Proof by exhaustion

Proof by exhaustion, also known as the brute force method or case analysis, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases, and each case is proved separately. A proof by exhaustion contains two stages:

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• A proof that the cases are exhaustive; i.e., that each instance of the statement to be proved matches the conditions of (at least) one of the cases.
• A proof of each of the cases.

In contrast, the method of exhaustion of Eudoxus of Cnidus was a geometrical and essentially rigorous way of calculating mathematical limits.

Related Topics:
Method of exhaustion - Eudoxus of Cnidus - Limit

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Proof by exhaustion: Example ►