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  "body": "\n## Definition\n\nLet $f \\colon \\mathbb{R} \\to \\mathbb{R}$ be a function.\nThe function $f$ is even if $f(-x) = f(x)$ for all $x \\in \\mathbb{R}$.\nIt is odd if $f(-x) = -f(x)$ for all $x \\in \\mathbb{R}$.\n\n## Remarks\n\nThe graph of an even function is symmetric about the $y$-axis. The graph of an odd function is symmetric about the origin.\nFor example, $x^2$ and $\\cos x$ are even, and $x^3$ and $\\sin x$ are odd.\nEach function splits in a unique way into an even part and an odd part: $f(x) = \\frac{f(x) + f(-x)}{2} + \\frac{f(x) - f(-x)}{2}$.\nLeonhard Euler introduced the two notions in 1727. Mathlib defines even functions as `Function.Even`.\n\n## Explanations\n\n### L1 human\n\nAn even function takes the same value at $x$ and at $-x$.\nAn odd function takes opposite values at $x$ and at $-x$.\n",
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