Making Sense of Ramanujan's Infinite Sum for General Audience.
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- čas přidán 11. 05. 2024
- In this video we will try to Intuitively understand why the weird sum 1+2+3 and so on till infinity or the famous Ramanujan sum. Which seems very counter intuitive at first sight!
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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)-
czcams.com/video/YuIIjLr6vUA/video.htmlsi=oqNokKAJSxnhUE-Z
In the Video I say beta function regularization
but wanted to say
zeta function regularization
sorry for that!
No ProbleZ
I eat all infinite apples and eat 1/12 of friend's apple too. Hence proved
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
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 ??
Thank you so much. I've been trying to understand this for ages.
I love your videos! thank you for making this one
Brilliant explanation! Kudos, man!
Yes great description very clearly explained and at an easy to digest pace too. Peace and love from Australia
absolutely fantastic video
This is what teaching is about....explaining why it happens....not how it happens....
👏👏👏
The way you explain, the accect , the simple example is magnificent
Thanks - very well explained!
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!
Bro explains everything so calmly. I love it.
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"
Thank you for the thoughtful explanation.
This video really made sense. Great explanation 👍🏻👍🏻
-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
Doing great!
Keep it up brother👍
Simple and easy explained. Thanks sir
Thank you very much. Your explanation is very simple to understand.
Well explained 👍
Keep going.......
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.
Well explained.
Amazing 🔥🔥
Very well explained brother 💚
This is the best video ive seen about this summation, subscribed
Thank you
Great video
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
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
Thank u for explain 😊
This is the best work in 2024 that I have done by subscribing ur channel brother
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 👍
Amazing this video makes so much sense
You just now earned a sub
Please make a proof video for this as well sharing insights of Sri Ramanujan.
beautifully covered
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
Very nice video😃
Congratulations for future 500k
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!
Hello. What is the Ramanujan summation?
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.
Can you tell us about more new and informative mathematical concepts and tricks?
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 ?
Thanks for the videos welcome back sir🙏. Can you please make a video on how to excel in maths like a genius would
Sir please do a topic on linear equations graph
...and all delivered while still wearing your pyjamas. Kudos.
Well made
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
@@sytherplayz ∞^2+∞-1/6=0 even worse
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.
Wow, you gave the feel to me to understand that which i really can't understand 😊
Nice sir🎉😅😅
"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.
Thanks
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.
Top notch
Your voice is beautiful bro. 😊
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 😞
Nice channel
Wow😮
So it's about convergent divergent tests this is about?
I saw this in Calc 2
He explained it like he doesn't like the smell of this equcation.
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.
When we multiplied the decimal number extending infinitely by 10, is the product we assumed here accurate ?
what do you think?
It shows up in the zeta function too.
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.
nice
how come it can be a negative number..
Can u please explain solution of this equation ?!
Thanks Sir , How to visualize the Methods like Beta-Regualization , Ramanujan's Summation to make sense
❤
A infinite so many never runs out
While writing, his nervous hand would have shaken a little, resulting in the minus sign
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.
Bro can you make vidoes on jee advanced maths chapters pls !
I still have a doubt that how did the sum of natural number become negetive and an integer. Like that's not possible in any world!
And if we are handling infinity as any possible number then is it also possible that 2i (an imaginary number) or √2 ( an irrational number) becomes the sum of infinite natural numbers?
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.
When something is not defined, anyone suggesting anything about that cannot be taken for granted, even if the person is Ramanujan.
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!!
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.
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 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.
Sum of n is by Gauss n(n+1)/2...???
I have a question and hope someone can help me with this question. Suppose you want to travel from A to B, If you start by traveling half the distance and then proceed by traveling half of the half of the distance and continue in this manner repeatedly, would you be able to reach B?
this is called the zeno paradox, In our world we can travel from A to B that means there must be a unit of length which cant be halved.
@@mathOgenius Thanks for pointing me to the right direction. I've googled Zeno's paradox and found the answer which confirms my surmise...
Just playing with numbers very clever but just hocus-pocus
With infinity, you can prove that anything is equal to anything
my dear brother if put two mirrors front of each other then
the infinite mirrors will appear ?? eheather it can be said as imaginary
*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... 😅
I like your outro: "Always remember that, meth is everything"
Bhiya Can You Do Give Away Ones More Time 🙏🥺
I got feel about maths
So tell me what number is closest to 1 without being equal to one?
its the last one of the numbers which are between 0 and 1..
The only explanation is that Ramanujan has Apeirophobia (fear of Infinity)
This video doesnt explain why its -1/12 but explains why i could be -1/12.
Because in math theres almost like a phase change there at the end of infinity.
is it true infinity is physical quantity in higher dimentions??
It depends on which dimension. Not in the Euclidean space but there are Geometric spaces that allows a point of infinity to exist.
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.
I give you 2 numbers: One number is 0.999 till infinity and the other number is exactly the same with only one random digit not being 9. I don't tell you which one is which and I ask to identify which one of them is equal to 1 and which one isn't. Can you solve it?
I would need the location of the changed digit otherwise its uncertain.
I am waiting for your 500k subscribe
Why
Because of telescope giveaway 😅
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
I studied it in class 9th seriously 😳
😂LOL😂
Than?