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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$ be a set that is not bounded above, and let $f \\colon D \\to \\mathbb{R}$ be a function.\nA real number $L$ is the limit of $f$ at $+\\infty$ if for each $\\varepsilon \u003e 0$ there is $M$ with $|f(x) - L| \u003c \\varepsilon$ for all $x \\in D$ with $x \u003e M$.\nThe notation is $\\lim_{x \\to \\infty} f(x) = L$.\nThe limit at $-\\infty$ is defined in the same way, with $x \u003c M$.\n\n## Remarks\n\nA sequence is a function on $\\mathbb{N}$. For sequences this definition gives the [[limit of a sequence|0XKWSSY8P2]].\nFor example, $\\lim_{x \\to \\infty} 1/x = 0$.\nMathlib expresses $x \\to \\infty$ by the filter `Filter.atTop`.\n\n## Explanations\n\n### L1 human\n\nThe limit at infinity is the value that $f(x)$ approaches as $x$ grows without bound.\nThe graph then gets close to a horizontal line $y = L$.\n",
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