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  "body": "\n## Definition\n\nLet $m$ and $n$ be [[integers|0C4JS9RF5M]].\nThe notation $m \\le n$ means that $n - m$ is a [[natural number|0MWKJ44V5A]], that is, when $n - m \\in \\{0, 1, 2, \\dots\\}$.\nThe notation $m \u003c n$ means that $m \\le n$ and $m \\neq n$.\n\n## Remarks\n\nThis relation is a total order on $\\mathbb{Z}$, and on $\\mathbb{N}$ it agrees with the [[order on the natural numbers|0Y9H52BT03]].\nIf $m \\le n$, then $m + k \\le n + k$ for each integer $k$. If $m \\le n$ and $0 \\le k$, then $m k \\le n k$.\nThus $\\mathbb{Z}$ is an ordered ring. Unlike $\\mathbb{N}$, it has no least element.\n\n## Explanations\n\n### L1 human\n\nOn the number line, $m \\le n$ means that $m$ is at the same place as $n$ or to the left of it.\nFor example, $-5 \\le -2$ because $-2 - (-5) = 3$ is a natural number.\n",
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