jaydfox Wrote:No, the slog function is only defined for bases greater than 1. For bases between 0 and 1, the tetration function is not one-to-one, so its inverse is not a function, because there are multiple values. It's much like saying that y=x^2 does not have an inverse function. y=sqrt(x) only covers part of the domain of the original function.Surely, by "arbitrary" I meant: also for .

I was referring to

andydude Wrote:and I suppose would you could call the elliptic? interval , which is what my definition of the super-logarithm is valid forhowever in his pdf he defined it for bases .

(Quite ridiculous how misunderstandings reach its maximum in the communication between Jay and me ...)

Quote:Also, there's a question about whether you consider the slog function to only apply to the inverse of the function of iterated exponentials/logarithms from 1. For b=2, for example, the domain of slog is negative infinity to 2.Dont understand this, maps to , so the slog is defined on ?

Quote: However, you can perform iterated exponentials/logarithms from any real number as a starting point, so you could also include the graph for x>4 and the corridor between 2 and 4.If you use the fixed point method however for base you have to specify which fixed point you use in case you start with between these fixed points.