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  "body": "\n## Summary\n\nMathematical induction is a method to prove that a property $P(n)$ holds for every [[natural number|0MWKJ44V5A]] $n$.\nA proof by induction has two steps.\nThe base case proves $P(0)$.\nThe induction step proves, for an arbitrary natural number $n$, that $P(n)$ implies $P(n + 1)$.\nThen $P(n)$ holds for every natural number $n$.\n\n## Remarks\n\nThe method is valid because of the induction axiom of the [[Peano axioms|0QFT7Z76N5]].\nIn the induction step, the assumption $P(n)$ is the induction hypothesis.\nCommon variants are [[induction from an arbitrary base case|0GF6AJEBZ0]] and [[strong induction|0KMVFSHFGZ]].\n\n## Explanations\n\n### L1 human\n\nThink of a line of dominoes that never ends.\nIf the first domino falls, and each falling domino knocks over the next one, then every domino falls.\nThe base case is the first domino, and the induction step is the rule that each domino knocks over the next one.\n",
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