User blog comment:SuperJedi224/Question/@comment-5029411-20141124132603/@comment-4297047-20141126015955

Alright. Thanks.

Now, I know \(\underset{\alpha\rightarrow\omega^{-}}{lim}\varphi(1,\underset{\alpha}{\underbrace{0,0,...,0}})=\vartheta(\Omega^{\omega})\), but what about \(\underset{\alpha\rightarrow\omega^{-}}{lim}\varphi(\vartheta(\Omega^{\omega})+1,\underset{\alpha}{\underbrace{0,0,...,0}})\)? Would that be \(\vartheta(\Omega^{\omega}*2)\)?