FANDOM


[1[1][2]2] = [1[1[...[1[1]2]...]2]2] = [1[1[...[2]...]2]2] has level BHO

[1[1[1][2]2]2[1][2]2] has level theta(e(W+1),1)

[1[2[1][2]2]2[1][2]2] has level theta(e(W+1)+1)

[1[1[1[1][2]2]2[1][2]2]2[1][2]2] has level theta(e(W+1)*2)

[1[1][2]3] = [1[1[...[1[1[1][2]2]2[1][2]2]...]2[1][2]2]2[1][2]2] has level theta(e(W+2))

[1[1][2]1[2]2] = [1[1][2][1[1][2][...]]] has level theta(e(W*2))

[1[1][2]1[3]2] has level theta(e(W^2))

[1[1][2]1[1[1][2]2]2] has level theta(e(e(W+1)))

[1[2][2]2] = [1[1][2]1[1[1][2]1[...[1[1][2]1[1[1][2]1]2]...]2]2] has level theta(z(W+1))

[1[[1[2]2][2]2][2]2] has level theta(phi(w,W+1))

[1[1[2]2][2]2] has level theta(phi(W,1))

[1[1[1][2]2][2]2] has level theta(W_2)

[1[1][3]2] = [1[1[...[1[1][2]2]...][2]2][2]2] has level theta(e(W_2+1))

[1[1][[1[2]2]]2] has level theta(W_w)

[1[1][1[2]2]2] has level theta(W_W)

[1[1][1[1][2]2]2] has level theta(W_W_2)

[1[1][1][2]2] = [1[1][1[1][...[1[1][1]2]...]2]2] has level psi(psi_I(0))

[1[1][2][2]2] has level psi(e(I+1))

[1[1][[1[2]2]][2]2] has level psi(W_{I+w})

[1[1][1][3]2] has level psi(psi_{I_2}(0))

[1[1][1][[1[2]2]]2] has level psi(psi_{I_w}(0))

[1[1][1][1[1][1][2]2]2] has level psi(psi_{I_I}(0))

[1[1][1][1][2]2] has level psi(psi_{I(1,0)}(0))

Limit is [1[1][1]...[1][2]2] or psi(psi_{I(w,0)}(0))

Rules

Let # is rest of array and #2 is rest of ultra array ([#]_[#]...[#]_[#]).

  • <a,b>[1] = a,a...a,a/w b a's
  • <a,b>[c+1 #] = <a,b>[c #] [c+1 #] <a,b>[c #] ... <a,b>[c #] [c+1 #] <a,b>[c #]/w b-1 [c #]'s
  • <a,b>[1 [1] c #] = <a,b>[c #]
  • <a,b>[1 [c+1] d+1 #] = <a,b>[1 [c][1 [c][...[1 [c][1 [c][b][c+1] d #][c+1] d #]...][c+1] d #][c+1] d #]/w b nested
    • Nested arrays are accepted.
  • <a,b>[[b] #]= <a,b>[b #]
  • <a,b>[1[y+1][1]...[1][z+1]#2x+1 #] = <a,b>[1[y][1]...[1][z+1]#21[1][1]...[1[y][1]...[1][z+1]#21[1][1]...[...[1[y][1]...[1][z+1]#21[1][1]...[1][z]#22[y+1][1]...[1][z+1]#2x #]...][z]#22[y+1][1]...[1][z+1]#2x #][z]#22[y+1][1]...[1][z+1]#2x #]/w b nested
  • <a,b>[# x[0]#2y #] = <a,b>[# x+y #]
  • <a,b>[# {#2}[1] #] = <a,b>[# #2 #]

Ultra Array Notation II

Let [1 -> [x]] = [1 -> [x-1]]_[1 -> [x-1]]...[1 -> [x-1]]_[2 -> [x-1]] and [x -> [1]] = [1].

[1[1->[2]]2] has level psi(psi_{I(w,0)}(0))

[1[1->[2]]3] has level psi(psi_{I(w,0)}(1))

Then [1[1->[2]][x+1]2] = [1[1[1[...][x]2->[2]][x]2->[2]][x]2]

[1[1->[2]][2]2] has level psi(psi_{I(w,0)+1}(0))

[1[1->[2]][1->[2]]2] has level psi(psi_{I(w,1)}(0))

[1[1->[3]]2] has level psi(psi_{I(w,w)}(0))

And [1[2]->[x]] = [1->[1->[...[1->[2[2]->[x-1]][2]->[x-1]]...][2]->[x-1]][2]->[x-1]]

The limit level is [1[1[1[...]->[2]]->[2]]2].

Rules coming soon!

Ultra Array Notation III

Coming Soon!

Ultra Array Notation IV

Coming Soon!

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