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strong fffz分析Part6:修订间差异

来自Googology Wiki
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创建页面,内容为“<math>\psi_Z[\omega^\omega](\omega^\omega) = (0)(1^\omega)</math> <math>\psi_Z[\omega^\omega, \omega^\omega + \omega](\omega^\omega + \omega) = (0)(1^\omega)(1)(2)</math> <math>\psi_Z[\omega^\omega, \omega^\omega + \omega](\psi_Z[\omega^\omega](\omega^\omega)) = (0)(1^\omega)(1)(2, 1^\omega)</math> <math>\psi_Z[\omega^\omega](\omega^\omega + \omega) = (0)(1^\omega)(1,1)</math> <math>\psi_Z[\omega^\omega, \omega^\omega + \omega^2](\omega^\omega + \omega^2) =…”
 
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<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega)) = (0)(1^\omega)(2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega)) = (0)(1^\omega)(2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega+1)) = (0)(1^\omega)(2,2)(2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega \times 2)) = (0)(1^\omega)(2,2)(2,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega^2)) = (0)(1^\omega)(2,2)(2,1,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega^\omega)) = (0)(1^\omega)(2,2)(2,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega^{\omega + 1})) = (0)(1^\omega)(2,2)(2,1^\omega)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega^{\omega \times 2})) = (0)(1^\omega)(2,2)(2,1^\omega)(3,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\omega^{\omega^\omega})) = (0)(1^\omega)(2,2)(2,1^\omega)(3,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega \times 2](\psi_Z(\omega))) = (0)(1^\omega)(2,2)(2,1^\omega)(3,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega \times 2)) = (0)(1^\omega)(2,2)(2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2](\omega^2)) = (0)(1^\omega)(2,2)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^\omega](\omega^\omega)) = (0)(1^\omega)(2,2)(3,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^\omega](\omega^{\omega^2})) = (0)(1^\omega)(2,2)(3,1,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^\omega](\omega^{\omega^\omega})) = (0)(1^\omega)(2,2)(3,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^\omega](\psi_Z(\omega))) = (0)(1^\omega)(2,2)(3,1^\omega)(4,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2](\omega^\omega)) = (0)(1^\omega)(2,2)(3,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^\omega](\omega^\omega)) = (0)(1^\omega)(2,2)(3,3,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2](\omega^2)) = (0)(1^\omega)(2,2,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2](\omega^3)) = (0)(1^\omega)(2,2,1,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\omega^\omega)) = (0)(1^\omega)(2,2,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\omega^{\omega+1})) = (0)(1^\omega)(2,2,1^\omega)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\omega^{\omega \times 2})) = (0)(1^\omega)(2,2,1^\omega)(3,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\omega^{\omega^\omega})) = (0)(1^\omega)(2,2,1^\omega)(3,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\psi_Z(\omega))) = (0)(1^\omega)(2,2,1^\omega)(3,1^\omega)(4,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\psi_Z[\omega^2](\omega^2))) = (0)(1^\omega)(2,2,1^\omega)(3,1^\omega)(4,2,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^\omega](\psi_Z[\omega^2,\omega^\omega](\omega^\omega))) = (0)(1^\omega)(2,2,1^\omega)(3,1^\omega)(4,2,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2](\omega^\omega)) = (0)(1^\omega)(2,2,1^\omega)(3,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2, \omega^{\omega^\omega}](\omega^{\omega^\omega})) = (0)(1^\omega)(2,2,1^\omega)(3,2,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2](\omega^{\omega^\omega})) = (0)(1^\omega)(2,2,1^\omega)(3,2,1^\omega)(4,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^2](\psi_Z(\omega))) = (0)(1^\omega)(2,2,1^\omega)(3,3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega^2)) = (0)(1^\omega)(2,2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^\omega](\omega^\omega)) = (0)(1^\omega)(2^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+1})) = (0)(1^\omega)(2^\omega)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^\omega](\omega^\omega))) = (0)(1^\omega)(2^\omega)(3^\omega)</math>
<math>\psi_Z[\omega^\omega](\omega^{\omega+1}) = (0)(1^{\omega+1})</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\omega^{\omega+2}) = (0)(1^{\omega+1})(2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\omega^{\omega \times 2}) = (0)(1^{\omega+1})(2,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\omega^{\omega^2}) = (0)(1^{\omega+1})(2,1,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\omega^{\omega^\omega}) = (0)(1^{\omega+1})(2,1^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}, \omega^{\omega^{\omega+1}}](\omega^{\omega^{\omega+1}}) = (0)(1^{\omega+1})(2,1^\omega)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}, \omega^{\omega^{\omega+1}}](\psi_Z[\omega^\omega](\omega^{\omega+1})) = (0)(1^{\omega+1})(2,1^\omega)(3,2^\omega,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\omega^{\omega^{\omega+1}}) = (0)(1^{\omega+1})(2,1^{\omega+1})</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z(\omega)) = (0)(1^{\omega+1})(2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega](\omega^\omega)) = (0)(1^{\omega+1})(2^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}, \psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+1})](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+1})) = (0)(1^{\omega+1})(2^\omega)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+1})) = (0)(1^{\omega+1})(2^\omega,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+2})) = (0)(1^{\omega+1})(2^\omega,1)(3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega \times 2}](\omega^{\omega \times 2})) = (0)(1^{\omega+1})(2^\omega,1)(3,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega \times 2}](\omega^{\omega^{\omega+1}})) = (0)(1^{\omega+1})(2^\omega,1)(3,1^{\omega+1})</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega \times 2}](\psi_Z(\omega))) = (0)(1^{\omega+1})(2^\omega,1)(3,1^{\omega+1})(4,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega \times 2}](\psi_Z[\omega^\omega](\omega^\omega))) = (0)(1^{\omega+1})(2^\omega,1)(3,1^{\omega+1})(4,2^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega \times 2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega+1}))) = (0)(1^{\omega+1})(2^\omega,1)(3,1^{\omega+1})(4,2^\omega,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega \times 2})) = (0)(1^{\omega+1})(2^\omega,1)(3,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}, \omega^{\omega^2}](\omega^{\omega^{\omega+1}})) = (0)(1^{\omega+1})(2^\omega,1)(3,2,1^{\omega+1})</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega^2})) = (0)(1^{\omega+1})(2^\omega,1)(3,2,2)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega^\omega})) = (0)(1^{\omega+1})(2^\omega,1)(3,2^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\omega^{\omega^{\omega+1}})) = (0)(1^{\omega+1})(2^\omega,1)(3,2^\omega,1)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z(\omega))) = (0)(1^{\omega+1})(2^\omega,1)(3,3)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega, \omega^{\omega+1}](\psi_Z[\omega^\omega](\omega^\omega))) = (0)(1^{\omega+1})(2^\omega,1)(3^\omega)</math>
<math>\psi_Z[\omega^\omega, \omega^{\omega+2}](\psi_Z[\omega^\omega](\omega^{\omega+1})) = (0)(1^{\omega+1})(2^{\omega+1})</math>
<math>\psi_Z[\omega^\omega](\omega^{\omega+2}) = (0)(1^{\omega+2})</math>
<math>\psi_Z[\omega^\omega](\omega^{\omega \times 2}) = (0)(1^{\omega \times 2})</math>
<math>\psi_Z[\omega^\omega](\omega^{\omega^2}) = (0)(1^{\omega^2})</math>
<math>\psi_Z[\omega^\omega](\psi_Z(\omega)) = (0)(1^{(0)(1,1)})</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z(\omega+1)) = (0)(1^{(0)(1,1)})(2)</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z[\omega \times 2](\omega \times 2)) = (0)(1^{(0)(1,1)})(2,1)</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z[\omega \times 2](\psi_Z(\omega))) = (0)(1^{(0)(1,1)})(2,1^{(0)(1,1)})</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z[\omega \times 2](\psi_Z(\omega+1))) = (0)(1^{(0)(1,1)})(2,1^{(0)(1,1)})(3)</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z(\omega \times 2)) = (0)(1^{(0)(1,1)})(2,2)</math>
<math>\psi_Z[\omega^\omega, \psi_Z(\omega+1)](\psi_Z[\omega^\omega](\psi_Z(\omega))) = (0)(1^{(0)(1,1)})(2^{(0)(1,1)})</math>
<math>\psi_Z[\omega^\omega](\psi_Z(\omega+1)) = (0)(1^{(0)(1,1)(0)})</math>
<math>\psi_Z[\omega^\omega](\psi_Z[\omega^\omega](\omega^\omega)) = (0)(1^{(0)(1^\omega)})</math>
<math>\psi_Z(\omega^\omega) = (0)(1^\Omega)</math>
[[分类:分析]]

2026年8月2日 (日) 07:03的最新版本

ψZ[ωω](ωω)=(0)(1ω)

ψZ[ωω,ωω+ω](ωω+ω)=(0)(1ω)(1)(2)

ψZ[ωω,ωω+ω](ψZ[ωω](ωω))=(0)(1ω)(1)(2,1ω)

ψZ[ωω](ωω+ω)=(0)(1ω)(1,1)

ψZ[ωω,ωω+ω2](ωω+ω2)=(0)(1ω)(1,1)(2)

ψZ[ωω](ωω+ω2)=(0)(1ω)(1,1,1)

ψZ[ωω](ωω×2)=(0)(1ω)(1ω)

ψZ[ωω,ωω+1](ωω+1)=(0)(1ω)(2)

ψZ[ωω,ωω+1](ωω+1+ωω)=(0)(1ω)(2)(1ω)

ψZ[ωω,ωω+1,ωω×2](ωω×2)=(0)(1ω)(2)(3)

ψZ[ωω,ωω+1](ωω×2)=(0)(1ω)(2,1)

ψZ[ωω,ωω+1,ωω2](ωω2)=(0)(1ω)(2,1)(3)

ψZ[ωω,ωω+1](ωω2)=(0)(1ω)(2,1,1)

ψZ[ωω,ωω+1](ωω3)=(0)(1ω)(2,1,1,1)

ψZ[ωω,ωω+1](ωωω)=(0)(1ω)(2,1ω)

ψZ[ωω,ωω+1](ωωω+1)=(0)(1ω)(2,1ω)(2)

ψZ[ωω,ωω+1](ωωω+ω)=(0)(1ω)(2,1ω)(2,1)

ψZ[ωω,ωω+1](ωωω×2)=(0)(1ω)(2,1ω)(2,1ω)

ψZ[ωω,ωω+1](ωωω+1)=(0)(1ω)(2,1ω)(3)

ψZ[ωω,ωω+1,ωωω×2](ωωω×2)=(0)(1ω)(2,1ω)(3)(4)

ψZ[ωω,ωω+1](ωωω×2)=(0)(1ω)(2,1ω)(3,1)

ψZ[ωω,ωω+1](ωωωω)=(0)(1ω)(2,1ω)(3,1ω)

ψZ[ωω,ωω+1](ψZ(ω))=(0)(1ω)(2,2)

ψZ[ωω,ωω+1](ψZ(ω+1))=(0)(1ω)(2,2)(2)

ψZ[ωω,ωω+1](ψZ[ω×2](ω×2))=(0)(1ω)(2,2)(2,1)

ψZ[ωω,ωω+1](ψZ[ω×2](ω2))=(0)(1ω)(2,2)(2,1,1)

ψZ[ωω,ωω+1](ψZ[ω×2](ωω))=(0)(1ω)(2,2)(2,1ω)

ψZ[ωω,ωω+1](ψZ[ω×2](ωω+1))=(0)(1ω)(2,2)(2,1ω)(3)

ψZ[ωω,ωω+1](ψZ[ω×2](ωω×2))=(0)(1ω)(2,2)(2,1ω)(3,1)

ψZ[ωω,ωω+1](ψZ[ω×2](ωωω))=(0)(1ω)(2,2)(2,1ω)(3,1ω)

ψZ[ωω,ωω+1](ψZ[ω×2](ψZ(ω)))=(0)(1ω)(2,2)(2,1ω)(3,2)

ψZ[ωω,ωω+1](ψZ(ω×2))=(0)(1ω)(2,2)(2,2)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2](ω2))=(0)(1ω)(2,2)(3)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω))=(0)(1ω)(2,2)(3,1)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω2))=(0)(1ω)(2,2)(3,1,1)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωωω))=(0)(1ω)(2,2)(3,1ω)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ(ω)))=(0)(1ω)(2,2)(3,1ω)(4,2)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ω2](ωω))=(0)(1ω)(2,2)(3,2)

ψZ[ωω,ωω+1,ψZ[ω2](ω2)](ψZ[ωω](ωω))=(0)(1ω)(2,2)(3,3,1ω)

ψZ[ωω,ωω+1](ψZ[ω2](ω2))=(0)(1ω)(2,2,1)

ψZ[ωω,ωω+1](ψZ[ω2](ω3))=(0)(1ω)(2,2,1,1)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ωω))=(0)(1ω)(2,2,1ω)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ωω+1))=(0)(1ω)(2,2,1ω)(3)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ωω×2))=(0)(1ω)(2,2,1ω)(3,1)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ωωω))=(0)(1ω)(2,2,1ω)(3,1ω)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ψZ(ω)))=(0)(1ω)(2,2,1ω)(3,1ω)(4,2)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ψZ[ω2](ω2)))=(0)(1ω)(2,2,1ω)(3,1ω)(4,2,1)

ψZ[ωω,ωω+1](ψZ[ω2,ωω](ψZ[ω2,ωω](ωω)))=(0)(1ω)(2,2,1ω)(3,1ω)(4,2,1ω)

ψZ[ωω,ωω+1](ψZ[ω2](ωω))=(0)(1ω)(2,2,1ω)(3,2)

ψZ[ωω,ωω+1](ψZ[ω2,ωωω](ωωω))=(0)(1ω)(2,2,1ω)(3,2,1ω)

ψZ[ωω,ωω+1](ψZ[ω2](ωωω))=(0)(1ω)(2,2,1ω)(3,2,1ω)(4,2)

ψZ[ωω,ωω+1](ψZ[ω2](ψZ(ω)))=(0)(1ω)(2,2,1ω)(3,3)

ψZ[ωω,ωω+1](ψZ(ω2))=(0)(1ω)(2,2,2)

ψZ[ωω,ωω+1](ψZ[ωω](ωω))=(0)(1ω)(2ω)

ψZ[ωω,ωω+1](ψZ[ωω,ωω+1](ωω+1))=(0)(1ω)(2ω)(3)

ψZ[ωω,ωω+1](ψZ[ωω,ωω+1](ψZ[ωω](ωω)))=(0)(1ω)(2ω)(3ω)

ψZ[ωω](ωω+1)=(0)(1ω+1)

ψZ[ωω,ωω+2](ωω+2)=(0)(1ω+1)(2)

ψZ[ωω,ωω+2](ωω×2)=(0)(1ω+1)(2,1)

ψZ[ωω,ωω+2](ωω2)=(0)(1ω+1)(2,1,1)

ψZ[ωω,ωω+2](ωωω)=(0)(1ω+1)(2,1ω)

ψZ[ωω,ωω+2,ωωω+1](ωωω+1)=(0)(1ω+1)(2,1ω)(3)

ψZ[ωω,ωω+2,ωωω+1](ψZ[ωω](ωω+1))=(0)(1ω+1)(2,1ω)(3,2ω,1)

ψZ[ωω,ωω+2](ωωω+1)=(0)(1ω+1)(2,1ω+1)

ψZ[ωω,ωω+2](ψZ(ω))=(0)(1ω+1)(2,2)

ψZ[ωω,ωω+2](ψZ[ωω](ωω))=(0)(1ω+1)(2ω)

ψZ[ωω,ωω+2,ψZ[ωω,ωω+1](ωω+1)](ψZ[ωω,ωω+1](ωω+1))=(0)(1ω+1)(2ω)(3)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωω+1))=(0)(1ω+1)(2ω,1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωω+2))=(0)(1ω+1)(2ω,1)(3)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω×2](ωω×2))=(0)(1ω+1)(2ω,1)(3,1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω×2](ωωω+1))=(0)(1ω+1)(2ω,1)(3,1ω+1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω×2](ψZ(ω)))=(0)(1ω+1)(2ω,1)(3,1ω+1)(4,2)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω×2](ψZ[ωω](ωω)))=(0)(1ω+1)(2ω,1)(3,1ω+1)(4,2ω)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω×2](ψZ[ωω,ωω+1](ωω+1)))=(0)(1ω+1)(2ω,1)(3,1ω+1)(4,2ω,1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωω×2))=(0)(1ω+1)(2ω,1)(3,2)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1,ωω2](ωωω+1))=(0)(1ω+1)(2ω,1)(3,2,1ω+1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωω2))=(0)(1ω+1)(2ω,1)(3,2,2)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωωω))=(0)(1ω+1)(2ω,1)(3,2ω)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ωωω+1))=(0)(1ω+1)(2ω,1)(3,2ω,1)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ψZ(ω)))=(0)(1ω+1)(2ω,1)(3,3)

ψZ[ωω,ωω+2](ψZ[ωω,ωω+1](ψZ[ωω](ωω)))=(0)(1ω+1)(2ω,1)(3ω)

ψZ[ωω,ωω+2](ψZ[ωω](ωω+1))=(0)(1ω+1)(2ω+1)

ψZ[ωω](ωω+2)=(0)(1ω+2)

ψZ[ωω](ωω×2)=(0)(1ω×2)

ψZ[ωω](ωω2)=(0)(1ω2)

ψZ[ωω](ψZ(ω))=(0)(1(0)(1,1))

ψZ[ωω,ψZ(ω+1)](ψZ(ω+1))=(0)(1(0)(1,1))(2)

ψZ[ωω,ψZ(ω+1)](ψZ[ω×2](ω×2))=(0)(1(0)(1,1))(2,1)

ψZ[ωω,ψZ(ω+1)](ψZ[ω×2](ψZ(ω)))=(0)(1(0)(1,1))(2,1(0)(1,1))

ψZ[ωω,ψZ(ω+1)](ψZ[ω×2](ψZ(ω+1)))=(0)(1(0)(1,1))(2,1(0)(1,1))(3)

ψZ[ωω,ψZ(ω+1)](ψZ(ω×2))=(0)(1(0)(1,1))(2,2)

ψZ[ωω,ψZ(ω+1)](ψZ[ωω](ψZ(ω)))=(0)(1(0)(1,1))(2(0)(1,1))

ψZ[ωω](ψZ(ω+1))=(0)(1(0)(1,1)(0))

ψZ[ωω](ψZ[ωω](ωω))=(0)(1(0)(1ω))

ψZ(ωω)=(0)(1Ω)