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  "body": "\n## Definition\n\nLet $A$ and $B$ be sets and let $n \\ge 0$ be an integer.\nWrite $A^n$ for the [[Cartesian product|09CEDJYBKP]] of $n$ copies of $A$, the set of $n$-tuples of elements of $A$.\nHere $A^0$ is the set whose only element is the empty tuple.\n\n1. A [[function|0EPAT51DXQ]] $f \\colon A^n \\to B$ has *arity* $n$.\n2. A relation $R \\subseteq A^n$ has *arity* $n$.\n\nA function or relation of arity $n$ is called $n$-ary.\n\n## Remarks\n\nExample: the map $(x, y, z) \\mapsto x y + z$ from $\\R^3$ to $\\R$ has arity $3$, because its domain is $\\R^3$.\n\nNon-example: the map $\\R \\to \\R^2$, $x \\mapsto (x, x)$, has arity $1$ and not $2$, because the arity counts the factors of the domain, not of the codomain.\n\nThe arity of a function depends on how its domain is written as a power.\nA map on $\\R^2$ can be seen as a binary function on $\\R$ or as a unary function on the set $\\R^2$.\nThe words nullary, unary, binary and ternary are used for arities $0$, $1$, $2$ and $3$.\n",
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