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NOCF（Nothing Ordinal Collapse Function）是 [[序数坍缩函数|OCF]] 的一种。 === 理念 === 由于 NOCF 没有完整的定义，这里给出它的理念： <math>\psi_\alpha(0)=\Omega_\alpha\quad(\Omega_0=1)</math>，<math>\psi_\alpha(\#+1)=\psi_\alpha(\#)+1</math>；在 OCF 内遇到 <math>\Omega_\alpha</math> 的处理方式与 [[序数坍缩函数#MOCF|MOCF]] 一致。 === 分析 === 下列分析的等号左侧为 NOCF，右侧为 MOCF。<ref>SuzukaCat (2025). NOCF vs MOCF. ''(EB/OL), Zhihu''. Available at: https://zhuanlan.zhihu.com/p/1928160006743789750</ref> * <math>\psi_0(0)=1</math> * <math>\psi_0(\psi_0(0))=2</math> * <math>\psi_0(\psi_0(\psi_0(0)))=3</math> * <math>\psi_0(\psi_1(0))=\omega</math> * <math>\psi_0(\psi_1(\psi_0(0)))=\omega+1</math> * <math>\psi_0(\psi_1(\psi_0(\psi_1(0))))=\omega\times2</math> * <math>\psi_0(\psi_1(\psi_1(0)))=\omega^2</math> * <math>\psi_0(\psi_1(\psi_1(\psi_0(\psi_1(\psi_1(0))))))=\omega^2\times2</math> * <math>\psi_0(\psi_1(\psi_1(\psi_1(0))))=\omega^3</math> * <math>\psi_0(\psi_1(\psi_1(\psi_1(\psi_1(0)))))=\omega^4</math> * <math>\psi_0(\psi_2(0))=\omega^\omega</math> * <math>\psi_0(\psi_2(\psi_0(\psi_2(0))))=\omega^\omega\times2</math> * <math>\psi_0(\psi_2(\psi_1(0)))=\omega^{\omega+1}</math> * <math>\psi_0(\psi_2(\psi_1(\psi_1(0))))=\omega^{\omega+2}</math> * <math>\psi_0(\psi_2(\psi_1(\psi_2(0))))=\omega^{\omega\times2}</math> * <math>\psi_0(\psi_2(\psi_1(\psi_2(\psi_1(\psi_2(0))))))=\omega^{\omega\times3}</math> * <math>\psi_0(\psi_2(\psi_2(0))=\omega^{\omega^2}</math> * <math>\psi_0(\psi_2(\psi_2(\psi_1(0)))=\omega^{\omega^2+1}</math> * <math>\psi_0(\psi_2(\psi_2(\psi_1(\psi_2(\psi_2(0)))))=\omega^{\omega^2\times2}</math> * <math>\psi_0(\psi_2(\psi_2(\psi_2(0))))=\omega^{\omega^3}</math> * <math>\psi_0(\psi_3(0))=\omega^{\omega^\omega}</math> * <math>\psi_0(\psi_3(\psi_1(0)))=\omega^{\omega^\omega+1}</math> * <math>\psi_0(\psi_3(\psi_2(0)))=\omega^{\omega^{\omega+1}}</math> * <math>\psi_0(\psi_3(\psi_3(0)))=\omega^{\omega^{\omega^2}}</math> * <math>\psi_0(\psi_4(0))=\omega^{\omega^{\omega^\omega}}</math> * <math>\psi_0(\psi_\omega(0))=\psi(0)</math> * <math>\psi_0(\psi_\omega(\psi_0(\psi_\omega(0))))=\psi(0)\times2</math> * <math>\psi_0(\psi_\omega(\psi_1(0)))=\omega^{\psi(0)+1}</math> * <math>\psi_0(\psi_\omega(\psi_1(\psi_2(0))))=\omega^{\psi(0)+\omega}</math> * <math>\psi_0(\psi_\omega(\psi_1(\psi_\omega(0))))=\omega^{\psi(0)\times2}</math> * <math>\psi_0(\psi_\omega(\psi_2(0)))=\omega^{\omega^{\psi(0)+1}}</math> * <math>\psi_0(\psi_\omega(\psi_2(\psi_\omega(0))))=\omega^{\omega^{\psi(0)\times2}}</math> * <math>\psi_0(\psi_\omega(\psi_\omega(0)))=\psi(1)</math> * <math>\psi_0(\psi_\omega(\psi_\omega(\psi_\omega(0))))=\psi(2)</math> * <math>\psi_0(\psi_{\omega+1}(0))=\psi(\omega)</math> * <math>\psi_0(\psi_{\omega+1}(\psi_\omega(0)))=\psi(\omega+1)</math> * <math>\psi_0(\psi_{\omega+1}(\psi_\omega(\psi_{\omega+1}(0))))=\psi(\omega\times2)</math> * <math>\psi_0(\psi_{\omega+1}(\psi_{\omega+1}(0)))=\psi(\omega^2)</math> * <math>\psi_0(\psi_{\omega+2}(0))=\psi(\omega^\omega)</math> * <math>\psi_0(\psi_{\omega+3}(0))=\psi(\omega^{\omega^\omega})</math> * <math>\psi_0(\psi_{\omega\times2}(0))=\psi(\psi(0))</math> * <math>\psi_0(\psi_{\omega\times2}(\psi_\omega(0)))=\psi(\psi(0)+1)</math> * <math>\psi_0(\psi_{\omega\times2}(\psi_\omega(\psi_{\omega\times2}(0))))=\psi(\psi(0)\times2)</math> * <math>\psi_0(\psi_{\omega\times2}(\psi_{\omega+1}(0)))=\psi(\omega^{\psi(0)+1})</math> * <math>\psi_0(\psi_{\omega\times2}(\psi_{\omega\times2}(0)))=\psi(\psi(1))</math> * <math>\psi_0(\psi_{\omega\times2+1}(0))=\psi(\psi(\omega))</math> * <math>\psi_0(\psi_{\omega\times3}(0))=\psi(\psi(\psi(0)))</math> * <math>\psi_0(\psi_{\omega^2}(0))=\psi(\Omega)</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega}(0)))=\psi(\Omega+1)</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega}(\psi_{\omega\times2}(0))))=\psi(\Omega+\psi(0))</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega}(\psi_{\omega^2}(0))))=\psi(\Omega+\psi(\Omega))</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega+1}(0)))=\psi(\Omega+\omega^{\psi(\Omega)+1})</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega\times2}(0)))=\psi(\Omega+\psi(\Omega+1))</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega\times3}(0)))=\psi(\Omega+\psi(\Omega+\psi(\Omega+1)))</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega^2}(0)))=\psi(\Omega\times2)</math> * <math>\psi_0(\psi_{\omega^2}(\psi_{\omega^2}(\psi_{\omega^2}(0))))=\psi(\Omega\times3)</math> * <math>\psi_0(\psi_{\omega^2+1}(0))=\psi(\Omega\times\omega)</math> * <math>\psi_0(\psi_{\omega^2+1}(\psi_{\omega^2}(0)))=\psi(\Omega\times\omega+\Omega)</math> * <math>\psi_0(\psi_{\omega^2+1}(\psi_{\omega^2}(\psi_{\omega^2+1}(0))))=\psi(\Omega\times\omega\times2)</math> * <math>\psi_0(\psi_{\omega^2+1}(\psi_{\omega^2+1}(0)))=\psi(\Omega\times\omega^2)</math> * <math>\psi_0(\psi_{\omega^2+2}(0))=\psi(\Omega\times\omega^\omega)</math> * <math>\psi_0(\psi_{\omega^2+\omega}(0))=\psi(\Omega\times\psi(0))</math> * <math>\psi_0(\psi_{\omega^2\times2}(0))=\psi(\Omega\times\psi(\Omega))</math> * <math>\psi_0(\psi_{\omega^3}(0))=\psi(\Omega^2)</math> * <math>\psi_0(\psi_{\omega^3}(\psi_{\omega}(0)))=\psi(\Omega^2+1)</math> * <math>\psi_0(\psi_{\omega^3}(\psi_{\omega^2}(0)))=\psi(\Omega^2+\Omega)</math> * <math>\psi_0(\psi_{\omega^3}(\psi_{\omega^2}(\psi_{\omega^3}(0))))=\psi(\Omega^2+\Omega\times\psi(\Omega^2))</math> * <math>\psi_0(\psi_{\omega^3}(\psi_{\omega^3}(0)))=\psi(\Omega^2\times2)</math> * <math>\psi_0(\psi_{\omega^3+1}(0))=\psi(\Omega^2\times\omega)</math> * <math>\psi_0(\psi_{\omega^3\times2}(0))=\psi(\Omega^2\times\psi(\Omega^2))</math> * <math>\psi_0(\psi_{\omega^4}(0))=\psi(\Omega^3)</math> * <math>\psi_0(\psi_{\omega^\omega}(0))=\psi(\Omega^\omega)</math> * <math>\psi_0(\psi_{\psi_0(\psi_\omega(0))}(0))=\psi(\Omega^{\psi(0)})</math> * <math>\psi_0(\psi_{\psi_0(\psi_{\omega^\omega}(0))}(0))=\psi(\Omega^{\psi(\Omega^\omega)})</math> * <math>\psi_0(\psi_{\psi_0(\psi_{\psi_0(\psi_\omega(0))}(0))}(0))=\psi(\Omega^{\psi(\Omega^{\psi(0)})})</math> * <math>\psi_0(\psi_{\psi_1(0)}(0))=\psi(\Omega^\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_0(\psi_{\psi_1(0)}(0))))=\psi(\Omega^\Omega)\times2</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(0)))=\omega^{\psi(\Omega^\Omega)+1}</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_\omega(0))))=\omega^{\psi(\Omega^\Omega)+\psi(0)}</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0))))=\omega^{\psi(\Omega^\Omega)\times2}</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0))))))=\omega^{\psi(\Omega^\Omega)\times3}</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_2(0)))))=\omega^{\omega^{\psi(\Omega^\Omega)+1}}</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_\omega(0)))))=\psi(\Omega^\Omega+1)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_\omega(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0))))))=\psi(\Omega^\Omega+\psi(\Omega^{\Omega}))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\omega\times2}(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0))))))=\psi(\Omega^\Omega+\psi(\Omega^{\Omega}+\psi(\Omega^\Omega)))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\omega^2}(0)))))=\psi(\Omega^\Omega+\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\omega^3}(0)))))=\psi(\Omega^\Omega+\Omega^2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0)))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_{\psi_0(\psi_{\psi_1(0)}(0)}(0))))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_0(0)))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_0(\psi_1(0))))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(0))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_0(\psi_{\psi_1(0)}(0))))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)}\times\psi(\Omega^\Omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_1(0)))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)+1})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0)))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)\times2})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(\psi_\omega(0))))}(0))))=\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega+1)})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(0))))=\psi(\Omega^\Omega\times2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(0))))))=\psi(\Omega^\Omega\times3)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(0)))=\psi(\Omega^\Omega\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_0(\psi_{\psi_1(0)}(0))}(0))))=\psi(\Omega^\Omega\times\psi(\Omega^\Omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(0))))=\psi(\Omega^{\Omega+1})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(0))))))=\psi(\Omega^{\Omega+1}+\Omega^\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(\psi_2(0)))))))=\psi(\Omega^{\Omega+1}+\Omega^\Omega\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(0))))))))=\psi(\Omega^{\Omega+1}\times2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(0))))))=\psi(\Omega^{\Omega+2})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_3(0)))=\psi(\Omega^{\Omega+\omega})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(0))))=\psi(\Omega^{\Omega\times2})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(0))))))=\psi(\Omega^{\Omega\times2+1})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(\psi_2(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(0))))))))=\psi(\Omega^{\Omega\times3})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(\psi_3(\psi_{\psi_1(0)}(0))))))=\psi(\Omega^{\Omega^2})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_4(0)))=\psi(\Omega^{\Omega^\omega})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_4(\psi_{\psi_1(0)}(0))))=\psi(\Omega^{\Omega^\Omega})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(0)))=\psi(\psi_1(0))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_1(\psi_{\psi_1(0)}(0)))))=\psi(\psi_1(0)+\Omega^\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_1(\psi_{\psi_1(0)}(\psi_\omega(0))))))=\psi(\psi_1(0)\times2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_2(0))))=\psi(\psi_1(0)\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_2(\psi_{\psi_1(0)}(0)))))=\psi(\Omega^{\psi_1(0)+1})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_2(\psi_{\psi_1(0)}(\psi_\omega(0))))))=\psi(\Omega^{\psi_1(0)\times2})</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_\omega(0))))=\psi(\psi_1(1))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_{\omega+1}(0))))=\psi(\psi_1(\omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_\omega(\psi_{\psi_1(0)}(0))))=\psi(\psi_1(\Omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega+1}(0)))=\psi(\psi_1(\Omega\times\omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega+1}(\psi_{\psi_1(0)}(0))))=\psi(\psi_1(\Omega^2))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega\times2}(0)))=\psi(\psi_1(\psi_1(0)))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(0)))=\psi(\Omega_2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_1(\psi_{\psi_1(0)}(\psi_{\omega^2}(0))))))=\psi(\Omega_2+\psi_1(\Omega_2))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_\omega(0))))=\psi(\Omega_2+\psi_1(\Omega_2+1))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_{\omega\times2}(0))))=\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2+1)))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_{\omega^2}(0))))=\psi(\Omega_2\times2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_{\omega^2+1}(0))))=\psi(\Omega_2\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2}(\psi_{\psi_1(0)}(0))))=\psi(\Omega_2\times\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2+\omega}(0)))=\psi(\Omega_2\times\psi_1(0))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^2\times2}(0)))=\psi(\Omega_2\times\psi_1(\Omega_2))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^3}(0)))=\psi({\Omega_2}^2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\omega^\omega}(0)))=\psi({\Omega_2}^\omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(0)))=\psi({\Omega_2}^\Omega)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(0))))))=\psi({\Omega_2}^\Omega+\psi_1({\Omega_2}^\Omega))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(\psi_{\omega}(0))))=\psi({\Omega_2}^\Omega+\psi_1({\Omega_2}^\Omega+1))</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(\psi_{\omega\times2}(0))))=\psi({\Omega_2}^\Omega+\Omega_2)</math> * <math>\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(0))))=\psi({\Omega_2}^\Omega\times2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_0(0))}(0))=\psi({\Omega_2}^\Omega\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(\psi_0(\psi_1(0)))}(0))=\psi({\Omega_2}^\Omega\times\psi(0))</math> * <math>\psi_0(\psi_{\psi_1(\psi_0(\psi_{\psi_1(0)}(\psi_\omega(0))))}(0))=\psi({\Omega_2}^\Omega\times\psi(\psi_1(0)))</math> * <math>\psi_0(\psi_{\psi_1(\psi_0(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(0))))}(0))=\psi({\Omega_2}^\Omega\times\psi({\Omega_2}^\Omega))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(0))=\psi({\Omega_2}^\Omega\times\Omega)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_1(\psi_{\psi_1(\psi_1(0))}(0))))=\psi({\Omega_2}^\Omega\times\Omega+\psi_1({\Omega_2}^\Omega\times\Omega))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_\omega(0)))=\psi({\Omega_2}^\Omega\times\Omega+\psi_1({\Omega_2}^\Omega\times\Omega+1))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\omega^2}(0)))=\psi({\Omega_2}^\Omega\times\Omega+\Omega_2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(0)}(0)))=\psi({\Omega_2}^\Omega\times\Omega+{\Omega_2}^\Omega)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(0)}(\psi_{\psi_1(\psi_1(0))}(0))))=\psi({\Omega_2}^\Omega\times\Omega\times2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_0(0))}(0)))=\psi({\Omega_2}^\Omega\times\Omega\times\omega)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_0(0))}(\psi_{\psi_1(\psi_1(0))}(0))))=\psi({\Omega_2}^\Omega\times\Omega^2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_0(\psi_1(0)))}(0)))=\psi({\Omega_2}^\Omega\times\psi_1(0))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_0(\psi_1(\psi_1(0))))}(0)))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(0)))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(0)}(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(0))))))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega)\times2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_0(\psi_1(0)))}(0))))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega+1))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(0))}(0))))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times2))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_0(0)))}(0))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\omega))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_1(0)))}(0))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\Omega))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_1(0)))}(\psi_{\psi_1(0)}(\psi_{\psi_1(\psi_1(\psi_1(0)))}(0))))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\Omega)\times2)</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_1(0)))}(\psi_{\psi_1(\psi_1(0))}(\psi_{\psi_1(\psi_1(\psi_1(0)))}(0))))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\Omega\times2))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_1(0)))}(\psi_{\psi_1(\psi_1(\psi_1(0)))}(0)))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega)))</math> * <math>\psi_0(\psi_{\psi_1(\psi_1(\psi_1(\psi_1(0))))}(0))=\psi({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\psi_1({\Omega_2}^\Omega\times\Omega)))</math> * <math>\psi_0(\psi_{\psi_1(\psi_2(0))}(0))=\psi({\Omega_2}^{\Omega+1})</math> * <math>\psi_0(\psi_{\psi_1(\psi_2(\psi_1(\psi_2(0))))}(0))=\psi({\Omega_2}^{\Omega+2})</math> * <math>\psi_0(\psi_{\psi_1(\psi_2(\psi_2(0)))}(0))=\psi({\Omega_2}^{\Omega+\omega})</math> * <math>\psi_0(\psi_{\psi_1(\psi_{\psi_1(0)}(0))}(0))=\psi({\Omega_2}^{\Omega\times2})</math> * <math>\psi_0(\psi_{\psi_1(\psi_{\psi_1(0)}(\psi_1(\psi_{\psi_1(0)}(0))))}(0))=\psi({\Omega_2}^{\Omega\times3})</math> * <math>\psi_0(\psi_{\psi_1(\psi_{\psi_1(0)}(\psi_\omega(0)))}(0))=\psi({\Omega_2}^{\psi_1(0)})</math> * <math>\psi_0(\psi_{\psi_1(\psi_{\psi_1(0)}(\psi_{\psi_1(0)}(0)))}(0))=\psi({\Omega_2}^{\psi_1({\Omega_2}^\Omega)})</math> * <math>\psi_0(\psi_{\psi_2(0)}(0))=\psi({\Omega_2}^{\Omega_2})</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_1(\psi_{\psi_2(0)}(0))))=\psi({\Omega_2}^{\Omega_2}+\psi_1({\Omega_2}^{\Omega_2}))</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(0)))=\psi({\Omega_2}^{\Omega_2}+\psi_1({\Omega_2}^{\Omega_2})\times\omega)</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(\psi_{\psi_1(\psi_{\psi_2(0)}(0))}(0))))=\psi({\Omega_2}^{\Omega_2}+\psi_1({\Omega_2}^{\Omega_2})^2)</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(\psi_{\psi_1(\psi_{\psi_2(0)}(0))}(\psi_\omega(0)))))=\psi({\Omega_2}^{\Omega_2}+\psi_1({\Omega_2}^{\Omega_2}+1))</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(\psi_{\psi_1(\psi_{\psi_2(0)}(0))}(\psi_{\omega^2}(0)))))=\psi({\Omega_2}^{\Omega_2}+\Omega_2)</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(\psi_{\psi_1(\psi_{\psi_2(0)}(0))}(\psi_{\psi_1(\psi_{\psi_2(0)}(0))}(0)))))=\psi({\Omega_2}^{\Omega_2}+\Omega_2^{\psi_1({\Omega_2}^{\Omega_2})})</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_2(\psi_{\psi_2(0)}(0))))=\psi({\Omega_2}^{\Omega_2}\times2)</math> * <math>\psi_0(\psi_{\psi_2(0)}(\psi_\omega(0)))=\psi(\psi_2(0))</math> * <math>\psi_0(\psi_{\psi_3(0)}(0))=\psi({\Omega_3}^{\Omega_3})</math> * <math>\psi_0(\psi_{\psi_3(0)}(\psi_\omega(0)))=\psi(\psi_3(0))</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(0))=\psi(\Omega_\omega)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_1(\psi_{\psi_\omega(0)}(0))))=\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_2(\psi_{\psi_\omega(0)}(0))))=\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_\omega(0)))=\psi(\Omega_\omega\times2)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_\omega(\psi_\omega(0))))=\psi(\Omega_\omega\times3)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_\omega(\psi_{\psi_1(0)}(0))))=\psi(\Omega_\omega\times\Omega)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_\omega(\psi_{\psi_\omega(0)}(0))))=\psi({\Omega_\omega}^2)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_\omega(\psi_{\psi_\omega(0)}(\psi_\omega(0)))))=\psi({\Omega_\omega}^2+\Omega_\omega)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_{\omega+1}(0)))=\psi({\Omega_\omega}^2\times\omega)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_{\omega+1}(\psi_{\psi_\omega(0)}(0))))=\psi({\Omega_\omega}^3)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_{\omega+2}(0)))=\psi({\Omega_\omega}^\omega)</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_{\omega+2}(\psi_{\psi_\omega(0)}(0))))=\psi({\Omega_\omega}^{\Omega_\omega})</math> * <math>\psi_0(\psi_{\psi_\omega(0)}(\psi_{\omega\times2}(0)))=\psi(\psi_\omega(0))</math> * <math>\psi_0(\psi_{\psi_{\omega+1}(0)}(0))=\psi({\Omega_{\omega+1}}^{\Omega_{\omega+1}})</math> * <math>\psi_0(\psi_{\psi_{\omega\times2}(0)}(0))=\psi({\Omega_{\omega\times2}})</math> * <math>\psi_0(\psi_{\psi_{\omega\times2}(0)}(\psi_\omega(0)))=\psi({\Omega_{\omega\times2}}+\Omega_\omega)</math> * <math>\psi_0(\psi_{\psi_{\omega\times2}(0)}(\psi_{\omega\times2}(0)))=\psi({\Omega_{\omega\times2}}\times2)</math> * <math>\psi_0(\psi_{\psi_{\omega\times2}(0)}(\psi_{\omega\times3}(0)))=\psi({\psi_{\omega\times2}}(0))</math> * <math>\psi_0(\psi_{\psi_{\omega^2}(0)}(0))=\psi(\Omega_{\omega^2})</math> * <math>\psi_0(\psi_{\psi_{\psi_1(0)}(0)}(0))=\psi(\Omega_\Omega)</math> * <math>\psi_0(\psi_{\psi_{\psi_2(0)}(0)}(0))=\psi(\Omega_{\Omega_2})</math> * <math>\psi_0(\psi_{\psi_{\psi_\omega(0)}(0)}(0))=\psi(\Omega_{\Omega_\omega})</math> * <math>\psi_0(\psi_{\psi_{\psi_{\psi_1(0)}(0)}(0)}(0))=\psi(\Omega_{\Omega_\Omega})</math> * <math>\color{red}{limit=\psi(\psi_I(0))}</math> == 参考资料 == <references />{{默认排序:序数记号}} [[分类:记号]] [[分类:分析]]
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