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  "body": "\n## Statement\n\nThe set $\\mathbb{Q}$ of rational numbers is [[countably infinite|0SEZ3JGZP7]].\n\n## Remarks\n\nProof: each rational number has a unique form $p/q$ with $p \\in \\mathbb{Z}$, $q \\ge 1$ and $\\gcd(p, q) = 1$. The map $p/q \\mapsto (p, q)$ is an injection into $\\mathbb{Z} \\times \\mathbb{N}$, which is countable. And $\\mathbb{Q}$ is infinite.\nThe rationals are dense in $\\mathbb{R}$, but they are countable, and $\\mathbb{R}$ is [[not countable|0518MM6BE1]].\n\n## Explanations\n\n### L1 human\n\nWrite the fractions $p/q$ in a grid, with $p$ along one side and $q$ along the other.\nList the grid diagonal by diagonal, and skip each fraction that is not in lowest terms.\nEach rational number appears exactly one time.\n",
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