strong fffz分析Part1：修订间差异

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2026年7月25日 (六) 16:06的版本

$ψ_{Z} (0) = 1$

$ψ_{Z} [1] (1) = 2$

$ψ_{Z} [1] (ψ_{Z} [1] (1)) = 3$

$ψ_{Z} (1) = ω$

$ψ_{Z} [2] (2) = ω + 1$

$ψ_{Z} [2] (ψ_{Z} (1)) = ω \times 2$

$ψ_{Z} [2] (ψ_{Z} [2] (2)) = ω \times 2 + 1$

$ψ_{Z} (2) = ω^{2}$

$ψ_{Z} [ω] (ω) = ω^{ω}$

$ψ_{Z} [ω] (ω + 1) = ω^{ω + 1}$

$ψ_{Z} [ω] (ω^{2}) = ω^{ω^{2}}$

$ψ_{Z} [ω] (ψ_{Z} [ω] (ω)) = ω^{ω^{ω}}$

$ψ_{Z} (ω) = (0) (1, 1)$

$ψ_{Z} (ω + 1) = (0) (1, 1) (1)$

$ψ_{Z} [ω \times 2] (ω \times 2) = (0) (1, 1) (1) (2)$

$ψ_{Z} [ω \times 2] (ω^{ω}) = (0) (1, 1) (1) (2) (3)$

$ψ_{Z} [ω \times 2] (ψ_{Z} (ω)) = (0) (1, 1) (1) (2, 1)$

$ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω \times 2)) = (0) (1, 1) (1) (2, 1) (2) (3)$

$ψ_{Z} (ω \times 2) = (0) (1, 1) (1, 1)$

$ψ_{Z} [ω^{2}] (ω^{2}) = (0) (1, 1) (2)$

$ψ_{Z} [ω^{2}, ω^{2} + ω] (ω^{2} + ω) = (0) (1, 1) (2) (1) (2)$

$ψ_{Z} [ω^{2}] (ω^{2} + ω) = (0) (1, 1) (2) (1, 1)$

$ψ_{Z} [ω^{2}] (ω^{2} \times 2) = (0) (1, 1) (2) (1, 1) (2)$

$ψ_{Z} [ω^{2}] (ω^{3}) = (0) (1, 1) (2) (2)$

$ψ_{Z} [ω^{2}, ω^{ω}] (ω^{ω}) = (0) (1, 1) (2) (3)$

$ψ_{Z} [ω^{2}, ω^{ω}] (ψ_{Z} (ω)) = (0) (1, 1) (2) (3, 1)$

$ψ_{Z} [ω^{2}, ω^{ω}] (ψ_{Z} [ω^{2}, ω^{ω}] (ω^{ω})) = (0) (1, 1) (2) (3, 1) (4) (5)$

$ψ_{Z} [ω^{2}] (ω^{ω}) = (0) (1, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω} + ω) = (0) (1, 1) (2, 1) (1, 1)$

$ψ_{Z} [ω^{2}, ω^{ω} \times 2] (ω^{ω} \times 2) = (0) (1, 1) (2, 1) (1, 1) (2) (3)$

$ψ_{Z} [ω^{2}] (ω^{ω} \times 2) = (0) (1, 1) (2, 1) (1, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω + 1}) = (0) (1, 1) (2, 1) (2)$

$ψ_{Z} [ω^{2}] (ω^{ω + 1} + ω^{ω}) = (0) (1, 1) (2, 1) (2) (1, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω + 2}) = (0) (1, 1) (2, 1) (2) (2)$

$ψ_{Z} [ω^{2}, ω^{ω \times 2}] (ω^{ω \times 2}) = (0) (1, 1) (2, 1) (2) (3)$

$ψ_{Z} [ω^{2}, ω^{ω \times 2}] (ψ_{Z} (ω)) = (0) (1, 1) (2, 1) (2) (3, 1)$

$ψ_{Z} [ω^{2}, ω^{ω \times 2}] (ψ_{Z} [ω^{2}, ω^{ω \times 2}] (ω^{ω \times 2})) = (0) (1, 1) (2, 1) (2) (3, 1) (4, 1) (4) (5)$

$ψ_{Z} [ω^{2}] (ω^{ω \times 2}) = (0) (1, 1) (2, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω^{2}}) = (0) (1, 1) (2, 1) (3)$

$ψ_{Z} [ω^{2}] (ω^{ω^{2} + ω}) = (0) (1, 1) (2, 1) (3) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω^{3}}) = (0) (1, 1) (2, 1) (3) (3)$

$ψ_{Z} [ω^{2}, ω^{ω^{ω}}] (ω^{ω^{ω}}) = (0) (1, 1) (2, 1) (3) (4)$

$ψ_{Z} [ω^{2}, ω^{ω^{ω}}] (ψ_{Z} (ω)) = (0) (1, 1) (2, 1) (3) (4, 1)$

$ψ_{Z} [ω^{2}, ω^{ω^{ω}}] (ψ_{Z} [ω^{2}, ω^{ω^{ω}}] (ω^{ω^{ω}})) = (0) (1, 1) (2, 1) (3) (4, 1) (5, 1) (6) (7)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω}}) = (0) (1, 1) (2, 1) (3, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω} + ω}) = (0) (1, 1) (2, 1) (3, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω + 1}}) = (0) (1, 1) (2, 1) (3, 1) (3)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω \times 2}}) = (0) (1, 1) (2, 1) (3, 1) (3, 1)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω^{2}}}) = (0) (1, 1) (2, 1) (3, 1) (4)$

$ψ_{Z} [ω^{2}, ω^{ω^{ω^{ω}}}] (ω^{ω^{ω^{ω}}}) = (0) (1, 1) (2, 1) (3, 1) (4) (5)$

$ψ_{Z} [ω^{2}] (ω^{ω^{ω^{ω}}}) = (0) (1, 1) (2, 1) (3, 1) (4, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω)) = (0) (1, 1) (2, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω) + ω) = (0) (1, 1) (2, 2) (1, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω) \times 2) = (0) (1, 1) (2, 2) (1, 1) (2, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω + 1)) = (0) (1, 1) (2, 2) (2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω + 1) + ψ_{Z} (ω)) = (0) (1, 1) (2, 2) (2) (1, 1) (2, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω + 2)) = (0) (1, 1) (2, 2) (2) (2)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω \times 2)] (ψ_{Z} [ω \times 2] (ω \times 2)) = (0) (1, 1) (2, 2) (2) (3)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω \times 2)] (ψ_{Z} (ω \times 2)) = (0) (1, 1) (2, 2) (2) (3, 1)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω \times 2)] (ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω \times 2)] (ψ_{Z} [ω \times 2] (ω \times 2))) = (0) (1, 1) (2, 2) (2) (3, 1) (4, 2) (4) (5)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω \times 2)) = (0) (1, 1) (2, 2) (2, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω \times 2 + 1)) = (0) (1, 1) (2, 2) (2, 1) (2)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω \times 3)] (ψ_{Z} [ω \times 2] (ω \times 3)) = (0) (1, 1) (2, 2) (2, 1) (2) (3)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω \times 3)) = (0) (1, 1) (2, 2) (2, 1) (2, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω^{2})) = (0) (1, 1) (2, 2) (2, 1) (3)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ω^{ω})] (ψ_{Z} [ω \times 2] (ω^{ω})) = (0) (1, 1) (2, 2) (2, 1) (3) (4)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω^{ω})) = (0) (1, 1) (2, 2) (2, 1) (3, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ω^{ω^{ω}})) = (0) (1, 1) (2, 2) (2, 1) (3, 1) (4, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} (ω))) = (0) (1, 1) (2, 2) (2, 1) (3, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} (ω) + ω)) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (2, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} (ω + 1))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3)$

$ψ_{Z} [ω^{2}, ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω \times 2))] (ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω \times 2))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3) (4)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω \times 2))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω^{2}))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ω^{ω}))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4, 1)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω \times 2] (ψ_{Z} [ω \times 2] (ψ_{Z} (ω))) = (0) (1, 1) (2, 2) (2, 1) (3, 2) (3, 1) (4, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} (ω \times 2)) = (0) (1, 1) (2, 2) (2, 2)$

$ψ_{Z} [ω^{2}] (ψ_{Z} [ω^{2}] (ω^{2})) = (0) (1, 1) (2, 2) (3)$

@@ 第102行： / 第102行： @@
 <math>\psi_Z[\omega^2](\psi_Z(\omega)) = (0)(1,1)(2,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega) + \omega) = (0)(1,1)(2,2)(1,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega) \times 2) = (0)(1,1)(2,2)(1,1)(2,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega+1)) = (0)(1,1)(2,2)(2)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega+1) + \psi_Z(\omega)) = (0)(1,1)(2,2)(2)(1,1)(2,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega+2)) = (0)(1,1)(2,2)(2)(2)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega \times 2)](\psi_Z[\omega \times 2](\omega \times 2)) = (0)(1,1)(2,2)(2)(3)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega \times 2)](\psi_Z(\omega \times 2)) = (0)(1,1)(2,2)(2)(3,1)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega \times 2)](\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega \times 2)](\psi_Z[\omega \times 2](\omega \times 2))) = (0)(1,1)(2,2)(2)(3,1)(4,2)(4)(5)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega \times 2)) = (0)(1,1)(2,2)(2,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega \times 2+1)) = (0)(1,1)(2,2)(2,1)(2)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega \times 3)](\psi_Z[\omega \times 2](\omega \times 3)) = (0)(1,1)(2,2)(2,1)(2)(3)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega \times 3)) = (0)(1,1)(2,2)(2,1)(2,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega^2)) = (0)(1,1)(2,2)(2,1)(3)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\omega^\omega)](\psi_Z[\omega \times 2](\omega^\omega)) = (0)(1,1)(2,2)(2,1)(3)(4)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega^\omega)) = (0)(1,1)(2,2)(2,1)(3,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\omega^{\omega^\omega})) = (0)(1,1)(2,2)(2,1)(3,1)(4,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z(\omega))) = (0)(1,1)(2,2)(2,1)(3,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z(\omega) + \omega)) = (0)(1,1)(2,2)(2,1)(3,2)(2,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z(\omega+1))) = (0)(1,1)(2,2)(2,1)(3,2)(3)</math>
+<math>\psi_Z[\omega^2, \psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\omega \times 2))](\psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\omega \times 2))) = (0)(1,1)(2,2)(2,1)(3,2)(3)(4)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\omega \times 2))) = (0)(1,1)(2,2)(2,1)(3,2)(3,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\omega^2))) = (0)(1,1)(2,2)(2,1)(3,2)(3,1)(4)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\omega^\omega))) = (0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,1)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega \times 2](\psi_Z[\omega \times 2](\psi_Z(\omega))) = (0)(1,1)(2,2)(2,1)(3,2)(3,1)(4,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z(\omega \times 2)) = (0)(1,1)(2,2)(2,2)</math>
+<math>\psi_Z[\omega^2](\psi_Z[\omega^2](\omega^2)) = (0)(1,1)(2,2)(3)</math>