User blog comment:Googleaarex/Unlimitable Ordinals/@comment-25418284-20130823215256/@comment-1605058-20130825135917

For me, if we take limit of a->w^a and get to e_0, then limit of limit is limit of a->e_a, which is z_0, so with repeated use we get to phi(w,0), far from Gamma_0.

I don't think bracket notation is 3-rule. Rules don't specify when to remove $, no matter how obvious it is. There is also question what rule is? Are predefinitions of symbols rules?