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  "body": "\n## Statement\n\nLet $(a_n)$, $(b_n)$ and $(c_n)$ be real sequences and let $L$ be a real number.\nAssume that there is a natural number $N$ such that $a_n \\le c_n \\le b_n$ for all $n \\ge N$.\nAssume that $a_n \\to L$ and $b_n \\to L$ as $n \\to \\infty$.\nThen $c_n \\to L$ as $n \\to \\infty$.\n\n## Remarks\n\nThe theorem gives the existence of the limit of $(c_n)$. It does not assume it.\nFor example, $-1/n \\le \\sin(n)/n \\le 1/n$, so $\\sin(n)/n \\to 0$.\nThe same statement holds for the [[limit of a function|0TXTSEMHR5]] at a point.\nOther names are the sandwich theorem and, in some countries, the two policemen theorem.\n\n## Explanations\n\n### L1 human\n\nIf a sequence is trapped between two sequences that go to the same limit, it must go there too.\nFor large $n$, the upper and lower sequences are both close to $L$, and $c_n$ lies between them.\n",
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  "name": "Squeeze theorem",
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