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  "body": "\n## Statement\n\nLet $(a_n)$ be a decreasing real sequence: $a_n \\ge a_{n+1}$ for all $n \\in \\mathbb{N}$.\nAssume that $(a_n)$ is bounded below.\nThen $(a_n)$ converges, and its limit is the infimum $\\inf \\{a_n : n \\in \\mathbb{N}\\}$.\n\n## Remarks\n\nThe proof applies the [[monotone convergence theorem|0FM6N4R0VB]] to the increasing sequence $(-a_n)$.\nFor example, $1/n$ decreases and is bounded below by $0$. Its limit is its infimum $0$.\nTogether, the two statements say that a monotone sequence converges if and only if it is bounded.\n\n## Explanations\n\n### L1 human\n\nA decreasing sequence that cannot pass a floor must settle down.\nIt settles at the highest floor, which is the infimum of its terms.\n",
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