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  "body": "\n## Statement\n\nThe set $\\mathbb{R}$ of real numbers is [[uncountable|0X55M9XET4]].\n\n## Remarks\n\nCantor proved it in his article of 1874. That proof uses nested intervals.\nA later proof uses [[Cantor's diagonal argument|0XCH8QVDCQ]] on decimal or binary expansions.\nSince the algebraic numbers are countable, the result shows that transcendental numbers exist. Cantor gave this application in the same article.\n\n## Explanations\n\n### L1 human\n\nEach list of real numbers misses some real number.\nSo there are more real numbers than natural numbers, although both sets are infinite.\n",
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