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 $s \equiv \langle s_{\alpha}| \alpha < \gamma\rangle$ is a tail sequence in β if there exists an ε < β such that s is a normal sequence assuming all values in $\beta \setminus \epsilon.$