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