FANDOM


Normal ordinals

Catching function
\(\psi(\psi_I(0))\) \(C(\omega)\)
\(\psi(\psi_I(\psi_I(0)))\) \(C(\omega2)\)
\(\psi(\psi_I(I))\) \(C(\omega^2)\)
\(\psi(\psi_I(I^\omega))\) \(C(\omega^\omega)\)
\(\psi(\psi_I(I^{I\omega}))\) \(C(\omega^{\omega^2})\)
\(\psi(\psi_I(I^{I^\omega}))\) \(C(\omega^{\omega^\omega})\)
\(\psi(\psi_I(\varepsilon_{I+1}))\) \(C(\varepsilon_0)\)
\(\psi(\psi_I(\varepsilon_{I+\Omega_\omega}))\) \(C(\varepsilon_0+1)\)
\(\psi(\psi_I(\varepsilon_{I2}))\) \(C(\varepsilon_0\omega)\)
\(\psi(\psi_I(\varepsilon_{I2}\Omega_\omega))\) \(C(\varepsilon_0\omega+1)\)

Beyond \(C(\varepsilon_0\omega+1)\)

Thanks to Hyp cos I know the right value of \(C(\varepsilon_0\omega+1)\), now I can continue my blog post.

Normal ordinals Catching function
\(\psi(\psi_I(\varepsilon_{I2}\Omega_{\Omega_\omega}))\) \(C(\varepsilon_0\omega+2)\)
\(\psi(\psi_I(\varepsilon_{I2}\psi_I(0)))\) \(C(\varepsilon_0\omega+\omega)\)
\(\psi(\psi_I(\varepsilon_{I2}I))\) \(C(\varepsilon_0\omega^2)\)
\(\psi(\psi_I(\varepsilon_{I2}I^\omega))\) \(C(\varepsilon_0\omega^\omega)\)
\(\psi(\psi_I(\varepsilon_{I2}\varepsilon_{I+1}))\) \(C(\varepsilon_0^2)\)
\(\psi(\psi_I(\varepsilon_{I2}^\omega))\) \(C(\varepsilon_0^\omega)\)
\(\psi(\psi_I(\varepsilon_{I2+1}))\) \(C(\varepsilon_1)\)
\(\psi(\psi_I(\varepsilon_{I2+\Omega_\omega}))\) \(C(\varepsilon_1+1)\)
\(\psi(\psi_I(\varepsilon_{I3}))\) \(C(\varepsilon_2)\)
\(\psi(\psi_I(\varepsilon_{I\omega}))\) \(C(\varepsilon_\omega)\)
\(\psi(\psi_I(\varepsilon_{I^2}))\) \(C(\varepsilon_\omega\omega)\)
\(\psi(\psi_I(\varepsilon_{I^2+1}))\) \(C(\varepsilon_{\omega+1})\)
\(\psi(\psi_I(\varepsilon_{\varepsilon_{I+1}}))\) \(C(\varepsilon_{\varepsilon_0})\)
\(\psi(\psi_I(\zeta_{I+1}))\) \(C(\zeta_0)\)
\(\psi(\psi_I(\varphi(\omega,{I+1})))\) \(C(\varphi(\omega,0))\)
\(\psi(\psi_I(\Omega_{I+1}))\) \(C(\vartheta(\Omega))\)
\(\psi(\psi_I(\Omega_{I+\omega}))\) \(C(C(0))\)
\(\psi(\psi_I(\Omega_{I2}))\) \(C(C(0)\omega)\)
\(\psi(\psi_{I_2}(0))\) \(C(C(\omega))\)
\(\psi(\psi_{I_\omega}(0))\) \(C(\Omega)\)
\(\psi(\psi_{I_I}(I))\) \(C(\Omega+\psi_{I_\omega}(0)\omega^2)\)
\(\psi(\psi_{I_I}(I+1))\) \(C(\Omega+\psi_{I_\omega}(1))\)
\(\psi(\psi_{I_I}(I2))\) \(C(\Omega+\psi_{I_\omega}(1)\omega)\)
\(\psi(\psi_{I_I}(I\omega))\) \(C(\Omega+\psi_{I_\omega}(\omega))\)
\(\psi(\psi_{I_I}(I^2))\) \(C(\Omega+\psi_{I_\omega}(\omega)\omega)\)
\(\psi(\psi_{I_I}(I^I))\) \(C(\Omega+\psi_{I_\omega}(\omega^\omega)\omega)\)
\(\psi(\psi_{I_I}(\varepsilon_{I+1}))\) \(C(\Omega+\psi_{I_\omega}(\varepsilon_0))\)
\(\psi(\psi_{I_I}(\Omega_{I+1}))\) \(C(\Omega+\psi_{I_\omega}(\Omega))\)
\(\psi(\psi_{I_I}(I_2))\) \(C(\Omega+\psi_{I_\omega}(I))\)
\(\psi(\psi_{I_I}(I_\omega))\) \(C(\Omega+\psi_{I_\omega}(I_\omega))\)
\(\psi(\psi_{I_I}(I_I))\) \(C(\Omega+\psi_{I_\omega}(I_\omega)\omega)\)
\(\psi(\psi_{I_{I+1}}(0))\) \(C(\Omega+\psi_{I_{\omega+1}}(0))\)
\(\psi(\psi_{I_{I+\omega}}(0))\) \(C(\Omega+\psi_{I_{\omega2}}(0))\)
\(\psi(\psi_{I_{I2}}(0))\) \(C(\Omega+\psi_{I_{\omega2}}(0)\omega)\)
\(\psi(\psi_{I_{I2+1}}(0))\) \(C(\Omega+\psi_{I_{\omega2+1}}(0))\)
\(\psi(\psi_{I_{I^2+1}}(0))\) \(C(\Omega+\psi_{I_{\omega^2+1}}(0))\)
\(\psi(\psi_{I_{\varepsilon_{I+1}}}(0))\) \(C(\Omega+\psi_{I_{\varepsilon_0}}(0))\)
\(\psi(\psi_{I_{\Omega_{I+1}}}(0))\) \(C(\Omega+\psi_{I_{\Omega}}(0))\)
\(\psi(\psi_{I_{I_2}}(0))\) \(C(\Omega+\psi_{I_{I}}(0))\)
\(\psi(\psi_{I_{I_\omega}}(0))\) \(C(\Omega2)\)
\(\psi(\psi_{I_{I_{I_\omega}}}(0))\)

\(C(\Omega3)\)

\(\psi(\psi_{I(1,0)}(0))\) \(C(\Omega\omega)\)
\(\psi(\psi_{I(1,0)}(\Omega_\omega))\) \(C(\Omega\omega+1)\)
\(\psi(\psi_{I(1,0)}(I))\) \(C(\Omega\omega+\psi_{I(1,0)}(0)\omega)\)
\(\psi(\psi_{I(1,0)}(I(1,0)))\) \(C(\Omega(\omega+1))\)
\(\psi(\psi_{I(1,0)}(\varepsilon_{I(1,0)+1}))\) \(C(\Omega(\varepsilon_0))\)
\(\psi(\psi_{I(1,\omega)}(0))\) \(C(\Omega^2)\)
\(\psi(\psi_{I(2,0)}(0))\) \(C(\Omega^2\omega)\)
\(\psi(\psi_{I(3,0)}(0))\) \(C(\Omega^3\omega)\)
\(\psi(\psi_{I(\omega,0)}(0))\) \(C(\Omega^\omega)\)

Beyond linear arrays

Normal ordinals Catching function
\(\psi(\psi_{I(\omega,0)}(0))\) \(C(\Omega^\omega)\)
\(\psi(\psi_{I(1,0,0)}(0))\) \(C(\Omega^\omega\omega)\)
\(\psi(\psi_{I(1,0,\omega)}(0))\) \(C(\Omega^{\omega+1})\)
\(\psi(\psi_{I(1,1,\omega)}(0))\) \(C(\Omega^{\omega+2})\)
\(\psi(\psi_{I(1,\omega,0)}(0))\) \(C(\Omega^{\omega2})\)
\(\psi(\psi_{I(2,0,0)}(0))\) \(C(\Omega^{\omega2}\omega)\)
\(\psi(\psi_{I(\omega,0,0)}(0))\) \(C(\Omega^{\omega^2})\)
\(\psi(\psi_{I(1,0,0,0)}(0))\) \(C(\Omega^{\omega^2}\omega)\)
\(\psi(\psi_{\chi(M^\omega)}(0))\) \(C(\Omega^{\omega^\omega})\)
\(\psi(\psi_{\chi(M^M)}(0))\) \(C(\Omega^{\omega^\omega}\omega)\)
\(\psi(\psi_{\chi(\varepsilon_{M+1})}(0))\) \(C(\Omega^{\varepsilon_0})\)
\(\psi(\psi_{\chi(\Omega_{M+1})}(0))\) \(C(\Omega^{\Gamma_0})\)
\(\psi(\psi_{\chi(\Omega_{M+\omega})}(0))\)

\(C(\Omega^{C(0)})\)

\(\psi(\psi_{\chi(I_{M+1})}(0))\) \(C(\Omega^{C(\omega)})\)
\(\psi(\psi_{\chi(M_2)}(0))\) \(C(\Omega^{C(\Omega^\omega\omega)})\)
\(\psi(\psi_{\chi(M_3)}(0))\) \(C(\Omega^{C(\Omega^{C(\Omega^\omega\omega)})})\)
\(\psi(\psi_{\chi(M_\omega)}(0))\) \(C(\Omega^\Omega)\)

Beyond!

Normal ordinals Catching function
\(\psi(\psi_{\chi(M_\omega)}(0))\) \(C(\Omega^\Omega)\)
\(\psi(\psi_{\chi(M_{M_\omega})}(0))\) \(C(\Omega^{\Omega}2)\)
\(\psi(\psi_{\chi(M(1,0))}(0))\) \(C(\Omega^{\Omega}\omega)\)
\(\psi(\psi_{\chi(M(\omega,0))}(0))\) \(C(\Omega^{\Omega\omega})\)
\(\psi(\psi_{\chi(M(\Xi(3,0),0))}(0))\) \(C(\Omega^{\Omega\omega}\omega)\)
\(\psi(\psi_{\chi(M(\Xi(3,\omega),0))}(0))\) \(C(\Omega^{\Omega^2})\)
\(\psi(\Psi_{\Xi(\omega,0)}(0))\) \(C(\Omega^{\Omega^\omega})\)
\(\psi(\Psi_{\Xi(\Omega_\omega,0)}(0))\) \(C(\Omega^{\Omega^\omega}+1)\)
\(\psi(\Psi_{\Xi(\psi_{I_\omega}(0),0)}(0))\) \(C(\Omega^{\Omega^\omega}+\Omega)\)
\(\psi(\Psi_{\Xi(\Xi(\omega,0),0)}(0))\) \(C(\Omega^{\Omega^\omega}\omega)\)

\(\psi(\Psi_{\Xi(K,0)}(0))\)

\(C(\Omega^{\Omega^\omega}\omega^2)\)
\(\psi(\Psi_{\Xi(\varepsilon_{K+1},0)}(0))\) \(C(\Omega^{\Omega^\omega}\varepsilon_0)\)
\(\psi(\Psi_{\Xi(K_\omega,0)}(0))\) \(C(\Omega^{\Omega^\omega+1})\)

The limit of NAN in Dollar function and the limit of PNAN (R function) might be \(C(\varepsilon_{\Omega+1})\).

Ad blocker interference detected!


Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.