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  "body": "\n## Definition\n\nLet $A$ be a set.\nA partition of $A$ is a set $P$ of [[subsets|0FE8Q5S42Y]] of $A$, called blocks, with these three properties:\n\n1. each block is nonempty;\n2. the blocks are pairwise [[disjoint|0W4RPA8QH3]];\n3. the union of the blocks is $A$.\n\nEquivalently, each element of $A$ is in exactly one block.\n\n## Remarks\n\nThe set $\\{\\{1, 3\\}, \\{2\\}\\}$ is a partition of $\\{1, 2, 3\\}$.\nThe even and the odd integers form a partition of $\\mathbb{Z}$ with two blocks.\nThe [[equivalence classes form a partition|01HT2CH8BH]], and each partition comes from exactly one equivalence relation. See [[the correspondence between equivalence relations and partitions|074482Q7CD]].\n\n## Explanations\n\n### L1 human\n\nA partition is a way to sort all elements into boxes.\nNo box is empty, and each element goes into exactly one box.\n",
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