I have given counting by imaginary and negative numbers a little bit of a "philosophical" thought. This is the first crude outcome:

From the point of view of given process where we have something- let us name them Things:

-Positive numbers count Things that exist

-Negative numbers count Things that does not exist, but can exist

-Positive Imaginary numbers count Things that neither exist, nor not exist- oscillatory existance- and they count the moments when they exist

-Negative imaginary numbers count the moments when these oscillatory Things that could both exist and not, does not exist.

Now obviously space of all negative numbers include all Things that does not exist but could exist- so quite naturally that Imaginary unit has a restriction on it- once it turns from oscillatiory Thing into one that does not exist, but could, it has to become a negative number- for some reason it is happening as multiplication: I*I=-I*-I= -1 The non-existant Things can be obtained either from existing part of oscillatiry unit, or non-existant- any one of them is not enough to create existing Thing. You need both, as can be seen in next paragraph.

If oscillatory Thing has to become existant, it can not avoid becoming one of those counted by positive numbers as there are no others, since there are no others: In mathematics that requires participation of both of its 2 states Hence -I*I=1 .

The question is what that would mean concerning negative and imaginary hyperoperations and iterations?

Operation seems not to be a Thing, but something working on Things.

Iteration is counting how much (how many times) Operation is working on Things.

Functions are usually defined via Operations (Is it) , so they represent combination of Operations.

Ivars

From the point of view of given process where we have something- let us name them Things:

-Positive numbers count Things that exist

-Negative numbers count Things that does not exist, but can exist

-Positive Imaginary numbers count Things that neither exist, nor not exist- oscillatory existance- and they count the moments when they exist

-Negative imaginary numbers count the moments when these oscillatory Things that could both exist and not, does not exist.

Now obviously space of all negative numbers include all Things that does not exist but could exist- so quite naturally that Imaginary unit has a restriction on it- once it turns from oscillatiory Thing into one that does not exist, but could, it has to become a negative number- for some reason it is happening as multiplication: I*I=-I*-I= -1 The non-existant Things can be obtained either from existing part of oscillatiry unit, or non-existant- any one of them is not enough to create existing Thing. You need both, as can be seen in next paragraph.

If oscillatory Thing has to become existant, it can not avoid becoming one of those counted by positive numbers as there are no others, since there are no others: In mathematics that requires participation of both of its 2 states Hence -I*I=1 .

The question is what that would mean concerning negative and imaginary hyperoperations and iterations?

Operation seems not to be a Thing, but something working on Things.

Iteration is counting how much (how many times) Operation is working on Things.

Functions are usually defined via Operations (Is it) , so they represent combination of Operations.

Ivars