Proof by infinite descent is used, for example, to prove the irrationality of sqrt2. But can it be used also to prove that a property holds true for an infinite set? If so, is there an example?
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2Infinite descent is equivalent to the contrapositive of induction., so pick any indutive proof that shows that a property holds true for all naturals and rewrite it in contrapositive descent form. – Bill Dubuque Jun 08 '19 at 21:03
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1The irrationality of $\sqrt{2}$ is a property of an infinite set: it says that the infinite set $\Bbb{N} \times \Bbb{N}$ contains no member $(i, j)$ with $i^2 = 2j^2$. – Rob Arthan Jun 08 '19 at 21:47
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Excellent. Thank you both for your answers. – Julian Beauchamp Jun 09 '19 at 15:46