possible tetration extension part 2

[Daniel]

[quote pid="11382" dateline="1666073629"]
Well I'm not sure that techniques that give different results can both be correct, but you have identified an important step in tetration research, the categorization of the different methods and the reconciliation of their different results.

Technically, for half derivatives, there's at least 2 methods which are mathematically demonstrated and correct in a way, but give different results. I just hope it's not the case here, and if it is, we'll have to arbitrary chose one by some criterias. Mine has several advantages like consistency, easily demonstrable, easy to compute/understand,...
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I believe most researchers evolve from algorithmic, algebraic to multi-disciplined approaches. But it is typically the multi-disciplined approached that generate new mathematics. Ultimately we are looking for new unexpected mathematical principles.