User blog comment:Rgetar/Simple way to create lists of ordinals/@comment-37129238-20181007202038

If I am correct, according to your definition the single expansion of \(\omega, \zeta_0\) would proceed as follows:


 * 1) \(\omega, \varepsilon_0, \zeta_0\)
 * 2) \(\omega, \omega^{\omega}, \varepsilon_0, \zeta_0\)
 * 3) \(\omega, \omega^2, \omega^{\omega}, \varepsilon_0, \zeta_0\)
 * 4) \(\omega, \omega*2 \omega^2, \omega^{\omega}, \varepsilon_0, \zeta_0\)
 * 5) \(\omega, \omega+1, \omega*2, \omega^2, \omega^{\omega}, \varepsilon_0, \zeta_0\)

So would the double expansion of \(\omega, \zeta_0\) would be the collective single expansions of \(\omega, \omega+1\), \(\omega+1, \omega*2\), \(\omega*2, \omega^2\), \(\omega^2, \omega^{\omega}\), \(\omega^{\omega}, \varepsilon_0\), and \(\varepsilon_0, \zeta_0\)?