to us but you were successful🎉❤
Ramanujan was a great genius , but was certainly sure that this inequality is of course not correct . You can get it by incorrect treatment
of diverging sums. There are similar results for conditionally convergent series ,for which Riemann proved that you can get any
number as the sum , by choosing different orders of summation.
Thanks sir for an amazing session
Thanks for the explanation. It's awesome indeed.
Ramanujan paradox kis book me milega
@@uniquemathematicscentre3754 I don't know. I usually search in UA-cam videos.
What does Ramanujan’s infinity concept mean? Does it mean that our universe has an end point, or does infinity have an end also?
Yes
@@adarshraina137 wat yes
this paradox happens because we dont know to use infinity yet..we cant subtract infinity to infinity, it wont give you zero or any positive or negative number..here in this equation this paradox happened because it took infinity substracted from infinity as ZERO which is actually not zero..but Ramanujam used this paradox to solve some divergent series..the paradox is neither true or false but just what its defined, and used for infinite series to solve equations
Excellent!
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
Ramanujan's story is mind blowing. Eyes tear when I hear about his magical mind of maths...😍