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