Proof by infinite descent
Summary
A proof by infinite descent shows that a statement has no solution in positive integers. It assumes a solution, and from it constructs a strictly smaller solution in positive integers. This gives an infinite decreasing sequence of positive integers, which is impossible.
Remarks
The method rests on the well-ordering of the natural numbers: each nonempty set of natural numbers has a least element. A classic use shows that is irrational: a solution of in positive integers gives a smaller one, . Fermat used the method to prove Fermat's right triangle theorem.
Where this leads
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Further reading
About this page
| Tag | 0EFYCFHYFG |
|---|---|
| URI | m2://0EFYCFHYFG |
| Aliases | infinite-descent, method-of-descent |
| Kind | concept |
| Writing | W0 stub |
| MSC | 11D99 |
| Specializes | Mathematical proof |
| Part of | Proof methods |
| Same as |
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