User blog comment:Wythagoras/FGH with transfinite ordinals/@comment-24509095-20140309141155/@comment-24509095-20140313120302

$$f_2(\omega2)=f_1^\omega(f_1^\omega(\omega2))=f_1^\omega(\omega^2)=\omega^3$$

$$f_2(\omega^3)=\omega^{\omega^2}$$

$$f_2(\omega^{\omega^2})=\omega^{\omega^{\omega^2}}$$

$$f_2^\omega(\omega2)=\varepsilon_0$$

$$f_2(\varepsilon_0)=\varepsilon_0^2$$

$$f_2(\varepsilon_0^2)=\varepsilon_0^{\varepsilon_0}$$

$$f_2(\varepsilon_0^{\varepsilon_0})=\varepsilon_0^{\varepsilon_0^{\varepsilon_0}}$$

$$f_2^\omega(\varepsilon_0)=\varepsilon_1$$