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  "body": "\n## Summary\n\nA successor order is a partial order with a successor map.\nThis map sends each non-maximal element to the least element strictly above it.\nIt abstracts the [[successor function|0AK9TGSNXY]] $n \\mapsto n + 1$ on the natural numbers.\nThe natural numbers, the integers, and every well-ordered set carry a successor order, while the rationals do not.\n\n## Explanations\n\n### L1 human\n\nIn the integers every number has a next number: after $n$ comes $n + 1$, and nothing lies strictly between them.\nA successor order is an order with such a \"next element\" map.\nIn the rationals there is no next number after $0$, since between $0$ and any positive rational there is another rational.\nSo the rationals have no successor order.\n",
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