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        "quote": "\n> [!definition] 朴素集合论的符号规则\n>\n> 1. 对任何常量或变量 $S$，“$S$ 是一个集合”是命题。\n> 2. 若 $P(x)$ 是命题，则 $\\{x\\mid P(x)\\}$ 是集合。\n> 3. 若 $S$ 是集合，$a\\in S$ 是命题，读作“$a$ 属于 $S$”。否定写作 $a\\notin S$。\n>\n> 对集合构造所作的朴素规定是\n>\n> $$\n> a\\in\\{x\\mid P(x)\\}\\Longleftrightarrow P(a).\n> $$\n>\n> 这些规则先规定合法的表达式；其中不受限制的集合构造会引出下面的<u class=\"concept-term\" data-concept-identity=\"urn:uuid:16a93206-68c6-4611-a639-0f12fe231a59\" data-concept-route=\"/concept-identities#concept-16a93206-68c6-4611-a639-0f12fe231a59\" id=\"first-a1a1dabeea070f314a31-zh\">罗素悖论(Russell&#x27;s paradox)</u>，不能直接当作现代公理集合论的完整体系。\n\n> [!definition] 外延公理\n>\n> 两个集合相等，当且仅当它们有完全相同的元素：\n>\n> $$\n> A=B\\Longleftrightarrow\\forall a\\,(a\\in A\\Longleftrightarrow a\\in B).\n> $$\n",
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