FANDOM


As I analysed, w/ operator isn't enough powerful and Multi-Dimensional arrays is ill-defined at all.

Hyperfactorial FGH
[1]w/[1] \phi(\omega,0)
[2]w/[1] \phi(\omega,0)+1
[[1]]w/[1] \phi(\omega,0)+\omega
[1,2]w/[1] = [1]w/[2] \phi(\omega,0)*2
[1,1,2]w/[1] = [1]w/[3] \phi(\omega,0)^2
[1,1,1,2]w/[1] = [1]w/[4] \phi(\omega,0)^\omega
[1,1,1,1,2]w/[1] = [1]w/[5] \epsilon_{\phi(\omega,0)+1}
[1]w/[1,2] \phi(\omega,1)
[1]w/[1,3] \phi(\omega,2)
[1]w/[1,1,2] \phi(\omega,\omega)
[1]w/[1,1,1,2] \phi(\omega,\omega^\omega)
[1]w/[1,1,1,1,2] \phi(\omega,\epsilon_0)
[1]w/[1]w/[1] \phi(\omega,\phi(\omega,0))
[1]w/[1]w/[1]w/[1] \phi(\omega,\phi(\omega,\phi(\omega,0)))
[1(1)2] \phi(\omega+1,0)
[1,2(1)2] \phi(\omega+1,0)*2
[1,1,2(1)2] \phi(\omega+1,0)^2
[1(1)2]w/[1] \phi(\omega,\phi(\omega+1,0)+1)
[1(1)2]w/[1,2] \phi(\omega,\phi(\omega+1,0)+2)
[1(1)2]w/[1,1,2] \phi(\omega,\phi(\omega+1,0)+\omega)
[1(1)2]w/[1]w/[1] \phi(\omega,\phi(\omega+1,0)+\phi(\omega,0))
[1(1)2]w/[1(1)2] \phi(\omega,\phi(\omega+1,0)*2)
[1(1)2]w/[1(1)2]w/[1(1)2] \phi(\omega,\phi(\omega,\phi(\omega+1,0)+1))
[1(1)3] \phi(\omega+1,1)
[1(1)4] \phi(\omega+1,2)
[1(1)[1]] \phi(\omega+1,\omega)
[1(1)1,2] \phi(\omega+1,\phi(\omega+1,0))
[1(1)1,2] \phi(\omega+1,\phi(\omega+1,0))
[1(1)1,3] \phi(\omega+1,\phi(\omega+1,0)*2)
[1(1)1,1,2] \phi(\omega+1,\phi(\omega+1,0)^2)
[1(1)1,1,1,2] \phi(\omega+1,\phi(\omega+1,0)^\omega)
[1(1)1,1,1,1,2] \phi(\omega+1,\epsilon_{\phi(\omega+1,0)+1})

There will be no notation for limit of [1(1)2], [1(1)1,2], [1(1)1,1,2], [1(1)1,1,1,2], ... Even though it was defined as [1(1)1]w/[1], [1(1)1] collapses into [1] and that forms a hole in entire system, not allowing to get to multiple dimensions. The limit of HAN is \phi(\omega+1,\phi(\omega,\phi(\omega+1,0)+1)), I believe.

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