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  "body": "\n## Description\n\nThe empty set is the [[set|0SJ3RX9TXA]] that has no [[elements|0EZ758XE73]].\nIt is written $\\varnothing$ or $\\{\\}$.\nFor each object $x$, $x \\notin \\varnothing$.\nBy the [[axiom of extensionality|0TB16T2C97]], there is only one empty set.\n\n## Remarks\n\nThe empty set is a [[subset|0FE8Q5S42Y]] of every set. This is a case of [[vacuous truth|0V4QXPGJQK]].\nIts [[cardinality|0JTGRV4WT4]] is $0$.\nThe set $\\{\\varnothing\\}$ is not empty: it has one element.\n\n## Explanations\n\n### L1 human\n\nThe empty set is an empty bag.\nFor example, the set of real numbers $x$ with $x^2 = -1$ is empty.\nIt is useful in the same way that the number $0$ is useful.\n",
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        "what": "section Invariants",
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