User blog comment:B1mb0w/From omega to epsilon nought/@comment-1605058-20150630080915

A technical mistake you are making (and I'm pretty sure you are aware of it, but it's never bad to point that out): You are writing equalities like $$\omega.3=\omega^2$$ as if this was equality of ordinals, which it of course isn't.

Onto real mistakes: in section "$$\omega^{\omega^2+\omega.2}$$ to $$\omega^{\omega^2.2}$$..." you write $$\omega^{\omega^2+\omega.2}.\omega = \omega^{\omega^2+\omega.3}$$ which is wrong, RHS should be $$\omega^{\omega^2+\omega.2+1}$$.

In last section, you seem to not have noticed that $$\omega^{\omega^2.2+2}.\omega=\omega^{\omega^2.2+3}=\omega^{\omega^2.2+\omega}$$.