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  "body": "\n## Definition\n\nIn a given context, fix a [[set|0SJ3RX9TXA]] $U$ such that all the sets under discussion are [[subsets|0FE8Q5S42Y]] of $U$.\nThe set $U$ is then the universal set, or the universe of discourse, of the context.\n\n## Remarks\n\nIn elementary number theory, $U$ can be the set $\\mathbb{Z}$ of integers.\nThe [[complement|0B1FSS1VZW]] of a set is taken relative to the universal set.\nIn [[Zermelo–Fraenkel set theory|0HE5WDQ9FJ]], no set contains all sets. This is a consequence of [[Russell's paradox|0HESMMSYEG]].\n\n## Explanations\n\n### L1 human\n\nThe universal set is the \"whole world\" of a problem.\nIn a problem about real numbers, it is $\\mathbb{R}$.\nIn a [[Venn diagram|0KCT6DPXJK]], it is the rectangle that contains all the circles.\n",
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