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  "body": "\n## Definition\n\nLet $A$ be a set and let $1 \\le k \\le n$ be integers.\nThe $k$-th $n$-ary *projection* on $A$ is the [[operation|EJ8YJVM9BW]] $\\pi^n_k \\colon A^n \\to A$ on the [[Cartesian power|09CEDJYBKP]] $A^n$ given by\n$$\\pi^n_k(a_1, \\dots, a_n) = a_k.$$\n\n## Remarks\n\nExample: on $A = \\Z$, the operation $\\pi^2_1(a, b) = a$ is a projection; it returns the first of its two arguments for every input.\nNon-example: on $\\Z$, the operation $(a, b) \\mapsto \\max(a, b)$ is not a projection, since $\\max(1, 0) = 1 \\ne 0$ rules out $\\pi^2_2$ and $\\max(0, 1) = 1 \\ne 0$ rules out $\\pi^2_1$.\nThe unary projection $\\pi^1_1$ is the identity map of $A$.\nIn any algebra with universe $A$, the term $x_k$, read as a term in the variables $x_1, \\dots, x_n$, has the term operation $\\pi^n_k$.\n",
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