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  "body": "\n## Statement\n\nFor each positive integer $n$, let $S_n$ be a statement that is either true or false.\nSuppose that $S_1$ is true.\nSuppose also that for every positive integer $k$, the truth of $S_k$ forces the truth of $S_{k+1}$.\nThen $S_n$ is true for every positive integer $n$.\n\n## Remarks\n\nThis is the form of [[induction|0ASJVEFA9J]] that starts at $1$.\nThe proof of $S_1$ is the base case.\nThe proof that $S_k$ implies $S_{k+1}$ is the induction step, and the assumption $S_k$ is the induction hypothesis.\n",
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        "url": "https://github.com/mitchkeller/applied-combinatorics/blob/ebd95d6bd59e23c633c65cf560bcb93efa912aae/source/s_induction_induction.ptx#L32"
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  "name": "Principle of mathematical induction for positive integers",
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