User blog comment:Eners49/The secret 0th hyper-operator?/@comment-2601:142:2:EC49:A496:CA1D:3DA2:B5DD-20180728144329/@comment-35532815-20180729203725

Thank you guys so much for all the rules you have given about the ? and ?? notations. I guess that with all this "dark magic" I've started creating I am going to get kicked out of math class.

So far I like the new definitions better, since the old one doesn't work and gets into the 1=3 problem (even though that is a very nice way to prove that 1=3). Negative hyperations HAVE to be different than positive hyperoperations, so perhaps 2+3 is not equal to 2?4 and vice versa.