User blog comment:Vel!/Ordinal BEAF/@comment-5150073-20130315133136/@comment-5529393-20130315143037

You can do something once, twice, thrice, etc. but that doesn't get you to X-ce. To define pentational arrays specifically, rather than have a multitude of possible notions, we need a rigorous definition. So you can't just go "keep adding 1 until you get to X^X^X..X^X^X";  you need a specific definition of what is included in hypernomials.

Note that it is not that hard to define hypernomials;  the hardest part is defining prime blocks for them. You have to make sure that the prime block goes all the way up to the original hypernomail.