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  "body": "\n## Definition\n\nLet $(A_i)_{i \\in I}$ be a [[family of sets|05Q6G4EH2G]].\nThe union of the family is the set\n$$\\bigcup_{i \\in I} A_i = \\{x \\mid \\exists i \\in I, \\, x \\in A_i\\}.$$\nSo $x$ is an element of the union when $x \\in A_i$ for at least one $i \\in I$.\n\n## Remarks\n\nFor $I = \\{1, 2\\}$, this is the [[union|07KVB4JSC7]] $A_1 \\cup A_2$.\nFor an empty index set, the union is the [[empty set|0ECVK59Y03]].\nExample: $\\bigcup_{n \\ge 1} [0, n] = [0, \\infty)$ in $\\mathbb{R}$.\n\n## Explanations\n\n### L1 human\n\nThe union of a family collects every element that appears in some member of the family.\nIt generalizes $A \\cup B$ from two sets to any number of sets.\n",
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