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  "body": "\n## Summary\n\nA subset $C$ of a preordered set $P$ is cofinal when every element of $P$ lies below some element of $C$.\nA cofinal subset reaches arbitrarily far up in $P$.\nFor example, $C$ and $P$ have the same upper bounds, so a supremum of $P$ can be computed from $C$ alone.\nThe least cardinality of a cofinal subset is the [[cofinality|BAWHE1W6MH]] of $P$.\n\n## Explanations\n\n### L1 human\n\nThink of $P$ as heights you can reach, and $C$ as a set of ladders.\nThe set $C$ is cofinal when, for any height, some ladder goes at least that high.\nIn the natural numbers, the even numbers are cofinal, and so are the powers of $2$.\nA finite set of natural numbers is never cofinal in $\\N$, because nothing in it is above its largest element plus one.\n",
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