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  "body": "\n## Example\n\nLet $C_0 = [0, 1]$. For $n \\ge 0$, let $C_{n+1}$ be the set that we get from $C_n$ when we remove the open middle third of each of its closed intervals. Thus $C_1 = [0, \\tfrac{1}{3}] \\cup [\\tfrac{2}{3}, 1]$.\nThe Cantor set is $C = \\bigcap_{n \\ge 0} C_n$, with the subspace topology of $\\mathbb{R}$.\n\n## Remarks\n\nEquivalently, $C$ is the set of $x \\in [0, 1]$ that have a base-3 expansion $x = \\sum_{n \\ge 1} a_n 3^{-n}$ with all $a_n \\in \\{0, 2\\}$.\nThe set $C$ is [[closed|01VT24J1SD]] and bounded, so it is [[compact|07PFYV65MB]]. It is [[totally disconnected|01CYW8S04D]] and has no isolated points.\nIt is uncountable, and it is [[homeomorphic to the space of binary sequences|0RQ8DHHR8V]]. Its Lebesgue measure is $0$, because $C_n$ has total length $(2/3)^n$.\nThe Cantor set is [[nowhere dense|0KSM23SN3H]] in $\\mathbb{R}$.\n\n## Explanations\n\n### L1 human\n\nStart with $[0, 1]$, remove the middle third, then remove the middle third of each piece that is left, and go on forever.\nWhat remains is a set with no length, but with as many points as $\\mathbb{R}$.\n",
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