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.🤔
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!
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)...
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)
5 месяцев назад
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? 💐🙏
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)
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
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.
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
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.
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!
