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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$${\displaystyle \beta \setminus \epsilon .}$$