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  "body": "\n## Statement\n\nLet $A$ and $B$ be finite sets with $|A| \u003e |B|$, and let $f : A \\to B$ be a function.\nThen there are elements $a \\neq a'$ of $A$ with $f(a) = f(a')$.\nIn other words, $f$ is not injective.\n\n## Remarks\n\nIn the usual image, if $n + 1$ pigeons sit in $n$ holes, then some hole has at least two pigeons.\nExample: among any $13$ people, two have their birthdays in the same month.\nThe [[generalized pigeonhole principle|0BY7GN3449]] gives a fibre with more than $n$ elements. The [[infinite pigeonhole principle|0FS3RHF6KE]] is a version for infinite sets.\n\n## Explanations\n\n### L1 human\n\nIf there are more objects than boxes, some box has two objects.\nFor example, in any group of 367 people, two share a birthday, because a year has at most 366 days.\n",
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  "name": "Pigeonhole principle",
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