User blog comment:Simplicityaboveall/The Construction of Extremely Large Numbers/@comment-11227630-20160726150520/@comment-5529393-20160728184038

Simplicityaboveall, the reason that your work does not "contradict mathematics" is because your terms are not well-defined yet, so it's too early to say whether your statements are true or false. That's all Hyp Cos was objecting to.

It's not clear that (w^^w)^^w is approximately w^^(w2), and in fact under the obvious definition of "^^" this is not true, as w^^(w2) will be just epsilon_0. So you need to be careful.