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  "body": "\n## Definition\n\nLet $A$ be a set.\nA well-order on $A$ is a [[total order|0316AYH1SC]] $\\le$ on $A$ such that each nonempty subset of $A$ has a [[least element|0T2NTJCV83]].\nThe pair $(A, \\le)$ is a well-ordered set.\n\n## Remarks\n\nThe usual order on $\\mathbb{N}$ is a well-order.\nThe usual orders on $\\mathbb{Z}$ and on $[0, 1]$ are not well-orders: $\\mathbb{Z}$ and $(0, 1]$ have no least element.\nA total order is a well-order exactly when its strict order $\u003c$ is [[well-founded|0230ECX1Q5]].\nThe [[well-ordering theorem|0N109NG5ZX]] says that each set has a well-order.\n\n## Explanations\n\n### L1 human\n\nIn a well-ordered set, each nonempty part has a first element.\nSo you can always say \"take the smallest element with this property\".\n",
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