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  "body": "\n## Definition\n\nLet $A$ be a set and let $A^0 = \\set{()}$ be the set whose only element is the empty tuple $()$.\nA *nullary operation* on $A$ is a [[finitary operation|EJ8YJVM9BW]] of arity $0$, that is, a function $c \\colon A^0 \\to A$.\nThe element $c(()) \\in A$ is the *constant* given by $c$.\n\n## Remarks\n\nThe map $c \\mapsto c(())$ is a bijection from the set of nullary operations on $A$ to $A$.\nSo a nullary operation is usually written as an element of $A$.\n\nExample: in $(\\Z, +, 0)$ the constant $0$ is the nullary operation $c$ with $c(()) = 0$.\n\nNon-example: on the empty set there is no nullary operation, because a function from the one-element set $A^0$ to $\\emptyset$ does not exist.\nThis is why an algebra with a constant has a nonempty universe.\n",
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