Have fun playing around with infinities! For a proof of this you can watch this video (If I did it, I will just repeat this proof)- th-cam.com/video/YuIIjLr6vUA/w-d-xo.htmlsi=oqNokKAJSxnhUE-Z In the Video I say beta function regularization but wanted to say zeta function regularization sorry for that!
Sir your explanation is 100% correct lekin, The series S= 1+2+3+4+5...∞ Is considered "divergent" We can understand it by this example Imagine you have a piggy bank, and on the first day, you put in ₹1, on the second day you put in ₹2, on the third day you put in ₹3, and so on. Every day, the amount you put in gets bigger. If you keep doing this forever, the amount of money in your piggy bank will just keep growing and growing without ever stopping. There is no limit to how much money you'll end up with. Means kabhi ye series khtm hi nhi hogi kyunki hum har din piggy bank me paise daal rhe hain. Same will happen in the series , and it won't give a finite value because it will just grow bigger and bigger without ever stopping and issi ko hum "Divergent" kehte hain. So, jab hum kehte hain ki ye series -1/12 ke equal hai ye iss principle ke hisab se fit nhi hoti hai jo ki hai "Divergent series"
@@mridulacharya8250There exists infinite real number between two distinct real numbers..then how did you concluded there is no real number between 0.999999.... and 1 ??
i remember i used to talk to you when there was a whatsup group...you are still the best person whom i could talk to abt maths and astrophysics. Keep going! im proud of you!
Amazing! Really eye-opening to see! Before, I was wondering how this divergent series could converge in such a peculiar way, but now I understand the general idea! I would love to see your version of a simplified mathematical proof in a future video. Once again, great explanation!
Been following your channel for i think 2 years now when you had less than 50k subscribers. Thanks for the quality content you provide! Learned something new today.
Thank you, my South Asian brother. Your explanation makes so much sense. Far better than the Western rubbish that most YT videos say. Ramanujan would love you.
"Physics is the medium to perceive the Universe; Mathematics is the language to communicate with the Universe." - Universe is always speaking, humans only have to listened in the right direction, and with the right tools (mathematics).
The best explanation I have seen. Here are couple of things - take the 1 + 2 + 3 infinite series and add 1 to it. Is this allowed? If allowed will the answer be 11/12? What’s the sum of other infinite series - 1 + 4 + 9 + 16 etc.
This is one of a way for developing and giving a relative mathematical value for the summation of infinitely many terms. Your explanation is very appreciated 👍
Just like division by zero is not allowed, addition, subtraction, multiplication and division involving infinity is not allowed in maths Because infinity+infinity is again infinity and not 2 infinity
A guy playing with math, breaking all well-agreed definitions and common sense. No, you can not add positive numbers and get anything negative. There are definitions for convergence. What you can do is use math in your own way and get absurd results. Ramanujan turns in his grave being mentioned in this.
@@Param_Hayaran Infinity can be handled as a group or set and yes it does have distributive and associative properties but ONLY as a group. These do not translate when infinity is used as a number in an equation
Very simple and easy to understand explanation! Please make follow-up video to explain how it's intelligently handled by infinity concept/beta function and its implications in the real world.
Very good job on bridging the gap between the intuitive impossibility of adding apples and never getting -1/12 and how that intution is wrong since we truely have no intuition for infinity.
Infinity is weird and you should not expect that infinity will behave like a normal finite number. Infinity is not a number it can be a number but using it like a number will give you weird results.
-1/12 is the true result under WRONG assumption. The proof is based on the assumption that THE series converges to a number, but it is NOT. End of story.
Problem in handling infinity is that since it's a concept and can never itself be reached, it must be handled by considering the rate of approach to infinity... Infinity x 1 = infinity Infinity x 2 = infinity still but it's rate of approach is now 2x faster.
Good video. I swear most advanced mathematicians don’t understand infinity 😂 Infinity is nonending (c) - 🤣 But to accomplish these types of math tricks, they start by treating infinity as ending. Still, like a child, I love the magic tricks.
0:04 Gauss equation n(n+1)/2 is sum of numbers from 1 to n. Assume n=infinity. Then n(n+1)/2=-1/12 So infinity= -1/2+square root of 1/12 and -1/2 -square root of 1/12
The Following will give you a little bit of insight into what it is all about. 1/3 is a rational number that we can express as 0.3+0.1/3 =0.33+0.01/3 =0.333+0.001/3 =0.3333+0.0001/3 and so on infinitely. Each of above expression is an absolute number (1/3) without use of infinity. But abstract concept of infinity enters scene when you express it as 0.333.. It's only in case of absolute value 1/3 that you can go on adding infinite number of 3's. We know that Numerator/Denominator =Quotient+(Remainder/Denominator) 12/10=1+(2/10) In the same way, 10/10=1+(0/10), but we can also express it like 10/10=0.9+(1/10)=0.99+(0.1/10)=0.999+(0.01/10)=0.9999+(0.001/10)=0.99999+(0.0001/10). So 10/10=1=0.99999.. Remember that adding 9's at the end infinite number of times is only possible because of left remainders 0.1, 0.01, 0.001, 0.0001 and so on.
Thanks for clarification. So that means the equal sign in 1=0.99999.... to infinite is only valid when you add the term +0.0000......1 behind the expression right? Otherwise we should not say 0.9999.... = 1, rather stick to its conventional mathemathical expression: limit n to infinite for 0.9999n approaches 1.
This can't be made by humans.. ramanujan was something else he was a fellow of God and God gave some equations that is the key to go in the other world or universe 😌😌 Only one more fellow of God only can find that key lock We should find that fellow 😞
Moral of the story is you must not try sum up a divergent series upto infinity. Even if you find the sum of a divergent series in terms of 'n' then don't try to evaluate that sum with the limit 'n' tends to infinity !!!
It's just an example of how infinity does not behave like a normal finite number. 0.9999.. is a convergent series so the proof is a lot more concrete than the 1+2+3+4+...+∞ which is divergent.
Sir to be very frank...... Your video although informative in its own right raises more questions than it answers. You should have also tackled the how it happens/the proof behind the expression also along with the why it happens in maths. And you can see those questions in your comments. Please make a video tackling those.
*my teacher talking about adding apples to teach us addition* me: “what about negative apples?” teacher: “well you can’t have negative apples” *starts exponentially mass producing apples*
What I derive from this is that since infinity has no relation to reality, any equation containing it is also devoid of reality, as a natural extension. I would also suppose that, in this case the result could be pretty much anything. I assume -1/12 just stands in as an example of this.
I would argue only thing in the world is infinity , we just look at a part of it and assume finiteness, infinity doesn't raise any question while finiteness does raise many questions, imagine the universe was of size x which is not infinite then that raises an immediate question why this arbitrary value x out of the infinite other values which has no satisfactory answer, the only satisfactory answer is that universe or existence is infinite and we are looking at a part of it which appears to be of size x, so infinity in truly the only real thing on which we apply our limitations to get illusion of finiteness. But this is philosophical argument unrelated to this sum or its analytical values.
Question: How is it that the infinite sum of this series diverges only upto -1/12 and not other possibilities if we may have the freedom to handle the sum by the concept of infinity ?
OK, infinity is not a number. But then we treat it exactly like a number when we multiply 0.99999 ---> by 10 to get 9.99999 -->. And then we go and perform subtraction on it. It seems we get to pick and choose when and when not to treat infinity as a number.
Many times people say things that are absurd to try to seem profound. If you try to add up an infinite series that never converges then it's one example. If you assume something false (that this series converges) then you can prove anything.
Hello my son watch your vedio,s regularly,He is so weak in Liner equation.Pleas teach him how to slove liner equation in quick time.Please make a vedio about this topic.Waiting for your vedio.
The equation only valids if you believe that oo + 1 > oo.. ( oo is not an exact number) As long as you don't believe it (oo + 1 > oo), it means the equation (1+2+..+oo =1/12 is logically wrong...
Something infinity and something undefined are two different things . Infinity may be defined as the representative of the largest real real number. It's not a number but has a well defined existence. For example : limit is infinity and limit not defined are two different things. Intuition must be cleared. Geometry can better explain this equation.
The 1 that you are talking about is not exactly equal to 1...it is approaching 1 remember....so you are essentially calculating the limit when the base is very very little less than 1 or little more than 1, Powered to infinity.....cus if it is actually much more than 1 then it'll lead to infinity and in case it is less than 1 then 0....so 1^infinity is essentially indeterminate form
At 3:43 you subtracted 9.9999... -0.9999... --------------- 9.0000...... So here after decimal .9999... are non terminating recurring number right? So at 4:39 9.990 -0.999 ------------ 8.991 Why you subtract with 9.990 instead with 9.999 because even removing infinity, the number after decimal should be recurring number just like done at 3:43 since we are following same procedure after removing infinity. Plz make me understand this.😮
Because the first equation had an infinite number of nines after the decimal point,while the second one had a finite number of nines(three),which are not recurring.
Have fun playing around with infinities!
For a proof of this you can watch this video (If I did it, I will just repeat this proof)-
th-cam.com/video/YuIIjLr6vUA/w-d-xo.htmlsi=oqNokKAJSxnhUE-Z
In the Video I say beta function regularization
but wanted to say
zeta function regularization
sorry for that!
No ProbleZ
I discovered ur channel today... Glad I did it
Finally few more intuitive math guys in my list
Welcome aboard!
me 2 lol
Me too
Sir your explanation is 100% correct lekin,
The series S= 1+2+3+4+5...∞ Is considered "divergent"
We can understand it by this example
Imagine you have a piggy bank, and on the first day, you put in ₹1, on the second day you put in ₹2, on the third day you put in ₹3, and so on. Every day, the amount you put in gets bigger.
If you keep doing this forever, the amount of money in your piggy bank will just keep growing and growing without ever stopping. There is no limit to how much money you'll end up with. Means kabhi ye series khtm hi nhi hogi kyunki hum har din piggy bank me paise daal rhe hain.
Same will happen in the series , and it won't give a finite value because it will just grow bigger and bigger without ever stopping and issi ko hum "Divergent" kehte hain.
So, jab hum kehte hain ki ye series -1/12 ke equal hai ye iss principle ke hisab se fit nhi hoti hai jo ki hai
"Divergent series"
Bro explains everything so calmly. I love it.
Thank you so much. I've been trying to understand this for ages.
I love your videos! thank you for making this one
The logical proof of " 0.999..=1" is that there exists no number between 1 and 0.999...and hence these two are exactly same
An example would be that 1/3 = 0.333… that x 3 would be .9999… but 1/3 x 3 should be 3/3
but if you do the same think for 0,888...=1 its the same but we fond that 0,999...=1 so how can 0,888...=0,999...=1 ?
this wont work for 0.88888
@@adam-denis
This won't work cuz
I can say 0.9 exists between 0.88888 and 1 na
@@mridulacharya8250There exists infinite real number between two distinct real numbers..then how did you concluded there is no real number between 0.999999.... and 1 ??
i remember i used to talk to you when there was a whatsup group...you are still the best person whom i could talk to abt maths and astrophysics. Keep going! im proud of you!
you can still join the discord server
The way you explain, the accect , the simple example is magnificent
Brilliant explanation! Kudos, man!
Amazing! Really eye-opening to see! Before, I was wondering how this divergent series could converge in such a peculiar way, but now I understand the general idea! I would love to see your version of a simplified mathematical proof in a future video. Once again, great explanation!
Been following your channel for i think 2 years now when you had less than 50k subscribers.
Thanks for the quality content you provide! Learned something new today.
Beacuse of support from people like you this channel is thriving
This is what teaching is about....explaining why it happens....not how it happens....
👏👏👏
Very brilliantly explained brother!!!! HATSS OFFFF
Thank you, my South Asian brother. Your explanation makes so much sense. Far better than the Western rubbish that most YT videos say. Ramanujan would love you.
Yes great description very clearly explained and at an easy to digest pace too. Peace and love from Australia
absolutely fantastic video
I pay big bucks to have your accent! Even though considered heavy by English natives it’s clear yet extremely captivating. When you speak I learn!
This is the best work in 2024 that I have done by subscribing ur channel brother
This guy is a Maths genius 🏅
I like his videos very much
He really deserves millions of likes and Subscriptions 👍👍
This is the best video ive seen about this summation, subscribed
Thank you
"Physics is the medium to perceive the Universe;
Mathematics is the language to communicate with the Universe."
- Universe is always speaking, humans only have to listened in the right direction, and with the right tools (mathematics).
Absolutely correct
The best explanation I have seen. Here are couple of things - take the 1 + 2 + 3 infinite series and add 1 to it. Is this allowed? If allowed will the answer be 11/12? What’s the sum of other infinite series - 1 + 4 + 9 + 16 etc.
This is one of a way for developing and giving a relative mathematical value for the summation of infinitely many terms.
Your explanation is very appreciated 👍
Just like division by zero is not allowed, addition, subtraction, multiplication and division involving infinity is not allowed in maths
Because infinity+infinity is again infinity and not 2 infinity
Infinity is not a number
@@fauzanree1983that's what he is saying.. infinity isn't distributive or associative
@@fauzanree1983 I think Infinite is higher dimension of Numbers
A guy playing with math, breaking all well-agreed definitions and common sense. No, you can not add positive numbers and get anything negative.
There are definitions for convergence.
What you can do is use math in your own way and get absurd results.
Ramanujan turns in his grave being mentioned in this.
@@Param_Hayaran Infinity can be handled as a group or set and yes it does have distributive and associative properties but ONLY as a group.
These do not translate when infinity is used as a number in an equation
Well explained 👍
Keep going.......
Very simple and easy to understand explanation! Please make follow-up video to explain how it's intelligently handled by infinity concept/beta function and its implications in the real world.
Bravo!!!! you explained very well and I appreciate it very much.
Please make a proof video for this as well sharing insights of Sri Ramanujan.
Very good job on bridging the gap between the intuitive impossibility of adding apples and never getting -1/12 and how that intution is wrong since we truely have no intuition for infinity.
Thanks - very well explained!
Thank you very much. Your explanation is very simple to understand.
Doing great!
Keep it up brother👍
This video really made sense. Great explanation 👍🏻👍🏻
Feels like he proves that infinities bring out mathematical superpositions
Infinity is weird and you should not expect that infinity will behave like a normal finite number. Infinity is not a number it can be a number but using it like a number will give you weird results.
-1/12 is the true result under WRONG assumption. The proof is based on the assumption that THE series converges to a number, but it is NOT. End of story.
What type of assumption should be?
First, one need to prove that the series converges to a number, but the series of natural numbers diverges that is infinite as it should be
Problem in handling infinity is that since it's a concept and can never itself be reached, it must be handled by considering the rate of approach to infinity...
Infinity x 1 = infinity
Infinity x 2 = infinity still but it's rate of approach is now 2x faster.
...and all delivered while still wearing your pyjamas. Kudos.
Thank you for the thoughtful explanation.
Your voice is beautiful bro. 😊
Wow, you gave the feel to me to understand that which i really can't understand 😊
Simple and easy explained. Thanks sir
Very well explained brother 💚
Good video.
I swear most advanced mathematicians don’t understand infinity 😂
Infinity is nonending (c) - 🤣
But to accomplish these types of math tricks, they start by treating infinity as ending.
Still, like a child, I love the magic tricks.
0:04 Gauss equation n(n+1)/2 is sum of numbers from 1 to n. Assume n=infinity. Then n(n+1)/2=-1/12 So infinity= -1/2+square root of 1/12 and -1/2 -square root of 1/12
U should solve quadratic in order to get the value of n
n²+n=-1/6
n²+n+1/6=0
Now by Sridharacharya formula
n= (-1+- rootunder 1/3)/2
Absurd.
@@kartikdd8678 😂 Might be an absurd solution but it makes a lil amount of sense
@@syther836 ∞^2+∞-1/6=0 even worse
Well explained.
The Following will give you a little bit of insight into what it is all about.
1/3 is a rational number that we can express as 0.3+0.1/3 =0.33+0.01/3 =0.333+0.001/3 =0.3333+0.0001/3 and so on infinitely. Each of above expression is an absolute number (1/3) without use of infinity. But abstract concept of infinity enters scene when you express it as 0.333.. It's only in case of absolute value 1/3 that you can go on adding infinite number of 3's.
We know that
Numerator/Denominator =Quotient+(Remainder/Denominator)
12/10=1+(2/10)
In the same way, 10/10=1+(0/10), but we can also express it like 10/10=0.9+(1/10)=0.99+(0.1/10)=0.999+(0.01/10)=0.9999+(0.001/10)=0.99999+(0.0001/10). So 10/10=1=0.99999..
Remember that adding 9's at the end infinite number of times is only possible because of left remainders 0.1, 0.01, 0.001, 0.0001 and so on.
Thanks for clarification. So that means the equal sign in 1=0.99999.... to infinite is only valid when you add the term +0.0000......1 behind the expression right?
Otherwise we should not say 0.9999.... = 1, rather stick to its conventional mathemathical expression: limit n to infinite for 0.9999n approaches 1.
This can't be made by humans.. ramanujan was something else he was a fellow of God and God gave some equations that is the key to go in the other world or universe 😌😌
Only one more fellow of God only can find that key lock
We should find that fellow 😞
Sir please do a topic on linear equations graph
Amazing 🔥🔥
When something is not defined, anyone suggesting anything about that cannot be taken for granted, even if the person is Ramanujan.
Congratulations for future 500k
Moral of the story is you must not try sum up a divergent series upto infinity. Even if you find the sum of a divergent series in terms of 'n' then don't try to evaluate that sum with the limit 'n' tends to infinity !!!
Thank you!!
Thanks for the videos welcome back sir🙏. Can you please make a video on how to excel in maths like a genius would
Can you tell us about more new and informative mathematical concepts and tricks?
Hello. What is the Ramanujan summation?
beautifully covered
This is a great video, but I think it is much easier to accept 0.999... = 1 than the Ramanujan sum.
Yes, Its just shown as an analogy.
It's just an example of how infinity does not behave like a normal finite number. 0.9999.. is a convergent series so the proof is a lot more concrete than the 1+2+3+4+...+∞ which is divergent.
He explained it like he doesn't like the smell of this equcation.
Sir to be very frank...... Your video although informative in its own right raises more questions than it answers. You should have also tackled the how it happens/the proof behind the expression also along with the why it happens in maths.
And you can see those questions in your comments. Please make a video tackling those.
Amazing this video makes so much sense
APPLY D ALHEBERT THUS THE SERIES NEVER CONVERGES TO GIVE A PERFECT NUMBER
BUT A GREAT BRAIN RAMANUJAN SHOULD ALWAYS BE RESPECTED
You just now earned a sub
*my teacher talking about adding apples to teach us addition*
me: “what about negative apples?”
teacher: “well you can’t have negative apples”
*starts exponentially mass producing apples*
Negative apples must b the rotting apples added in the beginning... 😅
What I derive from this is that since infinity has no relation to reality, any equation containing it is also devoid of reality, as a natural extension. I would also suppose that, in this case the result could be pretty much anything. I assume -1/12 just stands in as an example of this.
Thank you sharing this explanation I was getting confused since long, actually it's a question of class 9 maths ncert book.
I would argue only thing in the world is infinity , we just look at a part of it and assume finiteness, infinity doesn't raise any question while finiteness does raise many questions, imagine the universe was of size x which is not infinite then that raises an immediate question why this arbitrary value x out of the infinite other values which has no satisfactory answer, the only satisfactory answer is that universe or existence is infinite and we are looking at a part of it which appears to be of size x, so infinity in truly the only real thing on which we apply our limitations to get illusion of finiteness. But this is philosophical argument unrelated to this sum or its analytical values.
Question: How is it that the infinite sum of this series diverges only upto -1/12 and not other possibilities if we may have the freedom to handle the sum by the concept of infinity ?
With infinity, you can prove that anything is equal to anything
Thank u for explain 😊
OK, infinity is not a number. But then we treat it exactly like a number when we multiply 0.99999 ---> by 10 to get 9.99999 -->. And then we go and perform subtraction on it.
It seems we get to pick and choose when and when not to treat infinity as a number.
If someone doesn't know, Math is an universal language which resolves almost all the problems, even if you don't know about it. -Pythagoras
While writing, his nervous hand would have shaken a little, resulting in the minus sign
Many times people say things that are absurd to try to seem profound. If you try to add up an infinite series that never converges then it's one example. If you assume something false (that this series converges) then you can prove anything.
The fact that this result is used in string theory is compelling evidence that this absurd result is just that....absurd.
Hello my son watch your vedio,s regularly,He is so weak in Liner equation.Pleas teach him how to slove liner equation in quick time.Please make a vedio about this topic.Waiting for your vedio.
Thank you for beautiful explanation
Great video
❤ 1:00
the apple explanations makes more sence then teh entore vidio
hey i am interested in learning maths but i dont know how to start slef study and where to start from so can u help me or make a video on that topic?
Thanks Sir , How to visualize the Methods like Beta-Regualization , Ramanujan's Summation to make sense
Just playing with numbers very clever but just hocus-pocus
Numberphile disproved this
yes the second video I showed also ... does that, and what I explained is even then why this sum is there in the literature being used..
The equation only valids if you believe that oo + 1 > oo.. ( oo is not an exact number)
As long as you don't believe it (oo + 1 > oo), it means the equation (1+2+..+oo =1/12 is logically wrong...
A infinite so many never runs out
The only explanation is that Ramanujan has Apeirophobia (fear of Infinity)
3:00 video started 😊😊
It shows up in the zeta function too.
I studied it in class 9th seriously 😳
😂LOL😂
Than?
So?
After seeing all comments...I concluded...
Series of natural number is closely linked to -1/12 but the conventional sum is not that connection
I watched this video in 2X speed😂 , 2 minutes actual explanation is only here in this video
Very nice video😃
Let x and y be integers.
Y is x+1.
Now , as soon as you solve
X+y = -1/12 you got me.
Till then , its a joke.
That simple.
Can u please explain solution of this equation ?!
I have my cs 101 exam tomorrow.why i am watching this🎉
Something infinity and something undefined are two different things . Infinity may be defined as the representative of the largest real real number. It's not a number but has a well defined existence. For example : limit is infinity and limit not defined are two different things.
Intuition must be cleared.
Geometry can better explain this equation.
When we multiplied the decimal number extending infinitely by 10, is the product we assumed here accurate ?
what do you think?
Bro tell me y 1^ infinity is an indeterminate form
The 1 that you are talking about is not exactly equal to 1...it is approaching 1 remember....so you are essentially calculating the limit when the base is very very little less than 1 or little more than 1, Powered to infinity.....cus if it is actually much more than 1 then it'll lead to infinity and in case it is less than 1 then 0....so 1^infinity is essentially indeterminate form
At
3:43 you subtracted
9.9999...
-0.9999...
---------------
9.0000......
So here after decimal .9999... are non terminating recurring number right?
So at 4:39
9.990
-0.999
------------
8.991
Why you subtract with 9.990 instead with 9.999 because even removing infinity, the number after decimal should be recurring number just like done at 3:43 since we are following same procedure after removing infinity.
Plz make me understand this.😮
Because the first equation had an infinite number of nines after the decimal point,while the second one had a finite number of nines(three),which are not recurring.
second example was for non reoccurring one, to show what happens when we remove infinity
0.999... = 1 because you can make the number arbitrarily close to 1.