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  "body": "\n## Definition\n\nLet $A$ be a [[set|0SJ3RX9TXA]].\nThe identity function of $A$ is the [[function|0XHDTE5YMZ]] $\\mathrm{id}_A \\colon A \\to A$ with $\\mathrm{id}_A(a) = a$ for each $a \\in A$.\n\n## Remarks\n\nFor each function $f \\colon A \\to B$, $f \\circ \\mathrm{id}_A = f$ and $\\mathrm{id}_B \\circ f = f$. See [[function composition|07HF9YCWPP]].\nThe identity function is a [[bijection|0SNQEF7Z53]], and it is its own inverse.\nIts graph is the diagonal $\\{(a, a) \\mid a \\in A\\}$.\n\n## Explanations\n\n### L1 human\n\nThe identity function does nothing: each input comes out unchanged.\nIt plays the role for composition that the number $1$ plays for multiplication.\n",
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