FANDOM


TON (Taranovsky’s ordinal notation) will defined in here.

Up to \(\psi(\psi_I(1))\)

Let \(I\) will be \(\chi(0)\). TON vs further ordinals will begin here.

TON Ordinal
C(C(Ω2*2,0),0) \(\psi(\psi_I(0))\)
C(0,C(C(Ω2*2,0),0)) \(\psi(\psi_I(0))+1\)
C(1,C(C(Ω2*2,0),0)) \(\psi(\psi_I(0))+\omega\)
C(n,C(C(Ω2*2,0),0)) \(\psi(\psi_I(0))+\omega^n\)
C(Ω,C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+1)\)
C(Ω,C(Ω,C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+2)\)
C(C(0,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega)\)
C(C(0,C(0,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^2)\)
C(C(1,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^{\omega})\)
C(C(0,C(1,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^{\omega+1})\)
C(C(1,C(1,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^{\omega2})\)
C(C(2,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^{\omega^2})\)
C(C(n,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\omega^{\omega^n})\)
C(C(Ω,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega)\)
C(C(Ω,Ω),C(C(Ω,Ω),C(C(Ω2*2,0),0))) \(\psi(\psi_I(0)+\Omega2)\)
C(C(Ω,C(Ω,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^2)\)
C(C(C(Ω,Ω),Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^{\Omega})\)
C(C(C(Ω,Ω),C(C(Ω,Ω),Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^{\Omega2})\)
C(C(C(Ω,C(Ω,Ω)),Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^{\Omega^2})\)
C(C(C(C(Ω,Ω),Ω),Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^{\Omega^{\Omega}})\)
C(C(C(C(C(Ω,Ω),Ω),Ω),Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\Omega^{\Omega^{\Omega^{\Omega}}})\)
C(C(Ω2,Ω),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1})\)
C(C(Ω2,Ω),C(C(Ω2,Ω),C(C(Ω2*2,0),0))) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}*2)\)
C(C(0,C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}*\omega)\)
C(C(Ω,C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}*\Omega)\)
C(C(C(Ω,Ω),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}*\Omega^\Omega)\)
C(C(C(C(Ω2,Ω),Ω),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^2)\)
C(C(C(0,C(C(Ω2,Ω),Ω)),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^\omega)\)
C(C(C(Ω,C(C(Ω2,Ω),Ω)),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^\Omega)\)
C(C(C(C(Ω,Ω),C(C(Ω2,Ω),Ω)),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^{\Omega^\Omega})\)
C(C(C(C(C(Ω2,Ω),Ω),C(C(Ω2,Ω),Ω)),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^{\varepsilon_{\Omega+1}})\)
C(C(C(C(0,C(Ω2,Ω)),Ω),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^{\varepsilon_{\Omega+1}^\omega})\)
C(C(C(C(C(C(Ω2,Ω),Ω),C(Ω2,Ω)),Ω),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+1}^{\varepsilon_{\Omega+1}^{\varepsilon_{\Omega+1}}})\)
C(C(C(Ω2,Ω),C(Ω2,Ω)),C(C(Ω2*2,0),0)) \(\psi(\psi_I(0)+\varepsilon_{\Omega+2})\)

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.