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  "body": "\n## Statement\n\nLet $\\varepsilon$ be a real number with $\\varepsilon \u003e 0$.\nThen there is a natural number $n \\ge 1$ with $\\dfrac{1}{n} \u003c \\varepsilon$.\n\n## Remarks\n\nProof: since the [[reals are Archimedean|0A3GWZ86AY]], there is a natural number $n \u003e 1/\\varepsilon$. Then $n \\ge 1$ and $1/n \u003c \\varepsilon$.\nThus $\\inf \\{1/n : n \\ge 1\\} = 0$. There are no positive infinitely small real numbers.\nThe same holds in each Archimedean ordered field.\n\n## Explanations\n\n### L1 human\n\nThe fractions $1, 1/2, 1/3, \\dots$ get as small as you want.\nFor $\\varepsilon = 0.001$, the number $n = 1001$ works, because $1/1001 \u003c 0.001$.\n",
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