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  "body": "\n## Statement\n\nLet $D \\subseteq \\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$, let $a$ be a limit point of $D$, and let $L$ be a real number.\nThen $\\lim_{x \\to a} f(x) = L$ if and only if the following holds.\nFor each sequence $(x_n)$ in $D \\setminus \\{a\\}$ with $x_n \\to a$, $f(x_n) \\to L$.\n\n## Remarks\n\nThis turns facts about [[limits of sequences|0XKWSSY8P2]] into facts about limits of functions. Examples are the limit laws for sums, products, and quotients.\nIt is also a tool to show that a limit does not exist. Find two sequences tending to $a$ whose images have different limits.\nMathlib states a general form as `tendsto_nhds_iff_seq_tendsto`.\n\n## Explanations\n\n### L1 human\n\nThe function has limit $L$ at $a$ exactly when it sends every sequence approaching $a$ to a sequence approaching $L$.\nSo limits of functions reduce to limits of sequences.\n",
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