the inconsistency depending on fixpoint-selection

[bo198214]

and I checked it numerically in the bummer thread.

...as you did it. But I didn't recognize a final conclusion, usable for our case. Damn, I've much too little experience...

Hm, the conclusion is
a) dont trust numerical comparisons
b) We still have a uniqueness problem if we base the tetration extension on regular iteration of \( b^x \) at a fixed point (i.e. which fixed point to choose). This is besides the problem that there are no real fixed points for \( b>e^{1/e} \).