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  "body": "\n## Definition\n\nLet $D$ be a subset of $\\mathbb{R}$, let $f \\colon D \\to \\mathbb{R}$ be a function, and let $a$ be a [[limit point|07EGCNHAVW]] of $D$.\nA real number $L$ is the limit of $f$ at $a$ if the following holds.\nFor each open interval $V$ containing $L$ there is an open interval $U$ containing $a$ with $f(x) \\in V$ for all $x \\in U \\cap D$ with $x \\ne a$.\nThe notation is $\\lim_{x \\to a} f(x) = L$, or $f(x) \\to L$ as $x \\to a$.\n\n## Remarks\n\nThe value of $f$ at $a$ plays no role, and $a$ need not lie in $D$.\nThe [[epsilon-delta definition|0GBZDAFPX8]] states the same condition with numbers. The [[sequential characterization|000MXHEY22]] states it with sequences.\nThe limit is unique when it exists, since $a$ is a limit point of $D$.\nMathlib expresses limits with filters, as `Filter.Tendsto`.\n\n## Explanations\n\n### L1 human\n\nThe limit of $f$ at $a$ is the value that $f(x)$ approaches as $x$ comes close to $a$.\nOnly the values near $a$ matter, not the value at $a$ itself.\n",
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