UNBELIEVABLE: 1 x 2 x 3 x 4 x ... = √2π | Infinity Factorial / Product of Natural Numbers

[@aleenavirdee5656]

😱 Crazy result! Love your little mascots too!

[@someoneonthissite5008]

here to say i was the 619th subscriber. hope to see this channel grow!

[@Dinesh123lol]

How do you only have 200 subs?! This video is insane 🤯

[@jamesbentonticer4706]

Where Are the subscribers for this channel? You should have a lot more. Your videos are great. Very clear and neat and cool topics.

[@ConnerCobe]

One day, i will be seeing you next to 3blue1Brown, Mathologer and many more as one of the best mathmatical youtubers

[@psycteach242]

Great video! Keep up the good work!

[@aaronnanoo1887]

Crazy mathematical result very unexpected :)

[@archiigames3345]

Awesome stuff! My mind is boggled

[@debblez]

i got so excited at 6:00 when I saw where the proof was going extremely beautiful

[@AK56fire]

Very good explanation. How did you made those animations. Did you use manim?

[@Mathacy]

Thank you Amit! Our animations are made using Adobe.

[@AK56fire]

@@Mathacy Which software of Adobe..?

[@Mathacy]

@@AK56fire For our animation, we use After Effects.

[@amybajwa15]

👏🏽👏🏽 loving the videos!

[@skaur6838]

Brilliant!! 👏👏👏

[@ThaAwesome10]

Fun fact: this product x infinity > infinity. This is true, because if we multiply this by infinity, we get the factorial of infinity. Something fun about the factorial is, it’s the number of ways to arrange a set of things, which in this case, would be an infinite number of things. If we look at cantor’s diagonalization, we can prove that the number of real numbers is more than infinity. This can also be applied to the amount of ways to arrange an infinite number of objects. This value is exactly equal to the number of real numbers, and the power set of infinity. If we trust the continuum hypothesis, then we get the value of this product x infinity, which is aleph-one, or the smallest number with a value greater than aleph-null, which is what we usually refer to as infinity.

[@Platechicken]

The insanity of analytical continuation :-) You have to be careful

[@DiLLZGFX]

Amazing ! I never knew this 🤙🤙🤙

[@navneetkaur2445]

Very well explained thank you!

[@shanmugasundaram9688]

Infinite summation of natural numbers tends to a finite negative rational number by analytic continuation is well-known since Ramanujan's time.It is new to see an infinite product of natural numbers tends to a finite number.Twice the sum of logs of alternating natural numbers is equal to the log of Wallis product is genuine.Very interesting.

[@blueshoesrcool]

sqrt(2pi) turns up in the normal distribution. Any connection?

[@jsingh6931]

Awesome video thank you 😊 👍 well done

[@ChazyK]

I think the image in Analytic continuation part is wrong, because there is point, that has no derivative. This function cannot be analytic.

[@AirshipToday]

It is analytic because it can only diverge

[@gurpritkaur3795]

The maths world is sleeping on you! Here before you go viral 👦

[@kilogods]

How do you not have a million subs?

[@mirajsounds]

So helpful!

[@user-yt198]

How can you differentiate Riemann-Zeta function at s=0? If you think that you can do it, then you can also show that 1=2 or e=pi or whatever you want. This is not mathematics.

[@alnath_engore]

You see the idea isn't like that. The idea of regularisation is very natural once you read it. The way people try to popularise this sort of mathematical "black magic" is completely contrary to what one understands after reading. It goes as follows:- Suppose I have the series 1 + x + x^2 + x^3 + .... This is the well known GP series and it evaluates to 1/(1-x), provided |x| < 1. So, of course a statement like 1 + 2 + 4 + 8 + .... = -1 is a useless relation. The series sum diverges for x = 2, while 1/(1-x) for x = 2 is well behaved single valued number. However, what if I evaluate a new GP series -1+(x-2) - (x-2)^2 + (x-2)^3 - .... ? Check that this series also evaluates to 1/(1-x). Now if I put x = 2, I DO get the series summing (trivially) to -1. What I want to point out by this example is that 1/(1-x) is like a "Master Function". It doesn't care whether you represent it as the 1st GP series or 2nd GP series. The value of this Master Function at x=2 is -1 IRRESPECTIVE of ANY representation. The only problematic issue was that the 1st GP series was NOT ABLE to "mimic" this Master Function for |x| > 1. (On the other hand, the 2nd GP series can mimic the master function for 1

[@centralcityacademy]

It’s awesome

[@dr.rahulgupta7573]

Sir That is why , circumference of a circle having radius r is ( 1×2×3×4×5......)^(2) .r . vow !!

[@FaranAiki]

What? I got what you said, but not your point.

[@dr.rahulgupta7573]

@@FaranAiki sir my point is : circumference of the circle and infinity factorial both are related to pi .

[@FaranAiki]

@Dr. Rahul Gupta, you are right, but if this is your reasoning, then that (reasoning) is wrong. It does not make "sense" since 4! is already bigger than square root of two pi.

[@dr.rahulgupta7573]

@@FaranAiki Sir factorial of an 'infinite ' product is quite different from factorial of a ' ' 'finite' product . One is related to zeta function while other is not .

[@azurpourpre488]

It reminds me the stirling's formula that's awesome

[@abcdef2069]

watching movies are boring and could damage your brain. watching logic video like this is more fun, hope to see the beginning level of analytic continuation, related to complex derivatives, at 1:18 the rule is that s must be greater than 1 to work, putting s=-1, why? it is like saying lets say 1+2 =4 then one starts his false logic

[@CTJ2619]

1+2+3+4 …= 1/12 is not valid b/c the series does not converge same thing can be said for the answer to infinity factorial

[@alnath_engore]

You see the idea isn't like that. The idea of regularisation is very natural once you read it. The way people try to popularise this sort of mathematical "black magic" is completely contrary to what one understands after reading. It goes as follows:- Suppose I have the series 1 + x + x^2 + x^3 + .... This is the well known GP series and it evaluates to 1/(1-x), provided |x| < 1. So, of course a statement like 1 + 2 + 4 + 8 + .... = -1 is a useless relation. The series sum diverges for x = 2, while 1/(1-x) for x = 2 is well behaved single valued number. However, what if I evaluate a new GP series -1+(x-2) - (x-2)^2 + (x-2)^3 - .... ? Check that this series also evaluates to 1/(1-x). Now if I put x = 2, I DO get the series summing (trivially) to -1. What I want to point out by this example is that 1/(1-x) is like a "Master Function". It doesn't care whether you represent it as the 1st GP series or 2nd GP series. The value of this Master Function at x=2 is -1 IRRESPECTIVE of ANY representation. The only problematic issue was that the 1st GP series was NOT ABLE to "mimic" this Master Function for |x| > 1. (On the other hand, the 2nd GP series can mimic the master function for 1

[@CTJ2619]

@@alnath_engore thanks you for your detailed explanation

[@aashsyed1277]

It's analitic continuation of zeta

[@lalitupadhyay3460]

Even 22/7 is crazy number..... No end of last digit, it's repeated.

[@sukhibhamra5750]

👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👏🏻👍🏻👍🏻👍🏻

[@matze9713]

dot dot dot

[@pizizhangsg1319]

If something goes again our common sense, it is most likely wrong.

[@김은영-d7j]

HALLELUJA 💖💖💖

[@benjaminojeda8094]

This is absurd

[@giuseppemalaguti435]

Altra risposta....la matematica non serve a un cazzo