To what the ordinal \(\phi(\Gamma_0,1)\) is equivalent in psi function? Ikosarakt1 (talk ^ contribs) 18:38, July 6, 2013 (UTC)
\(\phi(\Gamma_0,1)\) is the limit ordinal of \(\phi(\alpha,\Gamma_0+1) = \phi(\alpha,\phi(\Gamma_0,0)+1)\) as \(\alpha \rightarrow \Gamma_0\)
- \(\psi(\Omega^\Omega) = \Gamma_0\)
- \(\psi(\Omega^\Omega+1) = \varepsilon_{\Gamma_0+1}\)
- \(\psi(\Omega^\Omega+\Omega) = \phi(2,\Gamma_0+1)\)
- \(\psi(\Omega^\Omega+\Omega^2) = \phi(3,\Gamma_0+1)\)
- \(\psi(\Omega^\Omega+\Omega^\omega) = \phi(\omega,\Gamma_0+1)\)
- \(\psi(\Omega^\Omega+\Omega^{\varepsilon_0}) = \phi(\varepsilon_0,\Gamma_0+1)\)
- etc.
So I guess that \(\phi(\Gamma_0,1)\) is equivalent to \(\psi(\Omega^\Omega+\Omega^{\psi(\Omega^\Omega)})\). -- ☁ I want more clouds! ⛅ 00:15, July 7, 2013 (UTC)
- Correct! Deedlit11 (talk) 04:29, July 7, 2013 (UTC)
- Okay, thanks. Ikosarakt1 (talk ^ contribs) 19:48, July 7, 2013 (UTC)