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  "body": "\n## Definition\n\nA [[set|0SJ3RX9TXA]] $A$ is countable when there is an [[injective function|0PVG1CRAJN]] $f \\colon A \\to \\mathbb{N}$.\n\n## Remarks\n\nEquivalently, $A$ is [[finite|0BBTH3YSZA]] or [[countably infinite|0SEZ3JGZP7]].\nA nonempty set is countable exactly when there is a [[surjection|0XKH881BZ7]] from $\\mathbb{N}$ to it.\nSome authors use \"countable\" only for countably infinite sets, and \"at most countable\" for this notion.\nSubsets of countable sets are countable.\n\n## Explanations\n\n### L1 human\n\nA countable set is one that you can list: first element, second element, and so on.\nThe list may stop, or it may go on forever, but each element appears at some finite position.\n",
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