User blog comment:Edwin Shade/Negatively Indexed Epsilon Numbers/@comment-1605058-20171224230129/@comment-28606698-20171225142306

Strictly speaking, epsilon-numbers were introduced by Georg Cantor as ordinals $$\alpha$$ such that $$\alpha=\omega^\alpha$$ and I prefer this definition:

$$\varepsilon_\alpha=\text{min}\{\beta|\beta=\omega^\beta\wedge\forall\gamma<\alpha:\beta>\varepsilon_\gamma\}$$

So finite ordinals as well as $$\omega$$ can not be epsilon number.