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  "body": "\n## Definition\n\nLet $D \\subseteq \\mathbb{R}$ and let $f \\colon D \\to \\mathbb{R}$ be a function.\nThe function $f$ is strictly increasing if $f(x) \u003c f(y)$ for all $x, y \\in D$ with $x \u003c y$.\nIt is strictly decreasing if $f(x) \u003e f(y)$ for all $x, y \\in D$ with $x \u003c y$.\nIt is strictly monotone if it is strictly increasing or strictly decreasing.\n\n## Remarks\n\nWith $\\le$ and $\\ge$ in place of $\u003c$ and $\u003e$, we get increasing, decreasing, and monotone functions.\nA strictly monotone function is injective.\nFor example, $x^3$ is strictly increasing on $\\mathbb{R}$, and $x^2$ is strictly increasing on $[0, \\infty)$.\nMathlib defines strictly increasing maps as `StrictMono`.\n\n## Explanations\n\n### L1 human\n\nA strictly increasing function always goes up: a larger input gives a larger output.\nIts graph rises from left to right, with no flat parts.\n",
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