Sorry Jay we dont speak about the same thing.

You ask me why I assume .

I answered: because your formula does not converge for some x if we allow .

You answered: that I didnt pay attention to .

I answered: there are despite values of x for which it doesnt converge.

And I can not relate your current answer to this problem.

To express it in formulas and numbers:

Your definition: For a given tetration for base compute another tetration for base by the formula

where is chosen accordingly that .

This formula is equivalent to

By definition , so if I chose

then .

If I now compute the sequence

say for bases and I get for :

For me this means your formula gives no result in this case.

You ask me why I assume .

I answered: because your formula does not converge for some x if we allow .

You answered: that I didnt pay attention to .

I answered: there are despite values of x for which it doesnt converge.

And I can not relate your current answer to this problem.

To express it in formulas and numbers:

Your definition: For a given tetration for base compute another tetration for base by the formula

where is chosen accordingly that .

This formula is equivalent to

By definition , so if I chose

then .

If I now compute the sequence

say for bases and I get for :

For me this means your formula gives no result in this case.