User blog comment:Hyp cos/Suggestions about Size Classes of Numbers/@comment-3427444-20170701073338

Here's a problem with the "Boundaries" section: The upper bounds on the classes can be different depending on which notation we choose to derive the bound. For example, in up-arrow notation level, if we only allowed writing down all the up-arrows, then the limit would be {10,10,106}. On the other hand, if we allowed writing the number of arrows in superscripts or used three-entry arrays instead, the limit would be {10,10,1010 6 }. Also in chained arrow notation level, if we used regular chains the limit would be a chain of 10^6 10's, but if we used 4-entry arrays the limit would be {10,10,10,10^10^6}.

Also, using multiple class limits may be confusing to newcomers. I suggest using a single value for the class limit, such as 10^6, 10^10^6 or a middle-ground value like 10^100 (which is used in Cookiefonster's PGLN).