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  "body": "\n## Summary\n\nIn mathematics, specifically in order theory, a [[binary relation|05AVARPXA2]] $\\,\\leq\\,$ on a [[vector space|000AYPA9AJ]] $X$ over the [[real|08J2M1JYAG]] or [[complex numbers|09FTAET5Z4]] is called **Archimedean** if for all $x \\in X,$ whenever there exists some $y \\in X$ such that $n x \\leq y$ for all positive integers $n,$ then necessarily $x \\leq 0.$ An **Archimedean (pre)ordered vector space** is a (pre)ordered vector space whose order is Archimedean. A preordered vector space $X$ is called **almost Archimedean** if for all $x \\in X,$ whenever there exists a $y \\in X$ such that $-n^{-1} y \\leq x \\leq n^{-1} y$ for all positive integers $n,$ then $x = 0.$\n",
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