In this video my goal was not to prove weather this is true or not but to give an intuitive sense to laymen people that this can be true when we handle infinities in creative ways ! Have fun playing around with infinities! For a proof of this you can watch this video (If I did it, I will just repeat this proof)- 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!
@@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 ??
-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.
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"
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!
"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.
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 ?
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.
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
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.
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.
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
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 👍
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.
I thought you where gonna tell the same proof for infinite sum bro.... you didn't do that but you are make me realize that infinite is a concept..... Tq bro
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.
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.
Since 0.99999... is a rational number this real number can be written in decimal form 0.9+0.09+0.009+... In enumerable order Also any interval is non enumerable so (0.99999...,1] is non enumerable therefore there exists infinitely many real numbers between here. But by density property of Rational in R There exists rational r€R , irrational s€R st. 0.999...
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.
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.
You can simply say that, in the 's series' the last digit is TRUNCATED. Like this - 10s - s = 9.99 - 0.999 By Truncating the last digit (a kind of approximation) the equation will be - 10s - s = 9.99 - 0.99 Now s = 1 is ACHIEVED. Such type of approximations are perfectly alright in Engineering, but not in Science or Mathematics.
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.
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.
What is the significance of the result that if one extends the partial sum formula (S(n) = n(n+1)/2) to real numbers, i.e., S(x) = x(x+1)/2, the integral from -1 to zero (the only domain in which the function is negative) is precisely -1/12 ?
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.
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.
I still find the explanation quite confusing 😕 I don't think you can operate on infinity like normal arithmetic since the last digit is not accountable. Like S=0.9999to infinite case. The thing is you assume all the point beyond decimals for 10S-S just subtract out perfectly, but how do you know the decimal points at infinity point for 10S is a 9 or a 0 since you multiply a 10? There is a danger in blindly believing everything authority say. String theory in my opinion just make the leap of faith to solve their infinity dilemma in their equation using this equation. The field has claimed many young bright mind to dedicate their entire life looking for way to force the nature to fit with their mathematics without much success.
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 !!!
Inf - Inf comes under 1 of the 8 indeterminate forms and is the value is not considered constant , because u see inf + any number still gives us inf but while subtracting we may end up with different numbers .For example please 5 + inf = Inf but Inf - Inf is not equal to 5 as inf minus inf can give any number. So it is neither inf nor 0 but considered as Indeterminate
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.
Is there a possibility that mathematics at some point its just broken and exist only as a math thought.. something similar to string theory in physics??
@@mrinalkashyap5364 may point was, based on the question is math discovered or invented, that the part that is invented at some point gone of the rails and went into mambo-jambo.
@@mrinalkashyap5364 One of the biggest channels on TH-cam about math is Numberphile. The channel provides even a demonstration of the 1+2+3.... problem. But at some point to me at least it seems the provider is manipulating the demonstration in order to come to the expected result
This is a theoretical sum only. It’s not consistent with one of the fundamental principles of general relativity and quantum physics which is that the universe is expanding unbounded. If the universe was indeed expanding infinitely, the infinite series would sum to infinity or an undefined value.
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...
*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*
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?
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?
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.
according to my knowledge in math two number is different if we can write a number between it so technically 0.999999... and 1 we cannot write any thats the main reason , as per main question it didnt clear anything for me
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?
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.
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
The S equal 1 proof is not correct even with infinity. Because no matter what the "value" of .9 repeating is. It will have 1 less place holder, always resulting in 8.9repeating till infinity then a 1. Great video, just challenging the concept. Infinity plus infinity still being infinity when it should be more like dividing by zero. It's undefined. Do you agree?
There's an easier way to think about .999... = 1 that isn't a mathematical proof. What can you add to .999... to get 1? What can you subtract from 1 to get .999...?There are no numbers in between them, so they must be the same. The mathematical proof also works, and 8.999... is also equal to 9.
@@alexandercurnell1142 there will always be a number between them. it will just be infinitely small. there is no whole number between 1 and 2 yet there are not equal. so once again the logic is flawed. Appears to be the same and is the same are different. .00001microns and .0002 microns are indistinguishable to the human eye. But the are different numbers. perception is not always reality
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.
In this video my goal was not to prove weather this is true or not but to give an intuitive sense to laymen people that this can be true when we handle infinities in creative ways !
Have fun playing around with infinities!
For a proof of this you can watch this video (If I did it, I will just repeat this proof)-
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
Sir please create a vdo on tetration..
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 ??
Bro explains everything so calmly. I love it.
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
same with me
YOUR LIST PLEASE
I love your videos! thank you for making this one
-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
Thats what is microlevel physics
Things are not defined there!
Brilliant explanation! Kudos, man!
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"
1+2+2^2+2^3+...=-1. It's true in some sense and people are using it.
reimann zeta function also proves it zeta(-1)=-1/12
Very brilliantly explained brother!!!! HATSS OFFFF
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
Thank you so much. I've been trying to understand this for ages.
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!
The way you explain, the accect , the simple example is magnificent
"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.
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 ?
My thoughts exactly
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
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
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.
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.
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
you are one of the best math explainers i've ever seem (I'm majoring in mathematics)
Please make a proof video for this as well sharing insights of Sri Ramanujan.
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 👍
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.
This guy is a Maths genius 🏅
I like his videos very much
He really deserves millions of likes and Subscriptions 👍👍
Yes great description very clearly explained and at an easy to digest pace too. Peace and love from Australia
Could this alternatively mean that we are not handling infinity well, we dont understand its concept fully, and we are manipulating it randomly ?
I thought you where gonna tell the same proof for infinite sum bro.... you didn't do that but you are make me realize that infinite is a concept..... Tq bro
absolutely fantastic video
Thanks Sir , How to visualize the Methods like Beta-Regualization , Ramanujan's Summation to make sense
This is the best work in 2024 that I have done by subscribing ur channel brother
This is what teaching is about....explaining why it happens....not how it happens....
👏👏👏
Watching this interesting video , during my online political science class .
This is the best video ive seen about this summation, subscribed
Thank you
Can u please explain solution of this equation ?!
With infinity, you can prove that anything is equal to anything
yes, 5*0 = 6*0, then 5=6
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
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!
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.
Sir If I take S=0.9999...infty and
10S=9.999...infty , the value changes as you have did in 2 derivation.
what is the reason to multiply s with 10 can we multiply with any other number?
Since 0.99999... is a rational number this real number can be written in decimal form 0.9+0.09+0.009+... In enumerable order
Also any interval is non enumerable so (0.99999...,1] is non enumerable therefore there exists infinitely many real numbers between here.
But by density property of Rational in R
There exists rational r€R , irrational s€R st. 0.999...
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.
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.
You can simply say that, in the 's series' the last digit is TRUNCATED. Like this -
10s - s = 9.99 - 0.999
By Truncating the last digit (a kind of approximation) the equation will be -
10s - s = 9.99 - 0.99
Now s = 1 is ACHIEVED.
Such type of approximations are perfectly alright in Engineering, but not in Science or Mathematics.
Sir please do a topic on linear equations graph
Well explained 👍
Keep going.......
Can you tell us about more new and informative mathematical concepts and tricks?
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.
But u didn't explain how 1+2+3+4+... Inifite= -1/12
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.
Doing great!
Keep it up brother👍
So what i understand is - “ Infinity is not physical ; it is spiritual “
What is the significance of the result that if one extends the partial sum formula (S(n) = n(n+1)/2) to real numbers, i.e., S(x) = x(x+1)/2, the integral from -1 to zero (the only domain in which the function is negative) is precisely -1/12 ?
Too good a video for mathematics . Math fellow forever !
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.
Bravo!!!! you explained very well and I appreciate it very much.
Hello. What is the Ramanujan summation?
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.
How u say infinity is not real
This infinite universe is expanding infinitely is the proof
When we multiplied the decimal number extending infinitely by 10, is the product we assumed here accurate ?
what do you think?
my dear brother if put two mirrors front of each other then
the infinite mirrors will appear ?? eheather it can be said as imaginary
Thank you very much. Your explanation is very simple to understand.
Your voice is beautiful bro. 😊
I still find the explanation quite confusing 😕 I don't think you can operate on infinity like normal arithmetic since the last digit is not accountable. Like S=0.9999to infinite case. The thing is you assume all the point beyond decimals for 10S-S just subtract out perfectly, but how do you know the decimal points at infinity point for 10S is a 9 or a 0 since you multiply a 10? There is a danger in blindly believing everything authority say. String theory in my opinion just make the leap of faith to solve their infinity dilemma in their equation using this equation. The field has claimed many young bright mind to dedicate their entire life looking for way to force the nature to fit with their mathematics without much success.
brilliantly explained..
salute.. ❤
This video really made sense. Great explanation 👍🏻👍🏻
Thanks - very well explained!
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!!
He explained it like he doesn't like the smell of this equcation.
While writing, his nervous hand would have shaken a little, resulting in the minus sign
Now the thing is.... is infinity-infinity=0 ? Or it's just infinity?
Inf - Inf comes under 1 of the 8 indeterminate forms and is the value is not considered constant , because u see inf + any number still gives us inf but while subtracting we may end up with different numbers .For example please 5 + inf = Inf but Inf - Inf is not equal to 5 as inf minus inf can give any number. So it is neither inf nor 0 but considered as Indeterminate
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.
Is there a possibility that mathematics at some point its just broken and exist only as a math thought.. something similar to string theory in physics??
Math is a language of the known things. If something is unknown you can't express it or have a value for it.
@@mrinalkashyap5364 aaaaand?? Why are you trying to say?
@@alexiachimciuc3199 what I mean to say is math isn't broken and isn't just a thought.
@@mrinalkashyap5364 may point was, based on the question is math discovered or invented, that the part that is invented at some point gone of the rails and went into mambo-jambo.
@@mrinalkashyap5364 One of the biggest channels on TH-cam about math is Numberphile. The channel provides even a demonstration of the 1+2+3.... problem. But at some point to me at least it seems the provider is manipulating the demonstration in order to come to the expected result
The video starts at 3:01
This is a theoretical sum only. It’s not consistent with one of the fundamental principles of general relativity and quantum physics which is that the universe is expanding unbounded. If the universe was indeed expanding infinitely, the infinite series would sum to infinity or an undefined value.
0.999... = 1 because you can make the number arbitrarily close to 1.
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...
*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... 😅
Start watching at 3:00😁😁
Aparently people disproved this a while ago. But then people are proving that it is both -1/12 and infinity. I am very confused.
now we know, we we say ''The Man who knew Infinity'' for Sir Ramanujan
Because he actually did
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...
When something is not defined, anyone suggesting anything about that cannot be taken for granted, even if the person is Ramanujan.
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?
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.
according to my knowledge in math two number is different if we can write a number between it so technically 0.999999... and 1 we cannot write any thats the main reason , as per main question it didnt clear anything for me
I expected that you would show us the proof why the sum equivalents to -1/12. dissapointed. Btw, you talk good, make good point. Thanks for that.
Love you bro ❤❤❤
Thank you for the thoughtful explanation.
Very well explained brother 💚
Amazing 🔥🔥
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?
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.
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.
If infinity is a 'concept' and not a number, then can you multiply a 'concept' by 10? Would you get 10 concepts?
You can multiply a concept by 10 but if the concept is ∞ then 10×∞=∞
Can u multiply a concept by itself to create that same concept but squared
@@AUSWQPCV You can multiply the concept ω by itself and get ω². ω is the smallest ordinal infinity.
I am OBC category person. Can i watch this?
Hein😂
Wtf?
😂??
No you already have 27% reservation
Exactly @@ExistingPriyanshu
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
The S equal 1 proof is not correct even with infinity. Because no matter what the "value" of .9 repeating is. It will have 1 less place holder, always resulting in 8.9repeating till infinity then a 1. Great video, just challenging the concept. Infinity plus infinity still being infinity when it should be more like dividing by zero. It's undefined. Do you agree?
There's an easier way to think about .999... = 1 that isn't a mathematical proof. What can you add to .999... to get 1? What can you subtract from 1 to get .999...?There are no numbers in between them, so they must be the same.
The mathematical proof also works, and 8.999... is also equal to 9.
@@alexandercurnell1142 there will always be a number between them. it will just be infinitely small. there is no whole number between 1 and 2 yet there are not equal. so once again the logic is flawed. Appears to be the same and is the same are different. .00001microns and .0002 microns are indistinguishable to the human eye. But the are different numbers. perception is not always reality
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.