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  "body": "\n## Definition\n\nAn [[ordered field|010JCV9J4E]] $F$ is Archimedean when, for all $x$ and $y$ in $F$ with $y \u003e 0$, there is a natural number $n$ with $n y \u003e x$.\nHere $n y$ means $y + y + \\dots + y$, with $n$ terms.\n\n## Remarks\n\nWith $y = 1$, the definition gives the [[Archimedean property|0A74SX55QP]]: for each $x$, some natural number exceeds $x$. Conversely, this property implies the definition.\nAn equivalent condition: for each $\\varepsilon \u003e 0$ in $F$, there is a natural number $n \\ge 1$ with $1/n \u003c \\varepsilon$.\nThe field of rational functions $\\mathbb{R}(t)$, with the order in which $t$ is larger than every real number, is not Archimedean.\n\n## Explanations\n\n### L1 human\n\nYou can reach any distance with enough small steps of a fixed size.\nIn an Archimedean field there is no number so large that no multiple of a given positive number can pass it.\n",
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