{
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  "body": "\n## Definition\n\nLet $f$ and $g$ be real functions defined on an interval $[x_0, \\infty)$.\nThe notation $f(x) = O(g(x))$ as $x \\to \\infty$ means that there are real numbers $C \u003e 0$ and $x_1 \\ge x_0$ with\n$$|f(x)| \\le C |g(x)| \\quad \\text{for all } x \\ge x_1.$$\n\n## Remarks\n\nThe same definition works as $x \\to a$, with $|x - a| \u003c \\delta$ in place of $x \\ge x_1$.\nIf $g(x) \\ne 0$ for large $x$, then $f = O(g)$ means that $f/g$ is bounded for large $x$.\nFor example, $3x^2 + 5x = O(x^2)$ as $x \\to \\infty$.\nMathlib defines it for filters, as `Asymptotics.IsBigO`.\n\n## Explanations\n\n### L1 human\n\nThe statement $f = O(g)$ says that $f$ grows at most as fast as $g$, up to a constant factor.\nIt ignores constant factors and small values of $x$.\n",
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