Tail sequence

In mathematics, specifically set theory, a tail sequence is an unbounded sequence of contiguous ordinals. Formally, let β be a limit ordinal. Then a γ-sequence [math]\displaystyle{ s \equiv \langle s_{\alpha}| \alpha \lt  \gamma\rangle }[/math] is a tail sequence in β if there exists an ε < β such that s is a normal sequence assuming all values in [math]\displaystyle{ \beta \setminus \epsilon. }[/math]