Attempt to formally generalize log, exp functions to 3,4,5..(n,m) log exp

[Ivars]

I know Ivars you are great in speculations, but perhaps then mathematics is not the right discipline for you. In mathematics there is the possibility (and the necessity) to verify things, to verify ideas. If you dont like verifying (and this impression is quite strong) then go to philosphy where nobody can disprove you for sure.
The gap between what you know and what you want to be true is just too huge.

Unfortunately I absolutely am sure that they both converge ultimately ( mathematics and philosophy). So there is no chance to prefer one over another, though the gap you mention is present in both, and my aim is to reduce it as much and as fast as possible using these speculations as motivators.

Excuse me for heating up much above the level of clarity of the problem statement I presented. Hyperoperations is the place where new things will be discovered, because they are required by nature to operate, and I want to be part of it, even if only as active observer, if not able to be a contributor really.

Ivars