SGH与FGH对照

本条目展示SGH与FGH的对照

$g_{{\epsilon }_0\times 2}(n)=g_{{\epsilon }_0+{\epsilon }_0[n]}(n)=(n\uparrow \uparrow n)\times 2$

$g_{{\epsilon }_0\times \omega }(n)=g_{{\epsilon }_0\times n}(n)=(n\uparrow \uparrow n)\times n$

$g_{{\epsilon }_0\times {\omega }^2}(n)=g_{{\epsilon }_0\times \omega \times n}(n)=(n\uparrow \uparrow n)\times n^2$

$g_{{\epsilon }_0\times {\omega }^{\omega }}(n)=g_{{\epsilon }_0\times {\omega }^n}(n)=(n\uparrow \uparrow n)\times n^n$

$g_{{\epsilon }_0\times {\omega }^{{\omega }^{\omega }}}(n)=(n\uparrow \uparrow n)\times (n\uparrow \uparrow 3)$

$g_{{\epsilon }_0^2}(n)=g_{{\epsilon }_0\times {\epsilon }_0[n]}(n)=(n\uparrow \uparrow n{)}^2$

$g_{{\epsilon }_0^3}(n)=(n\uparrow \uparrow n{)}^3$

$g_{{\epsilon }_0^{\omega }}(n)=g_{{\epsilon }_0^n}(n)=(n\uparrow \uparrow n{)}^n$

$g_{{\epsilon }_0^{{\omega }^{\omega }}}(n)=(n\uparrow \uparrow n{)}^{n^n}$

$g_{{\epsilon }_0^{{\epsilon }_0}}(n)=(n\uparrow \uparrow n{)}^{n\uparrow \uparrow n}=(n\uparrow \uparrow n)\uparrow \uparrow 2$

$g_{{\epsilon }_0^{{\epsilon }_0^{{\epsilon }_0}}}(n)=(n\uparrow \uparrow n)\uparrow \uparrow 3$

$g_{{\epsilon }_1}(n)=(n\uparrow \uparrow n)\uparrow \uparrow n\approx n\uparrow \uparrow (n\times 2)$

$g_{{\epsilon }_2}(n)=((n\uparrow \uparrow n)\uparrow \uparrow n)\uparrow \uparrow n\approx n\uparrow \uparrow (n\times 3)$

$n\uparrow \uparrow (n\times 3)\sim {\epsilon }_2$

$n\uparrow \uparrow (n\times 3+1)\sim {\epsilon }_2^{{\epsilon }_2}$

$n\uparrow \uparrow (n\times 3+2)\sim {\epsilon }_2^{{\epsilon }_2^{{\epsilon }_2}}$

$n\uparrow \uparrow (n\times 4)\sim {\epsilon }_3$

$n\uparrow \uparrow (n\times 5)\sim {\epsilon }_4$

\begin{align} & n\uparrow\uparrow(n^2)\sim\varepsilon_\omega\\ &n\uparrow\uparrow(n^2+1)\sim\varepsilon_\omega^{\varepsilon_\omega}\\&n\uparrow\uparrow(n^2+n)\sim\varepsilon_{\omega+1}\\&n\uparrow\uparrow(n^2\times2)\sim\varepsilon_{\omega\times2}\\&n\uparrow\uparrow(n^3)\sim\varepsilon_{\omega^2}\\&n\uparrow\uparrow(n^n)=n\uparrow\uparrow n\uparrow\uparrow2\sim\varepsilon_{\omega^\omega}\\&n\uparrow\uparrow(n^n+n)\sim\varepsilon_{\omega^\omega+1}\\&n\uparrow\uparrow(n^{n+1})\sim\varepsilon_{\omega^{\omega+1}}\\&n\uparrow\uparrow(n^{n^2})\sim\varepsilon_{\omega^{\omega^2}}\\&n\uparrow\uparrow n\uparrow\uparrow3\sim\varepsilon_{\omega^{\omega^\omega}}\\&n\uparrow\uparrow n\uparrow\uparrow n=n\uparrow\uparrow\uparrow 3\sim\varepsilon_{\varepsilon_0}\\&n\uparrow\uparrow (n\uparrow\uparrow n+n)\sim\varepsilon_{\varepsilon_0+1}\\&n\uparrow\uparrow ((n\uparrow\uparrow n)\times2)\sim\varepsilon_{\varepsilon_0\times2}\\&n\uparrow\uparrow ((n\uparrow\uparrow n)\uparrow\uparrow 2)\approx n\uparrow\uparrow n\uparrow\uparrow(n+1)\sim\varepsilon_{\varepsilon_0^{\varepsilon_0}}\\&n\uparrow\uparrow n\uparrow\uparrow(n\times2)\sim\varepsilon_{\varepsilon_1}\\&n\uparrow\uparrow n\uparrow\uparrow(n^2)\sim\varepsilon_{\varepsilon_\omega}\\&n\uparrow\uparrow n\uparrow\uparrow n\uparrow\uparrow n=n\uparrow\uparrow\uparrow4\sim\varepsilon_{\varepsilon_{\varepsilon_0}}\\&n\uparrow\uparrow\uparrow n\sim\zeta_0\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow n\sim\varepsilon_{\zeta_0+1}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\times2)\sim\varepsilon_{\zeta_0+2}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow n)\sim\varepsilon_{\zeta_0+\varepsilon_0}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\approx n\uparrow\uparrow\uparrow(n+1)\sim\varepsilon_{\zeta_0\times2}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\uparrow\uparrow n\sim\varepsilon_{\varepsilon_{\zeta_0+1}}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\sim\varepsilon_{\varepsilon_{\zeta_0\times2}}\\&(n\uparrow\uparrow\uparrow n)\uparrow\uparrow \uparrow n\approx n\uparrow\uparrow\uparrow(n\times2)\sim\zeta_1\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow n\sim\varepsilon_{\zeta_1+1}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow (n\uparrow\uparrow\uparrow n)\sim\varepsilon_{\zeta_1+\zeta_0}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow (n\uparrow\uparrow\uparrow(n\times2))\sim\varepsilon_{\zeta_1\times2}\\&(n\uparrow\uparrow\uparrow(n\times2))\uparrow\uparrow \uparrow n\approx n\uparrow\uparrow\uparrow(n\times3)\sim\zeta_2\\&n\uparrow\uparrow\uparrow(n^2)\sim\zeta_\omega\\&n\uparrow\uparrow\uparrow(n^n)\sim\zeta_{\omega^\omega}\\&n\uparrow\uparrow\uparrow(n\uparrow\uparrow n)\sim\zeta_{\varepsilon_0}\\&n\uparrow\uparrow\uparrow n\uparrow\uparrow\uparrow n \sim\zeta_{\zeta_0}\\&n\uparrow\uparrow\uparrow\uparrow n \sim\eta_0\\&(n\uparrow\uparrow\uparrow\uparrow n)\uparrow\uparrow\uparrow n \sim\zeta_{\eta_0+1}\\&n\uparrow\uparrow\uparrow\uparrow (n\times2) \sim\eta_1\\&n\uparrow^53 \sim\eta_{\eta_0}\\&n\uparrow^5n \sim\varphi(4,0)\\&n\uparrow^5(n\times2) \sim\varphi(4,1)\\&n\uparrow^6 n \sim\varphi(5,0)\\&n\uparrow^n n \sim\varphi(\omega,0)\\ \end{align}