Cauchy Induction
Cauchy Induction is a beautiful method of Proof by Induction discovered by Augustin Louis Cauchy.
Definition
For a given statement over the positive integers greater than or equal to 2, the technique of Cauchy Induction is to prove that
is true, and that
implies
. This implies that
is true for all positive
. Then prove that
implies
. Then
is true for all
.
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