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  "body": "\n## Summary\n\nA many-one reduction from a set $A$ to a set $B$ of natural numbers is a total [[computable function|KZSB5E471K]] $f$ with $x \\in A$ exactly when $f(x) \\in B$.\nIt turns every question about membership in $A$ into one question about membership in $B$.\nMany-one reductions compare how hard decision problems are, and they are the standard tool for proving that a problem is undecidable.\n\n## Explanations\n\n### L1 human\n\nThink of $f$ as a translator: it rewrites each question about $A$ as a question about $B$ with the same answer.\nIf someone could answer questions about $B$, they could then answer questions about $A$.\nSo $A$ is at most as hard as $B$.\nFor example, the set of even numbers reduces to the set $\\set{0}$ by sending each even number to $0$ and each odd number to $1$.\n",
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