But i realy liked this post and another post about teteatiob of square root of 2 equaks 2 , these 2 posts was the best math post i learned in my life , thank u very much master
love your quote man. also i watch your videos because i feel like it might help me someday in calculus class (even though I don't understand majority of what youre talking about)
I dont know what should contain your algebra series but I would like to see positive definite matrix and how to check that given matrix is positive definite ,symmetric matrices, similar matrices, characteristic equation, eigenvalues and eigenvectors , Cayley-Hamilton theorem , decompositions like diagonalization,Jordan form , SVD
G.STRANG done a brilliant series of lectures at MIT. It's quite a lot of ask from your host here, how about just one particular problem that might interest him and us, maybe comparing geometric multiplicity with algebraic multiplicity or diagonalization, or maybe just the eigenvalue problem. You decide what you would like and sure he might oblige.🤔
I used a slightly different method, still using LambertW but rearranging differently before using it. I had the solution: y = e^(-W(ln(1/x))). A bit of rearranging and plugging back into LambertW shows that this is equivalent to the solution used in the video.
y≤e implies that ln(1/x)≥-1/e. That is, that the argument of the W function is greater than -1/e. But -1/e is the lower bound of the LambertW argument itself. This function is only a tool being used to solve the infinite tetration problem. Why should it affect the bounds of the values which will converge for infinite tetration? They are mathematical constructs which are independent of each other. Perhaps y≤e is a limit of the method and not of the convergence itself? Or perhaps the connection between these two things goes deeper?
The formula you derived for y is undefined at x=1 because ln(1)=0 and W(0) = 0; however the infinite tetration of 1 is 1. If you use y(x) = e^(-W(ln(-x)), y(1) is e^0 or 1. Awesome videos!
In the second part of the video, how did you conclude that the maximum value of y is equal to e from 9:20 to 10:30 ?!!! I think the most important part of solution is missing!
Ignoring the {-1} branch of W(x) is as bad as leaving out the discussion about y = arccos(x) and +2πn or integration without a constant. I'm not even talking about the complex plane and manifolds, just plain real numbers (input and output)...
Hello, thank you for the video. It was very useful. So can we establish an equation like this? (x ↑ ↑ x) = (x ↑ x) Can you also talk about super-logarithm and how it relates to tetration? 💐🙏
I wasn't proving it. I wasn't trying to convince anyone. Just stating what is. If an infinite tetration converges, it, it converges to a number less than or equal to e. When I have proof, I'll share it. But no promises.
Good question, we need an 'inverse' factorial function (or operator); e.g. x! = 840, so x=!840 using the factorial operator precedent to the value (just my notation). I use successive division.. 840/2 = 420 420/3 = 140 140/4 = 35 35/5 = 7 7/6 = 1 rem 1 finished but not exact as there is a remainder? so 6
are there any proprieties in tetration? like in the exponentiation when you have to moltiplicate two numbers with the same base but different exponent you just add up the two exponent. is there something like this but with tetration?
There are a few laws, but significantly less than exponentiation I’d recommend watching a video on extending the tetration function to the reals (there isn’t an agreed way to do this, which shows how few rules we can use)
A little hard to understand how infinity can stop somewhere , infinity means never stop even to end of our lives , when we say tetration of 2 that means even after of our life that 2 still is going on power of 2 but when we say tetration of square root of 2 equals 2 still that infinity is going to power even after of my life and never stop , so if it never stop how it can be a certain number like 2 ?
you can accurately compare and define infinite sets against each other and rank them. take 1/∞ and then divide it again by 1/∞ ect. is a much smaller ∞ than any tetration tower. truly interesting stuff.
This is the real challenge: What is i^^∞ (i.e. the infinite tetration of sqrt(-1)? i^^0 = 1 i^^1 = i i^^2 = e^{-π/2} (principle branch, add 2πni) i^^3 = cos(π/2 e^(-π/2)) + i sin(π/2 e^(-π/2)) = 0.94716 + 0.32076 i
i⥣∞ =W(-log(i))/-log(i) = i (2/π)W(-i π/2) ~ 0.43828 + 0.36059 i , so at least complex infinite tower i^i^i^.. _appears_ to converge. There's a nice graphic of this at quora Does-the-infinite-tetration-of-i-converge
We were looking for real solutions and real parameters. i is not real, but complex. The problem is, that he completely ignores parts of the entire solution for real numbers (the W_{-1} branch)!
I can't wrap my head around your assertion, that y cannot go beyond e. You just claimed it, where is the proof? What has lim(1+1/n)^n to do with W(ln(1/x))/ln(1/x) (I mean directly)? And remember, that W_{-1}(ln(1/4)) = 4 * ln(1/4), thus y = 4. So this assertion is not just unproven, but false for the {-1} branch of W!
![เปิดบ้าน พี่ตูน Bodyslam หลังใหม่คนแรก ที่ภูเก็ต l [Nickynachat]](http://i.ytimg.com/vi/flFwcmyDQSk/mqdefault.jpg)
![Infinite tetration of rad2 = 2 [tetration]](/img/n.gif)
What a genius in explaning math! Thanks a lot!
Superb stuff! This is my favourite video of yours so far. You are an excellent teacher.
Your teaching is excellent. Greetings from a fellow teacher from Brazil!!
But i realy liked this post and another post about teteatiob of square root of 2 equaks 2 , these 2 posts was the best math post i learned in my life , thank u very much master
love your quote man. also i watch your videos because i feel like it might help me someday in calculus class (even though I don't understand majority of what youre talking about)
I dont know what should contain your algebra series but I would like to see
positive definite matrix and how to check that given matrix is positive definite ,symmetric matrices, similar matrices, characteristic equation, eigenvalues and eigenvectors , Cayley-Hamilton theorem , decompositions like diagonalization,Jordan form , SVD
G.STRANG done a brilliant series of lectures at MIT.
It's quite a lot of ask from your host here, how about just one particular problem that might interest him and us, maybe comparing geometric multiplicity with algebraic multiplicity or diagonalization, or maybe just the eigenvalue problem.
You decide what you would like and sure he might oblige.🤔
@@tomctutor yes i know but he started series of videos and in my opinion he does not finish it
@@holyshit922 Maths never 'finishes' you can go on to infinity further depths of dicovery.😉
@@tomctutor Thanks for that pointer to Gilbert Strang's lectures. They look excellent.
Your vids are so entertaining . More vids on tetration, Lambert w etc pls
woahh i think i saw this in a dream, i get to see it in real life too!
brother what u have dreams abt the lambert omega function hats off
Grandiosa explicación
I used a slightly different method, still using LambertW but rearranging differently before using it. I had the solution: y = e^(-W(ln(1/x))). A bit of rearranging and plugging back into LambertW shows that this is equivalent to the solution used in the video.
Good video
y≤e implies that ln(1/x)≥-1/e. That is, that the argument of the W function is greater than -1/e. But -1/e is the lower bound of the LambertW argument itself. This function is only a tool being used to solve the infinite tetration problem. Why should it affect the bounds of the values which will converge for infinite tetration? They are mathematical constructs which are independent of each other. Perhaps y≤e is a limit of the method and not of the convergence itself? Or perhaps the connection between these two things goes deeper?
You are so jinius sir, I want to be a person like you,
Genius*
@@auztenz thanks sir,,, can I mail you sir
thank you very much
The formula you derived for y is undefined at x=1 because ln(1)=0 and W(0) = 0; however the infinite tetration of 1 is 1. If you use y(x) = e^(-W(ln(-x)), y(1) is e^0 or 1. Awesome videos!
In the second part of the video, how did you conclude that the maximum value of y is equal to e from 9:20 to 10:30 ?!!! I think the most important part of solution is missing!
It is explained in the last part of the video (it's related to the domain of the Lambert-W function)
I love it🤓 but, what happens if x,y are element of C? Something is going to happen, I got no clue, and no vid has gone this way yet 🤪
Hello this vidoe is great! I wanna ask which chalk do uou use? Do uou use hagoromo chalk? That one is great i heard your chalk is also great!
Ignoring the {-1} branch of W(x) is as bad as leaving out the discussion about y = arccos(x) and +2πn or integration without a constant. I'm not even talking about the complex plane and manifolds, just plain real numbers (input and output)...
What if, at the start, you just took the yth root, then it would be the yth root of y. So if y=3, x=cube root of 3
Hello, thank you for the video. It was very useful.
So can we establish an equation like this?
(x ↑ ↑ x) = (x ↑ x)
Can you also talk about super-logarithm and how it relates to tetration? 💐🙏
Yeah , quite Amazing , but tell me what is it ' s opposite funcion , and it ' s opposite graph .
Not convincing why maximum value possible is e. This was explained in 3b1b video btw
I wasn't proving it. I wasn't trying to convince anyone. Just stating what is. If an infinite tetration converges, it, it converges to a number less than or equal to e. When I have proof, I'll share it. But no promises.
How to solve x! = 840
Good question, we need an 'inverse' factorial function (or operator);
e.g. x! = 840, so x=!840
using the factorial operator precedent to the value (just my notation).
I use successive division..
840/2 = 420
420/3 = 140
140/4 = 35
35/5 = 7
7/6 = 1 rem 1
finished but not exact as there is a remainder?
so 6
are there any proprieties in tetration? like in the exponentiation when you have to moltiplicate two numbers with the same base but different exponent you just add up the two exponent. is there something like this but with tetration?
I am not aware of such
There are a few laws, but significantly less than exponentiation
I’d recommend watching a video on extending the tetration function to the reals (there isn’t an agreed way to do this, which shows how few rules we can use)
A little hard to understand how infinity can stop somewhere , infinity means never stop even to end of our lives , when we say tetration of 2 that means even after of our life that 2 still is going on power of 2 but when we say tetration of square root of 2 equals 2 still that infinity is going to power even after of my life and never stop , so if it never stop how it can be a certain number like 2 ?
This is deep philosophy
you can accurately compare and define infinite sets against each other and rank them. take 1/∞ and then divide it again by 1/∞ ect. is a much smaller ∞ than any tetration tower. truly interesting stuff.
@@PrimeNewtons no , i dont like relate math to philosofy , math must be accurate
This is the real challenge: What is i^^∞ (i.e. the infinite tetration of sqrt(-1)?
i^^0 = 1
i^^1 = i
i^^2 = e^{-π/2} (principle branch, add 2πni)
i^^3 = cos(π/2 e^(-π/2)) + i sin(π/2 e^(-π/2)) = 0.94716 + 0.32076 i
Just done that in comment above, so i'll repeat here..
i⥣∞ =W(-log(i))/-log(i) = i (2/π)W(-i π/2) ~ 0.43828 + 0.36059 i
Y=y^(1/y) ive already solved it before
x = y root y
Er, it looks like it doesn't work for i^(1/i).
i⥣∞ =W(-log(i))/-log(i) = i (2/π)W(-i π/2) ~ 0.43828 + 0.36059 i ,
so at least complex infinite tower i^i^i^.. _appears_ to converge.
There's a nice graphic of this at quora Does-the-infinite-tetration-of-i-converge
We were looking for real solutions and real parameters. i is not real, but complex. The problem is, that he completely ignores parts of the entire solution for real numbers (the W_{-1} branch)!
@@rainerzufall42 Actually, i isn't complex, just imaginary.
@@lethalsub Well, the real part is zero, so it is both complex and imaginary. Just not real!
Notice, that I have suggested i^^∞ because of your comment!
I can't wrap my head around your assertion, that y cannot go beyond e. You just claimed it, where is the proof? What has lim(1+1/n)^n to do with W(ln(1/x))/ln(1/x) (I mean directly)?
And remember, that W_{-1}(ln(1/4)) = 4 * ln(1/4), thus y = 4. So this assertion is not just unproven, but false for the {-1} branch of W!
i got 1.444668
Maths..not math!
I don't remember the last time I heard maths. Maybe as a kid. Do the math.
I think its maths, cos the full form is mathematics. We dont usually use mathematic.