Addition, multiplication, ... what comes next? (It's not exponents)

This video begins with a search for a binary operation satisfying certain properties, and ends with the creation of a new number system: the exponential numbers. #SoME3 (finished late) Although I came up with these concepts independently, a commenter has pointed out that the operations defined in the first part of the video already have a name: the "commutative hyperoperations." https://en.wikipedia.org/wiki/Hyperoperation#Commutative_hyperoperations