User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-5529393-20130627000838/@comment-5150073-20130628105438

But isn't it true that $$\Omega^2+\Omega$$ is a limit for $$\Omega^2+\alpha$$ for countable $$\alpha$$?

I wonder if arithmetic for uncountable ordinals is so different from countable ones. We know that (a*b)*c = ab+bc and by that, $$(\Omega^2+\Omega)*\Omega = \Omega^2*\Omega+\Omega*\Omega = \Omega^3+\Omega^2$$.