I have stumbled upon Time calculus while searching for substructures of infinitesimals and how to include time in mathematics.

I thought it might give a handle on infinitesimals, since, how I understand, it, structureless linear infinitesimal h->0 in derivative definition is replaced in general case by graininess to obtain normal continuous derivative.

That means that infinite tetration etc of infinitesimal can be written(?):

lim :

And superroot :lim :

And self root: lim :

The limit may depend on how depends on t since it is not obvious what will happen faster- tetration or changes in .

Gut feeling is, these speeds may be comparable.

The next question is, what will happen with this tetration and time calculus if itself is hyperoperation?

for example, ? or ? Or ?

And generally, hyperoperations in time scales might be interesting.

Please point out obvious mistakes. Thank You in advance,

Ivars

I thought it might give a handle on infinitesimals, since, how I understand, it, structureless linear infinitesimal h->0 in derivative definition is replaced in general case by graininess to obtain normal continuous derivative.

That means that infinite tetration etc of infinitesimal can be written(?):

lim :

And superroot :lim :

And self root: lim :

The limit may depend on how depends on t since it is not obvious what will happen faster- tetration or changes in .

Gut feeling is, these speeds may be comparable.

The next question is, what will happen with this tetration and time calculus if itself is hyperoperation?

for example, ? or ? Or ?

And generally, hyperoperations in time scales might be interesting.

Please point out obvious mistakes. Thank You in advance,

Ivars