User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 2/@comment-5529393-20130527105642/@comment-7484840-20130527122145

in my notation, assuming [1...1,2]w/[1] is theta(omega), then theta(omega)+1 is just [2,1...1,2]w/[1] (same as before, but 1st 1 now = 2). Obviously, [1...1,2]w/[2] is a lot bigger than [2,1...1,2]w/[1]. This problem was encountered before with things like [1,1,k] = omega^k, and [1,1,[1]] = omega^omega, and then [1,1,[2]] =omega^(omega+1), and [1,1,[1,1,k]] = omega^(omega^k). If my notation worked like BEAF, your statement would be correct, but due to the arrays not always evaluating and working like ordinals, if there is an omega somewhere in the FGH that corresponds to a [1] in my notaion (here [1...1,2]w/[1] and theta(omega), then putting an array in the place of the [1] does work just like putting a larger ordinal in place of the omega.