User blog comment:B1mb0w/Fundamental Sequences/@comment-1605058-20151104112933/@comment-1605058-20151104153030

What does "expressing g in terms of limit ordinals" mean exactly? Is $$\omega^2$$ expressed like that? After all, $$2$$ is not a limit ordinal.

Is something like $$(\omega+\omega)^2$$ allowed?

I want to remark that I'm not actually asking these questions because I don't know what your answer will be. I'm asking them because this isn't specified in your definitions, and it has to be there.

Also note that you can't just "order the powers" in an expression. If you order $$\omega+\omega^2$$ into a decreasing sum as $$\omega^2+\omega$$, you are actually changing the ordinal (the former is equal to $$\omega^2$$, but the later isn't).

Lastly, $$(\omega+1)\omega\neq\omega^2+\omega$$, because multiplication is not right-distributive over addition for ordinals. In fact $$(\omega+1)\omega=\omega^2$$.