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  "body": "\n## Summary\n\nA proof by infinite descent shows that a statement has no solution in positive integers.\nIt assumes a solution, and from it constructs a strictly smaller solution in positive integers.\nThis gives an infinite decreasing sequence of positive integers, which is impossible.\n\n## Remarks\n\nThe method rests on the well-ordering of the natural numbers: each nonempty set of natural numbers has a least element.\nA classic use shows that $\\sqrt{2}$ is irrational: a solution of $a^2 = 2 b^2$ in positive integers gives a smaller one, $(2b - a, a - b)$.\nFermat used the method to prove [[Fermat's right triangle theorem|086BE0J3FZ]].\n\n## Explanations\n\n### L1 human\n\nYou cannot go down forever in the positive integers: you reach the bottom after finitely many steps.\nSo if each solution gives a smaller one, there can be no solution at all.\n",
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