User blog comment:Eners49/The secret 0th hyper-operator?/@comment-35470197-20180726231426/@comment-35470197-20180727011651

I like your assumptions very much, because the rule looks very interesting.

Usually, the successor is considered as one of the start points of defining operators, but it does not mean that the successor is the only answer. There could be other interesting directions under several different assumptions.

Although I do not know whether someone has defined a \(-1\)-st hyperoperator or not under some assumptions, you may possibly find a new one. Such trials might greatly help you to understand numbers in your own way.