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Sandwich theorem

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Not to be confused with the Ham Sandwich Theorem

Also known as the squeeze theorem

Suppose that $a_n, b_n, c_n$ are sequences such that $a_n, c_n$ converge to the same number $L$ and that $a_n \leq b_n \leq c_n$ for all $n$. Then $b_n$ also converges to $L$.

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