about power towers and base change

[sheldonison]

In fact isnt your function f(x) just the base change ?

Could it be you made a typo ?

Your value of 7.28 does not agree with my 6.65.
I used paper and you probably a computer.
But still I wonder, are we talking about the same things and if so , why is there such a difference ?

Thanks for your intrest.

I dont have much time either.

regards

tommy1729

The classic use of base change was to start with \( \text{cheta}(z)=\exp_\eta^{oz} \), and to generate \( \exp^{oz} = \lim_{n\to\infty}\log^{on}(\exp_\eta^{o(z+n)}) \).

The f(z) function isn't a superexponential, though it is related to the base change. It is just a function that tells you how fast any given base for tetration would grow; you can plug any pair of bases z=b1,b2 into f(b1), f(b2). And then if f(b2)=exp(f(b1)), you know b2^^n=b1^^(n+1). I did have a typo, in my previous post today, now fixed, but the value, ~=7.2855 is/was correct.
-Sheldon