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  "body": "\n## Summary\n\nA locally finite poset is a [[partially ordered set|0QV2JS9RJ3]] in which every closed interval $[x, y] = \\set{z : x \\le z \\le y}$ is finite.\nThis is the condition under which the [[incidence algebra|1H9SFWHYEB]] and the Möbius function of the poset are defined.\nMost posets of enumerative combinatorics are locally finite, even when they are infinite.\n\n## Explanations\n\n### L1 human\n\nA poset may be infinite, but you can ask that between any two comparable elements there are only finitely many others.\nThe integers satisfy this: between $3$ and $10$ there are eight integers.\nThe positive integers ordered by divisibility satisfy it too: between $2$ and $12$ lie only the divisors of $12$ that are multiples of $2$.\nThe rationals fail: between $0$ and $1$ there are infinitely many.\n",
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