Cauchy Induction

Cauchy Induction is a beautiful method of Proof by Induction discovered by Augustin Louis Cauchy.

Definition

For a given statement $s$ over the positive integers greater than or equal to 2, the technique of Cauchy Induction is to prove that $s(2)$ is true, and that $s(n)$ implies $s(2n)$ . This implies that $S(2^m)$ is true for all positive $m$ . Then prove that $s(n)$ implies $s(n-1)$ . Then $s(n)$ is true for all $n\geq 2$ . This article is a stub. Help us out by expanding it.

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Cauchy Induction

Definition