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  "body": "\n## Summary\n\nA proof by contradiction proves a [[proposition|0ZGC7ZESYN]] $p$ in two steps.\nIt assumes $\\neg p$, and it gets a contradiction from this assumption, that is, a statement $q$ together with $\\neg q$.\nThen $\\neg p$ is false, so $p$ is true by the [[double negation law|0NFAGWH84K]].\n\n## Remarks\n\nAnother name is reductio ad absurdum.\nA classical example: $\\sqrt{2}$ is irrational. Assume $\\sqrt{2} = a/b$ in lowest terms. Then $a$ and $b$ are both even, which is a contradiction.\nThe last step uses classical logic. A proof of $\\neg p$ from a contradiction with $p$ is valid also in intuitionistic logic.\n\n## Explanations\n\n### L1 human\n\nTo show that something is true, suppose that it is false and follow the consequences.\nIf you reach an impossible situation, the supposition was wrong.\nSo the statement must be true.\n",
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