User blog comment:Eners49/The secret 0th hyper-operator?/@comment-2601:142:2:EC49:A496:CA1D:3DA2:B5DD-20180728144329/@comment-2601:142:2:EC49:4C92:9410:FCC5:1802-20180729182030

I wrote a long thing about Extentisible-E but with ? notation, and it had some newly discovered rules about x??y, and THEN it got deleted because of some stupid reason or another. I don't want to type it all up again, so here's the tl;dr of it.

Extensible-? numbers are almost indistinguishable from normal Extensible-E numbers for numbers larger than 100###3. Because of that, they're pretty trivial.

Rules list of x??y

1: If y is at least 3, and x is 0 or less, than x??y = y+1. (Old rule)

2a: If x and y are equal, than x??y = x?2 (Old rule)

2b: If x is equal to y, and x is at most 0, than x??y = 3. (New rule)

Now for the bounding rules. These work the same way as the x?y bounding rules do, but scaled down another level.

3: If y is less than x, than x??y can be bounded between x?1 and x?2 (New rule)

4: If y is greater than 0, but less than 3, and x is less than y, than x??y can be bounded between y+1 and 3. (or 3 and y+1 depending on what y is.) (New rule)

And x??y solved! Yay.

PS: I made a spreadsheet of various x?y and x??y values in LibreOffice Calc, so if you ever need anything that could require that, you know who to ask!