Suppose $\{a_n\}$, $\{b_n\}$ are sequences in $\mathbb R$. Suppose $a_n\geq b_n$ and $\{b_n\}$ converges to $b$. Can we conclude that $\liminf a_n\geq b$. What if we further assume $\{a_n\}$ is bounded below?
2026-04-02 22:40:29.1775169629
If $a_n \geq b_n$ and $b_n$ converges to $b$ then $\liminf a_n\geq b$
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