User blog comment:Alejandro Magno/Googol Array Notation/@comment-5529393-20141004191340

Your rules aren't complete, but I can see where you're going with your notations, and you've overestimated the ordinal comparisons.

Planar arrays go up to w^w^2.

Multi-dimensional arrays go up to w^w^w.

Nested arrays go up to epsilon_0.