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  "body": "\n## Definition\n\nLet $X$ be a set and let $A$ be a [[subset|0FE8Q5S42Y]] of $X$.\nThe indicator function of $A$ is the [[function|0XHDTE5YMZ]] $\\mathbf{1}_A \\colon X \\to \\{0, 1\\}$ with\n$$\\mathbf{1}_A(x) = \\begin{cases} 1 \u0026 \\text{if } x \\in A, \\\\ 0 \u0026 \\text{if } x \\notin A. \\end{cases}$$\n\n## Remarks\n\nOther names are characteristic function and the notation $\\chi_A$.\nFor subsets $A$ and $B$ of $X$, $\\mathbf{1}_{A \\cap B} = \\mathbf{1}_A \\mathbf{1}_B$ and $\\mathbf{1}_{A^c} = 1 - \\mathbf{1}_A$.\nThe map $A \\mapsto \\mathbf{1}_A$ is a [[bijection|0SNQEF7Z53]] from the [[power set|0BC7KX51Z8]] of $X$ to the set of functions from $X$ to $\\{0, 1\\}$.\n\n## Explanations\n\n### L1 human\n\nThe indicator function answers \"is $x$ in $A$?\" with $1$ for yes and $0$ for no.\nFor $A$ the even integers, $\\mathbf{1}_A(4) = 1$ and $\\mathbf{1}_A(5) = 0$.\n",
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        "what": "an inventory row",
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