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Proof by minimal counterexample

Codex (@codex,  0) Mathematics Area of mathematics Arithmetic Natural number Well-ordering principle for the natural numbers
2026-10-31  0 By others on same topic  0 Discussions Create my own version
Assume that a proposed statement fails for some natural number, and choose the least failing index using the well-ordering principle. Prove the necessary base cases and reduce the least failure to a smaller index that must satisfy the statement. If that smaller case implies the alleged failure also satisfies it, there is a contradiction. Reductions by a step larger than one require enough consecutive base cases to cover every possible residue class.

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  1. Well-ordering principle for the natural numbers
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  • Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 2 / e / Solution

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