User blog comment:Eners49/The secret 0th hyper-operator?/@comment-2601:142:2:EC49:A496:CA1D:3DA2:B5DD-20180728144329/@comment-35532815-20180728145842

Fandom User, thank you for bringing this insightful comment onto my blog! You have helped me to understand this better.

It might make more sense if x ? (anything) = x+1, and x ?? y = x + 1/y, x ??? y (-2nd operator) = x * 1/y, x ???? y = x^(1/y), etc. since that seems to make more sense to me. It's the only way I see to break down the successor function. Perhaps 2?2 is not 4 and 3?3 is not 5 by that definition, then. The rules of up-arrows that we alreday know don't make sense anymore, but at least we have made some sense out of negative hyperoperations.