Rational operators (a {t} b); a,b > e solved

[bo198214]

It's just unfortunate that someone decided to call it "tetration" instead of "tertiation".

You mean "triation". Its greek numbering not latin
Actually I agree with you, in certain contexts I worked with it also seems more suitable to use addition as operation 0. (Even Ackermann did so.)
On the other hand, on different contexts there it seems more preferable to start with 1. E.g. to have the zero-th operation a [0] x = x+1.
And I dont think one can roll back the whole historic naming development, tetration, the forth operation is already ingrained in the minds.