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  "body": "\n## Statement\n\nLet $P(n)$ be a property of natural numbers $n$.\nSuppose that for each natural number $n$, if $P(k)$ holds for every natural number $k \u003c n$, then $P(n)$ holds.\nThen $P(n)$ holds for every natural number $n$.\n\n## Remarks\n\nThe hypothesis for $n = 0$ asks for a proof of $P(0)$ with no assumption, because no natural number is less than $0$.\nThe proof applies ordinary [[induction|0ASJVEFA9J]] to the property \"$P(k)$ holds for every $k \u003c n$\".\nA standard use is the proof that each integer $n \\ge 2$ is a product of primes.\n\n## Explanations\n\n### L1 human\n\nIn ordinary induction, you may use only the case just before $n$.\nIn strong induction, you may use all the cases before $n$.\nThis helps when $n$ breaks into smaller pieces that are not just $n - 1$, for example when $n = a b$ with $a$ and $b$ smaller than $n$.\n",
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