User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-24920136-20160725013617/@comment-27516045-20160728173205

@Simplicityaboveall First, Peng did not mean to not let you reply. It is not his fault. It is only a feature in the Wikia software that you can only reply to top-level comments. If you want Wikia to somehow fix it, I would contact them - but sorry, I can't help you there. And, your remarks sound awfully mean, I'm sure that continuing to sound like that could get you blocked (which means, you can't edit, not even this post). So, I'd recommend calming down.

Second, I don't think you can just say 10^^100 becomes w^^w^2 without explaining how exactly ^^ works on ordinals (as there is no agreed definition). You have to better define how things work. Writing the 10^^^10 in your notation would be equivalent to writing, say, 10^^^10 & 10 in BEAF, which is not exactly well defined, as Bowers has not defined how you would expand it. (Say although it's obvius that x^^^x decomposes to x^^x^^...x^^x, and even x^^x^2 becomes x^^(x*n), it is not obvious what x^^(x+1) becomes. And therefore, it is not obvious what ordinal 10^^11 corresponds to. I'm sorry, you can't just "handwave" the values all the time. 10^^11 could be any number of ordinals, such as just e_0, w^(e_0+1) = e_0*w, e_0^2, e_0^e_0, or even e_1.

TLDR version: It's not properly defined past e_0. Sorry.