Hmm..

Ok, and if we have speed of growth of operation defined, can we say that it is a derivative of operation vs. something?

Like

d(x[4]n)/dx= w[3]n ? Or will it be d(x[4]n)/dx= (w+lnx/x )[3]n?

d(x[4]oo/dx= w[4]oo ? or d(x[4]oo/dx =(w+ln(x)/x)[3]oo ?

and my beloved:

d(h(e^(pi/2)))/d(e^pi/2) = (w+pi/2)* w[4]oo ?? ( the coefficient pi/2 may not be correct , it is just intuitive placement that if base is not e, somewhere we have to see it, the speed of growth has to be faster if x>e; it may be also (w+pi/2)[3]oo).

And again, since h(e^(pi/2))) = i

d(i)/d(e^pi/2) = (w+pi/2)[4]oo or (w+I*pi/2)[4]oo

Probably these questions have been solved in more satisfactory manner without differentiating imaginary unit and i^(1/i) in infinitary calculus mentioned by Conway in his Book of numbers , but I could not find accessible readable reference.

Excuse me for allowing myself to post such unchecked conjectures.

Ivars

Ok, and if we have speed of growth of operation defined, can we say that it is a derivative of operation vs. something?

Like

d(x[4]n)/dx= w[3]n ? Or will it be d(x[4]n)/dx= (w+lnx/x )[3]n?

d(x[4]oo/dx= w[4]oo ? or d(x[4]oo/dx =(w+ln(x)/x)[3]oo ?

and my beloved:

d(h(e^(pi/2)))/d(e^pi/2) = (w+pi/2)* w[4]oo ?? ( the coefficient pi/2 may not be correct , it is just intuitive placement that if base is not e, somewhere we have to see it, the speed of growth has to be faster if x>e; it may be also (w+pi/2)[3]oo).

And again, since h(e^(pi/2))) = i

d(i)/d(e^pi/2) = (w+pi/2)[4]oo or (w+I*pi/2)[4]oo

Probably these questions have been solved in more satisfactory manner without differentiating imaginary unit and i^(1/i) in infinitary calculus mentioned by Conway in his Book of numbers , but I could not find accessible readable reference.

Excuse me for allowing myself to post such unchecked conjectures.

Ivars