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  "body": "\n## Summary\n\nAn order is dense when between any two elements with $x \u003c y$ there is a third element $z$ with $x \u003c z \u003c y$.\nThe rational numbers and the real numbers are dense, while the integers are not.\nBy [[Cantor's isomorphism theorem|ABN5PTXEHY]], every countable dense total order without endpoints, and with at least one element, looks exactly like the rationals.\n\n## Explanations\n\n### L1 human\n\nIn a dense order there are no gaps of the \"next element\" kind: any two distinct elements have something strictly between them.\nBetween the fractions $1/3$ and $1/2$ lies their average $5/12$.\nBetween the integers $1$ and $2$ there is no integer, so the integers are not dense.\nRepeating the argument, between two rationals there are infinitely many rationals.\n",
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