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  "body": "\n## Summary\n\nA finitary operation on a set $A$ takes $n$ elements of $A$ and returns an element of $A$, for a fixed natural number $n$.\nThe number $n$ is its [[arity|MSXX2P86CY]].\n[[Binary operations|0M418FE7BB]] such as addition are the most common case, but [[unary|Q2W26ZY10B]], [[nullary|9HPF7TE18C]] and [[ternary|WC47MFR6GW]] operations also occur.\n[[Algebraic structures|QJGPT2W0FT]] are sets equipped with finitary operations.\n\n## Explanations\n\n### L1 human\n\nAn operation is a rule that turns some elements of a set into one element of the same set.\n\"Finitary\" means that the number of inputs is a fixed natural number.\nOn the integers, $x \\mapsto -x$ uses one input, $(x, y) \\mapsto x + y$ uses two, and $(x, y, z) \\mapsto x - y + z$ uses three.\nThe result must stay inside the set: subtraction is an operation on the integers but not on the natural numbers.\nOperations with infinitely many inputs are called [[infinitary|WFVC137TYB]].\n",
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