Stability of I in tetration and scaled infinities/infinitesimals?

[bo198214]

Sorry Ivars but it just seems as this is a restart of the discussion about different infinities/infinitesimals. If you so believe in it, why not take a lesson in non-standard analysis. However for the classical approach to analysis there is only one infinity in:

\( \lim_{n\to\infty} b[4]n \)

and in that context it makes no sense to continue a useful discussion.
If you were inspired by quickfur's posts then thats again another thing, ordinal numbers. Here however again the advice: become familiar with (at least the basis of) the topic before starting with wild speculations.

Numbers like e , pi , i , irrationals, periodic decimals etc are not really constants but symbols, as they are incomputable, like infinity and 0.

Infinity is not a number, 0 is a number. e, pi, i, irrationals and periodic decimals are numbers too. There are uncomputable irrational numbers, however e, pi, i and periodic decimals are computable (in the sense that there is an algorithm to determine the n-th digit after the point).

So far, they have behaved like constants under differentation/integration as long as 3 usual operations only have been involved.

There is no reason to think they remain constants (i.e. has no internal structure) if tetration and higgher operations,as well as intermediate (fractional) and zeration is included.

This is mystics and mathematical nonsense with no base.