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  "body": "\n## Definition\n\nLet $A$ be a set and let $A^3$ be the [[Cartesian product|09CEDJYBKP]] $A \\times A \\times A$.\nA *ternary operation* on $A$ is a [[finitary operation|EJ8YJVM9BW]] of arity $3$, that is, a [[function|0EPAT51DXQ]] $f \\colon A^3 \\to A$.\n\n## Remarks\n\nExample: on $\\R$, the map $m(x, y, z)$ that returns the middle value of $x, y, z$ is a ternary operation.\nIt is defined for every triple and its value is one of $x, y, z$, so it lies in $\\R$.\nIt satisfies $m(x, x, y) = m(x, y, x) = m(y, x, x) = x$.\n\nNon-example: the map $(x, y, z) \\mapsto x / (y - z)$ is not a ternary operation on $\\R$, because it is not defined when $y = z$.\n\nA ternary operation is usually written in prefix form $f(x, y, z)$, since there is no standard infix notation for three arguments.\n",
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