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strong fffz分析Part3:修订间差异

来自Googology Wiki
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第37行: 第37行:
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 + \omega)) = (0)(1,1,1)(2,2)(3)(2,1)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 + \omega)) = (0)(1,1,1)(2,2)(3)(2,1)</math>


<math>\color{red}\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2), \psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)) = (0)(1,1,1)(2,2)(3)(2,1)(3)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2), \psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)) = (0)(1,1,1)(2,2)(3)(2,1)(3)</math>


<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)) = (0)(1,1,1)(2,2)(3)(2,1,1)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2, \omega^2 + \omega](\omega^2 \times 2)) = (0)(1,1,1)(2,2)(3)(2,1,1)</math>
第146行: 第146行:


<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^3](\omega^{\omega^2})) = (0)(1,1,1)(2,2)(3,3,1)(4,3,1)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^3](\omega^{\omega^2})) = (0)(1,1,1)(2,2)(3,3,1)(4,3,1)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^3](\psi_Z(\omega))) = (0)(1,1,1)(2,2)(3,3,1)(4,4)</math>
<math>\psi_Z[\omega^3,\psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^3, \psi_Z[\omega^2](\omega^2)](\psi_Z[\omega^2](\omega^2))) = (0)(1,1,1)(2,2)(3,3,1)(4,4)(5)</math>
<math>\psi_Z[\omega^3](\psi_Z[\omega^2](\omega^2)) = (0)(1,1,1)(2,2,1)</math>

2026年7月30日 (四) 14:41的版本

ψZ[ω3](ψZ(ω))=(0)(1,1,1)(2,2)

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

ψZ[ω3](ψZ(ω)×2)=(0)(1,1,1)(2,2)(1,1,1)(2,2)

ψZ[ω3](ψZ(ω+1))=(0)(1,1,1)(2,2)(2)

ψZ[ω3,ψZ[ω×2](ω×2)](ψZ[ω×2](ω×2))=(0)(1,1,1)(2,2)(2)(3)

ψZ[ω3](ψZ[ω×2](ω×2))=(0)(1,1,1)(2,2)(2,1)

ψZ[ω3,ψZ[ω×2](ω2)](ψZ[ω×2](ω2))=(0)(1,1,1)(2,2)(2,1)(3)

ψZ[ω3,ψZ[ω×2](ω2)](ψZ[ω×2](ωω))=(0)(1,1,1)(2,2)(2,1)(3,1)

ψZ[ω3,ψZ[ω×2](ω2)](ψZ(ω2))=(0)(1,1,1)(2,2)(2,1)(3,2,1)

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

ψZ[ω3](ψZ[ω×2](ω3))=(0)(1,1,1)(2,2)(2,1,1)(3)

ψZ[ω3](ψZ[ω×2](ωω))=(0)(1,1,1)(2,2)(2,1,1)(3,1)

ψZ[ω3](ψZ[ω×2](ωω2))=(0)(1,1,1)(2,2)(2,1,1)(3,1,1)

ψZ[ω3](ψZ[ω×2](ψZ(ω)))=(0)(1,1,1)(2,2)(2,1,1)(3,2)

ψZ[ω3](ψZ[ω×2](ψZ[ω×2](ω2)))=(0)(1,1,1)(2,2)(2,1,1)(3,2)(3,1,1)

ψZ[ω3](ψZ(ω×2))=(0)(1,1,1)(2,2)(2,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ω2))=(0)(1,1,1)(2,2)(3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ω2+1))=(0)(1,1,1)(2,2)(3)(2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ω2+ω](ω2+ω))=(0)(1,1,1)(2,2)(3)(2,1)

ψZ[ω3,ψZ[ω2](ω2),ψZ[ω2,ω2+ω](ω2×2)](ψZ[ω2,ω2+ω](ω2×2))=(0)(1,1,1)(2,2)(3)(2,1)(3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ω2+ω](ω2×2))=(0)(1,1,1)(2,2)(3)(2,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ω2+ω))=(0)(1,1,1)(2,2)(3)(2,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω))=(0)(1,1,1)(2,2)(3,1)

ψZ[ω3,ψZ[ω2](ω2),ψZ[ω2,ωω](ωω2)](ψZ[ω2,ωω](ωω2))=(0)(1,1,1)(2,2)(3,1)(4)

ψZ[ω3,ψZ[ω2](ω2),ψZ[ω2,ωω](ωω2)](ψZ(ω2))=(0)(1,1,1)(2,2)(3,1)(4,2,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω2))=(0)(1,1,1)(2,2)(3,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω2+ω))=(0)(1,1,1)(2,2)(3,1,1)(3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω2×2))=(0)(1,1,1)(2,2)(3,1,1)(3,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωω3))=(0)(1,1,1)(2,2)(3,1,1)(4)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωωω))=(0)(1,1,1)(2,2)(3,1,1)(4,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ωωω2))=(0)(1,1,1)(2,2)(3,1,1)(4,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ(ω)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ(ω+1)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(4)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ[ω×2](ω×2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(4,1)

ψZ[ω3,ψZ[ω2](ω2),ψZ[ω2,ωω](ψZ[ω×2](ω2))](ψZ[ω2,ωω](ψZ[ω×2](ω2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(4,1)(5)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ[ω×2](ω2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(4,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ(ω×2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(4,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ[ω2](ω2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(5)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ[ω2,ωω](ωω)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(5,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωω](ψZ[ω2,ωω](ωω2)))=(0)(1,1,1)(2,2)(3,1,1)(4,2)(5,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ωω))=(0)(1,1,1)(2,2)(3,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ωω×2))=(0)(1,1,1)(2,2)(3,2)(3,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ωω2))=(0)(1,1,1)(2,2)(3,2)(4)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2,ωωω](ωωω))=(0)(1,1,1)(2,2)(3,2)(4,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ωωω))=(0)(1,1,1)(2,2)(3,2)(4,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ψZ(ω)))=(0)(1,1,1)(2,2)(3,3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ(ω2))=(0)(1,1,1)(2,2)(3,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ(ω2+ω))=(0)(1,1,1)(2,2)(3,3,1)(2,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2×2](ω2×2))=(0)(1,1,1)(2,2)(3,3,1)(2,2)(3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2×2](ωω))=(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2×2](ψ(ω2)))=(0)(1,1,1)(2,2)(3,3,1)(2,2)(3,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2×2](ψ(ω2+1)))=(0)(1,1,1)(2,2)(3,3,1)(3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ(ω2×2))=(0)(1,1,1)(2,2)(3,3,1)(3,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3](ω3))=(0)(1,1,1)(2,2)(3,3,1)(4)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω](ωω))=(0)(1,1,1)(2,2)(3,3,1)(4,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω](ωω2))=(0)(1,1,1)(2,2)(3,3,1)(4,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω](ψZ(ω)))=(0)(1,1,1)(2,2)(3,3,1)(4,1,1)(5,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω](ψZ(ω2)))=(0)(1,1,1)(2,2)(3,3,1)(4,1,1)(5,2)(6,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3](ωω))=(0)(1,1,1)(2,2)(3,3,1)(4,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3](ωω×2))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(4,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ωω2))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2,ωωω](ωωω))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2,ωωω](ωωω2))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,1,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ωωω))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ(ω)))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ(ω2)))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3](ω3)))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)(6)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2,ψZ[ω3,ωω](ωω)](ψZ[ω3,ωω](ωω)))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)(6,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3,ωω](ωω)))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)(6,2)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3,ωω](ψZ(ω2))))=(0)(1,1,1)(2,2)(3,3,1)(4,2)(5,3,1)(6,2)(7,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3](ωω)))=(0)(1,1,1)(2,2)(3,3,1)(4,3)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3,ωω2](ωω2)))=(0)(1,1,1)(2,2)(3,3,1)(4,3)(5)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ωω2](ψZ[ω3,ωω2](ψZ(ω2))))=(0)(1,1,1)(2,2)(3,3,1)(4,3)(5,4,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3](ωω2))=(0)(1,1,1)(2,2)(3,3,1)(4,3,1)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3](ψZ(ω)))=(0)(1,1,1)(2,2)(3,3,1)(4,4)

ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω3,ψZ[ω2](ω2)](ψZ[ω2](ω2)))=(0)(1,1,1)(2,2)(3,3,1)(4,4)(5)

ψZ[ω3](ψZ[ω2](ω2))=(0)(1,1,1)(2,2,1)