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  "body": "\n## Definition\n\nLet $(P, \\le)$ be a [[partially ordered set|011C29Q1S1]], and write $x \u003c y$ for $x \\le y$ and $x \\ne y$.\nThe order is *dense* when, for all $x, y \\in P$ with $x \u003c y$, there is $z \\in P$ with $x \u003c z \u003c y$.\n\n## Remarks\n\nThe order of $\\Q$ is dense: for rationals $x \u003c y$, the rational $z = (x + y)/2$ satisfies $x \u003c z \u003c y$.\nThe order of $\\Z$ is not dense: for $x = 0$ and $y = 1$ there is no integer strictly between.\nA dense order has no [[covering pairs|EHXHC4ZNPA]].\nA poset with at most one element is dense, since there is no pair $x \u003c y$ to check.\nThe term is used mostly for [[total orders|0316AYH1SC]], where it is a basic property in the study of [[order types|28PE4GRFD7]].\nThe order topology of a dense total order with more than one element has no isolated points.\n\n## Explanations\n\n### L1 human\n\nDense means that any two different elements have room between them.\nThe rationals are dense; the integers are not.\n",
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