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  "body": "\n## Definition\n\nLet $X$ be a [[topological space|0CNQXVBHCX]] and let $D \\subseteq X$.\nThe set $D$ is dense in $X$ when its [[closure|0DRKT1QJR7]] is $X$, that is, $\\overline{D} = X$.\n\n## Remarks\n\nEquivalently, $D$ is dense if and only if $D$ meets each nonempty open set of $X$.\nIn a metric space, $D$ is dense if and only if for each $x \\in X$ and each $\\varepsilon \u003e 0$ there is $y \\in D$ with $d(x, y) \u003c \\varepsilon$.\nThe rationals $\\mathbb{Q}$ are dense in $\\mathbb{R}$: this is the [[density of the rationals|0STX0WRDNG]]. The irrationals are also dense in $\\mathbb{R}$.\n\n## Explanations\n\n### L1 human\n\nA dense set has points everywhere in the space: near each point of the space there are points of the dense set.\nEach real number has rational numbers as close to it as you want.\n",
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