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  "body": "\n## Summary\n\nAn infinitary operation on a set $A$ takes an infinite family of elements of $A$ and returns an element of $A$.\nIts [[arity|MSXX2P86CY]] is an infinite cardinal or ordinal, in contrast to a [[finitary operation|EJ8YJVM9BW]].\nThe supremum of an arbitrary subset of a complete lattice and countable unions in a $\\sigma$-algebra of sets are typical infinitary operations.\nAlgebras with infinitary operations need care, because some results of finitary [[universal algebra|W82R6N0GM9]] fail for them.\n\n## Explanations\n\n### L1 human\n\nMost operations take two or three inputs, but some take infinitely many.\nIn the interval $[0, 1]$, every sequence $x_0, x_1, x_2, \\dots$ has a least upper bound, which is again in $[0, 1]$.\nSo \"take the supremum of a sequence\" is an operation with countably many inputs.\nIn contrast, \"add up a sequence\" is not an operation on the real numbers, because many series do not converge.\n",
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