查看“︁Catching函数分析2：EBO~JO”︁的源代码

本条目展示[[Catching 函数|Catching函数]]在[[EBO]]到[[JO]]之间的过程。以下左为[[FGH]]，右为[[SGH]]。均为[[序数坍缩函数#MOCF 简介|MOCF]]

<math>\begin{align}.\\&f_3(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+1)\\&f_{\omega}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega^\omega)\\&f_{\psi(0)}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\psi_1(\Omega))\\&f_{\psi(\Omega_\omega)}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\psi_1(\Omega_\Omega))\\&f_{\psi(\Omega_{\Omega_\omega})}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\psi_1(\Omega_{\Omega_\Omega}))\\&f_{\psi(\psi_I(0))[n]}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\psi_1(\psi_I(0)))\\&f_{\psi(\psi_I(0)[n]+1)}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\psi_1(\psi_I(0)+1))\\&f_{\psi(\psi_I(0)[n]+\Omega)[n]}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_2)\\&f_{\psi(\psi_I(0)[n]+\Omega)}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_2\times\Omega)\\&f_{\psi(\psi_I(0)[n]+\Omega_2)}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_3\times\Omega)\\&f_{\psi(\psi_I(0)[n]+\Omega_\omega)[n]}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_\omega)\\&f_{\psi(\psi_I(0)[n]+\Omega_\omega)}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_\Omega)\\&f_{\psi(\psi_I(0)[n]+\Omega_{\Omega_\omega})}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)+\Omega_{\Omega_\Omega})\\&f_{\psi(\psi_I(0)[n]\times2)}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)\times2)\\&f_{\psi(\psi_I(0)[n]^2)}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)^2)\\&f_{\psi(\psi_I(0)[n]^{\psi_I(0)[n]})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(0)^{\psi_I(0)})\\&f_{\psi(\psi_{\Omega_{\psi_I(0)[n-1]+1}}(0))}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_{\Omega_{\psi_I(0)+1}}(0))\\&f_{\psi(\Omega_{\psi_I(0)[n-1]+1})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)+1})\\&f_{\psi(\Omega_{\psi_I(0)[n-1]+\omega})}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)+\Omega})\\&f_{\psi(\Omega_{\psi_I(0)[n-1]+\Omega_\omega})}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)+\Omega_\Omega})\\&f_{\psi(\psi_I(0)[n+1])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)\times2})\\&f_{\psi(\Omega_{\psi_I(0)[n]+1})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)\times2+1})\\&f_{\psi(\Omega_{\psi_I(0)[n]\times2})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)\times3})\\&f_{\psi(\Omega_{\psi_I(0)[n]\times\omega})}^n(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)\times\Omega})\\&f_{\psi(\Omega_{\psi_I(0)[n]^2})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(0)^2})\\&f_{\psi(\Omega_{\Omega_{\psi_I(0)[n]+1}})}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\Omega_{\psi_I(0)+1}})\\&f_{\psi(\psi_I(0)[n+2])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\Omega_{\psi_I(0)\times2}})\\&f_{\psi(\psi_I(0)[n\times2])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(1))\\&f_{\psi(\psi_I(0)[n\times2+1])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\Omega_{\psi_I(1)\times2})\\&f_{\psi(\psi_I(0)[n\times3])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(2))\\&f_{\psi(\psi_I(0)[n^2])}(f_{\psi(\psi_I(0))}(n))\sim\psi(\psi_I(\omega))\\&f_{\psi(\psi_I(0))}^2(n)\sim\psi(\psi_I(\psi(\psi_I(0))))\\&f_{\psi(\psi_I(0))}^3(n)\sim\psi(\psi_I(\psi(\psi_I(\psi(\psi_I(0))))))\\&f_{\psi(\psi_I(0))+1}(n)\sim\psi(\psi_I(\Omega))\\&f_{\psi(\psi_I(0))+2}(n)\sim\psi(\psi_I(\Omega)+\psi_{\Omega_2}(\psi_I(\Omega))\times\Omega)\\&f_{\psi(\psi_I(0)+\Omega)}(n)\sim\psi(\psi_I(\Omega)+\Omega_2)\\&f_{\psi(\psi_I(0)\times\Omega)}(n)\sim\psi(\psi_I(\Omega)\times\Omega_2)\\&f_{\psi(\psi_I(0)^2)+1}(n)\sim\psi(\psi_I(\Omega)^2)\\&f_{\psi(\psi_{\Omega_{\psi_I(0)+1}}(0))}(n)\sim\psi(\psi_{\Omega_{\psi_I(\Omega)+1}}(0))\\&f_{\psi(\Omega_{\psi_I(0)+1})}(n)\sim\psi(\Omega_{\psi_I(\Omega)+1})\\&f_{\psi(\Omega_{\Omega_{\psi_I(0)+1}})}(n)\sim\psi(\Omega_{\Omega_{\psi_I(\Omega)+1}})\\&f_{\psi(\psi_I(1))}(n)\sim\psi(\psi_I(\Omega+1))\\&f_{\psi(\psi_I(1)[n\times2])}(f_{\psi(\psi_I(1))}(n))\sim\psi(\psi_I(\Omega+2))\\&f_{\psi(\psi_I(1))}^2(n)\sim\psi(\psi_I(\Omega+\psi(\psi_I(\Omega))))\\&f_{\psi(\psi_I(1))+1}(n)\sim\psi(\psi_I(\Omega\times2))\\&f_{\psi(\psi_I(2))}(n)\sim\psi(\psi_I(\Omega\times2+1))\\&f_{\psi(\psi_I(\omega))}(n)\sim\psi(\psi_I(\Omega\times\omega))\\&f_{\psi(\psi_I(\omega))+1}(n)\sim\psi(\psi_I(\Omega^2))\\&f_{\psi(\psi_I(\omega+1))+1}(n)\sim\psi(\psi_I(\Omega^2+\Omega))\\&f_{\psi(\psi_I(\omega^\omega))+1}(n)\sim\psi(\psi_I(\Omega^\Omega))\\&f_{\psi(\psi_I(\psi(0)))+1}(n)\sim\psi(\psi_I(\psi_{\Omega_2}(\Omega)))\\&f_{\psi(\psi_I(\psi(\psi_I(0))))+1}(n)\sim\psi(\psi_I(\psi_{\Omega_2}(\psi_I(\Omega))))\\&f_{\psi(\psi_I(\Omega))}(n)\sim\psi(\psi_I(\Omega_2))\\&f_{\psi(\psi_I(\Omega_2))}(n)\sim\psi(\psi_I(\Omega_3))\\&f_{\psi(\psi_I(\Omega_3))}(n)\sim\psi(\psi_I(\Omega_4))\\& f_{\psi(\psi_I(\Omega_\omega))}(n)\sim\psi(\psi_I(\Omega_\omega))\\& C(\omega+1)=\psi(\psi_I(\Omega_\omega))\end{align}</math>

<nowiki>\begin{align}.\\\&f_{\psi(\psi_I(\Omega_\omega))+1}(n)\sim\psi(\psi_I(\Omega_\Omega))\\\&f_{\psi(\psi_I(\Omega_\omega))+2}(n)\sim\psi(\psi_I(\Omega_\Omega)\times\Omega)\\\&f_{\psi(\psi_I(\Omega_\omega)+1)}(n)\sim\psi(\psi_I(\Omega_\Omega)\times\psi_{\Omega_2}(\psi_I(\Omega_\Omega)+1))\\\&f_{\psi(\psi_I(\Omega_\omega)\times\Omega)}(n)\sim\psi(\psi_I(\Omega_\Omega)\times\Omega_2)\\\&f_{\psi(\psi_I(\Omega_\omega)^2)+1}(n)\sim\psi(\psi_I(\Omega_\Omega)^2)\\\&f_{\psi(\Omega_{\psi_I(\Omega_\omega)+1})}(n)\sim\psi(\Omega_{\psi_I(\Omega_\Omega)+1})\\\&f_{\psi(\psi_I(\Omega_\omega+1))}(n)\sim\psi(\psi_I(\Omega_\Omega+1))\\\&f_{\psi(\psi_I(\Omega_\omega+1))+1}(n)\sim\psi(\psi_I(\Omega_\Omega+\Omega))\\\&f_{\psi(\psi_I(\Omega_\omega+\psi(0)))}(n)\sim\psi(\psi_I(\Omega_\Omega+\psi_1(0)))\\\&f_{\psi(\psi_I(\Omega_\omega+\Omega))}(n)\sim\psi(\psi_I(\Omega_\Omega+\Omega_2))\\\&f_{\psi(\psi_I(\Omega_\omega\times2))}(n)\sim\psi(\psi_I(\Omega_\Omega+\Omega_\omega))\\\&f_{\psi(\psi_I(\psi_{\Omega_{\omega+1}}(0)))}(n)\sim\psi(\psi_I(\psi_{\Omega_{\Omega+1}}(0)))\\\&f_{\psi(\psi_I(\Omega_{\omega+1}))}(n)\sim\psi(\psi_I(\Omega_{\Omega+1}))\\\&f_{\psi(\psi_I(\Omega_{\omega\times2}))+1}(n)\sim\psi(\psi_I(\Omega_{\Omega\times2}))\\\&f_{\psi(\psi_I(\Omega_{\psi(0)}))}(n)\sim\psi(\psi_I(\Omega_{\psi_{1}(0)}))\\\&f_{\psi(\psi_I(\Omega_{\Omega}))}(n)\sim\psi(\psi_I(\Omega_{\Omega_2}))\\\&f_{\psi(\psi_I(\Omega_{\Omega_2}))}(n)\sim\psi(\psi_I(\Omega_{\Omega_3}))\\\&f_{\psi(\psi_I(\Omega_{\Omega_\omega}))}(n)\sim\psi(\psi_I(\Omega_{\Omega_\omega}))\\\&\color{red}{C(\omega+2)=\psi(\psi_I(\Omega_{\Omega_\omega}))}\\\&\color{red}{C(\omega\times2)=\psi(\psi_I(\psi_I(0)))}\\\&f_{\psi(\psi_I(\psi_I(0)))+1}(n)\sim\psi(\psi_I(\psi_I(\Omega)))\\\&f_{\psi(\psi_I(\psi_I(1)))+1}(n)\sim\psi(\psi_I(\psi_I(\Omega\times2)))\\\&f_{\psi(\psi_I(\psi_I(\Omega)))}(n)\sim\psi(\psi_I(\psi_I(\Omega_2)))\\\&f_{\psi(\psi_I(\psi_I(\Omega_\omega)))}(n)\sim\psi(\psi_I(\psi_I(\Omega_\omega)))\\\&\color{red}{C(\omega\times2+1)=\psi(\psi_I(\psi_I(\Omega_\omega)))}\\\&\color{red}{C(\omega\times2+2)=\psi(\psi_I(\psi_I(\Omega_{\Omega_\omega})))}\\\&\color{red}{C(\omega\times3)=\psi(\psi_I(\psi_I(\psi_I(0))))}\\\&\color{red}{C(\omega\times4)=\psi(\psi_I(\psi_I(\psi_I(\psi_I(0)))))}\\\&\Large\color{red}{C(\omega^2)=\psi(I)}\\\&f_3(f_{\psi(I)}(n))\sim\psi(I+1)\\\&f_{\psi(0)}^n(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(\Omega))\\\&f_{\psi(\Omega_\omega)[n]}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(\Omega_\omega))\\\&f_{\psi(\Omega_\omega)}^n(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(\Omega_\Omega))\\\&f_{\psi(\psi_I(0))}^n(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(\psi_I(\Omega)))\\\&f_{\psi(I)[n]}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(I))\\\&f_{\psi(\psi_I(I)[n]+1)}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_2}(I+1))\\\&f_{\psi(\psi_I(I)[n]+\Omega)[n]}(f_{\psi(I)}(n))\sim\psi(I+\Omega_2)\\\&f_{\psi(\psi_I(I)[n]+\psi_I(0))[n]}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(0))\\\&f_{\psi(\psi_I(I)[n]\times2)}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I))\\\&f_{\psi(\psi_{\Omega_{\psi_I(I)[n]+1}}(0))}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(0))\\\&f_{\psi(\psi_{\Omega_{\psi_I(I)[n]+1}}(\psi_I(0)))}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(\psi_I(0)))\\\&f_{\psi(\psi_{\Omega_{\psi_I(I)[n]+1}}(\psi_I(I)[n]))}(f_{\psi(I)}(n))\sim\psi(I+\psi_{\Omega_{\psi_I(I)+1}}(I))\\\&f_{\psi(\Omega_{\psi_I(I)[n]+1})}(f_{\psi(I)}(n))\sim\psi(I+\Omega_{\psi_I(I)+1})\\\&f_{\psi(\psi_I(\psi_I(I)[n-1]+1))}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I+1))\\\&f_{\psi(\psi_I(\psi_I(I)[n-1]+\Omega_\omega))}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I+\Omega_\omega))\\\&f_{\psi(\psi_I(\psi_I(I)[n-1]+\psi_I(0)))}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I+\psi_I(0)))\\\&f_{\psi(I)[n+1]}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I+\psi_I(I)))\\\&f_{\psi(I)[n+2]}(f_{\psi(I)}(n))\sim\psi(I+\psi_I(I+\psi_I(I+\psi_I(I))))\\\&f_{\psi(I)[n\times2]}(f_{\psi(I)}(n))\sim\psi(I\times2)\\\&f_{\psi(I)}^2(n)\sim\psi(I\times\psi(I))\\\&f_{\psi(I)+1}(n)\sim\psi(I\times\Omega)\\\&f_{\psi(I+1)}(n)\sim\psi(I\times\psi_{\Omega_2}(I+1))\\\&f_{\psi(I\times2)}(n)\sim\psi(I\times\psi_{\Omega_2}(I\times2))\\\&f_{\psi(I\times\Omega)}(n)\sim\psi(I\times\Omega_2)\\\&f_{\psi(I\times\Omega_2)}(n)\sim\psi(I\times\Omega_3)\\\&f_{\psi(I\times\Omega_\omega)}(n)\sim\psi(I\times\Omega_\omega)\\\&C(\omega^2+1)=\psi(I\times\Omega_\omega)\\\&C(\omega^2+2)=\psi(I\times\Omega_{\Omega_\omega})\\\&C(\omega^2+\omega)=\psi(I\times\psi_I(0))\\\&C(\omega^2+\omega+1)=\psi(I\times\psi_I(\Omega_\omega))\\\&C(\omega^2+\omega\times2)=\psi(I\times\psi_I(\psi_I(0)))\\\&{C(\omega^2\times2)=\psi(I\times\psi_I(I))\\\&f_{\psi(I\times\psi_I(I))+1}(n)\sim\psi(I\times\psi_I(I\times\Omega))\\\&f_{\psi(I\times\psi_I(I\times\Omega_\omega))}(n)\sim\psi(I\times\psi_I(I\times\Omega_\omega))\\\&{C(\omega^2\times2+1)=\psi(I\times\psi_I(I\times\Omega_\omega))\\\&{C(\omega^2\times2+\omega)=\psi(I\times\psi_I(I\times\psi_I(0)))\\\&{C(\omega^2\times3)=\psi(I\times\psi_I(I\times\psi_I(I)))\\\&{C(\omega^3)=\psi(I^2)\\\&f_{\psi(I^2)+1}(n)\sim\psi(I^2\times\Omega)\\\&{C(\omega^3+1)=\psi(I^2\times\Omega_\omega)\\\&{C(\omega^3+\omega)=\psi(I^2\times\psi_I(0))\\\&{C(\omega^3+\omega^2)=\psi(I^2\times\psi_I(I))\\\&{C(\omega^3\times2)=\psi(I^2\times\psi_I(I^2))\\\&{C(\omega^4)=\psi(I^3)\\\&{C(\omega^\omega)=\psi(I^\omega)\end{align}</nowiki>