User blog:Clarrity/List of ordinals (up to omega^omega^omega)

Let P (polynomial) to be \(\omega^{a_n}*b_n+\omega^{a_{n-1}}*b_{n-1}+\cdots+\omega^2*b_2+\omega*b_1+b_0\).

\(\omega^\omega\) \(\omega^\omega+1\) \(\omega^\omega+P\) \(\omega^\omega*2\) \(\omega^\omega*2+P\) \(\omega^\omega*a+P\) \(\omega^{\omega+1}\) \(\omega^{\omega+1}*a+\omega^\omega*b+P\) \(\omega^{\omega+2}*a+\omega^{\omega+1}*b+\omega^\omega*c+P\) \(\omega^{\omega*2}\)

Let P_2 to be \(\omega^{\omega+a_n}*b_n+\omega^{\omega+a_{n-1}}*b_{n-1}+\cdots+\omega^{\omega+2}*b_2+\omega^{\omega+1}*b_1+\omega^\omega*b_0+P\). \(\omega^{\omega*2}+1\) \(\omega^{\omega*2}+P\) \(\omega^{\omega*2}+\omega^\omega\) \(\omega^{\omega*2}+P_2\) \(\omega^{\omega*2}*2\)

To be continued...