Notes on proof by dichotomy

Laurent Fallot

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arXiv · 2310.04109

Notes on proof by dichotomy

Laurent Fallot

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Abstract

In this document we define a method of proof that we call proof by dichotomy. Its field of application is any proposition on the set of natural numbers N. It consists in the repetition of a step. A step proves the proposition for half of the members of an infinite subset U of N members for which we neither know if the proposition is verified nor not. We particularly study the case where the elements of U are separated by the parity of the quotient of euclidean division by 2 k. In such a case, we prove that if a natural n does not verify the proposition, then it is unique.

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BibTeX RIS

Laurent Fallot. 2023-10-06. Notes on proof by dichotomy. https://arxiv.org/abs/2310.04109

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