ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D1270
Eventually constant sequence
Formulation 0
A D62: Sequence $x : \mathbb{N} \to X$ is eventually constant if and only if \begin{equation} \exists \, a \in X : \exists \, N \in \mathbb{N} : \forall \, n \geq N : x_n = a \end{equation}