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

Here is my list of ordinals. It is supposed to show continuous beauty of their ascending.

\(0\) \(1\) \(2\) \(a\) \(\omega\) \(\omega+1\) \(\omega+2\) \(\omega+a\) \(\omega*2\) \(\omega*2+a\) \(\omega*3\) \(\omega*3+a\) \(\omega*4\) \(\omega^2\) \(\omega^2+1\) \(\omega^2+a\) \(\omega^2+\omega\) \(\omega^2+\omega+a\) \(\omega^2+\omega*2\) \(\omega^2+\omega*2+a\) \(\omega^2+\omega*3\) \(\omega^2+\omega*a+b\) \(\omega^2*2\) \(\omega^2*2+\omega*a+b\) \(\omega^2*3\) \(\omega^2*a+\omega*b+c\) \(\omega^3\) \(\omega^3*a+\omega^2*b+\omega*c+d\) \(\omega^4\) \(\omega^4*a+\omega^3*b+\omega^2*c+\omega*d+e\) \(\omega^5\) \(\omega^{a_1}*b_1+\omega^{a_2}*b_2+\omega^{a_3}*b_3+\cdots+\omega^{a_n}*b_n\) \(\omega^\omega\)