User blog comment:Googleaarex/Unlimitable Ordinals/@comment-5029411-20130825150207/@comment-5150073-20130826085230

I must agree with LittlePeng, as the first limit of $$\alpha \mapsto \omega^\alpha$$ is $$\epsilon_0$$, the second is $$\epsilon_1$$, and $$1+\alpha$$-th is $$\epsilon_\alpha$$. So, the limit of limits is actually $$\zeta_0$$.