Order type epsilon naught

Epsilon naught is a countable ordinal number equal to the union of all ordinals that can be expressed in Cantor normal form; that is, the set of ordinals containing zero and omega that is closed under ordinal succession, addition, multiplication, and exponentiation.

It is also the smallest epsilon number, which is an ordinal that satisfies $$\epsilon = \omega^\epsilon$$.

Limit Ordinal
Epsilon nought is a limit ordinal, with one of the expressions that produces it being $$ \omega \cup \omega^{\omega} \cup \omega^{\omega^{\omega}} \cup \omega^{\omega^{\omega^\omega}}, \dots$$.