Proof by Exhaustion

Proof by exhaustion, also called proof by cases, case analysis, complete induction, or the brute-force method, is a method of mathematical proof in which a statement is established by splitting the argument into several distinct cases and showing the statement holds in every case. Computers have greatly extended what this method can practically handle, most famously in the 1976 proof of the four color theorem, which checked a large but finite number of cases by machine. The approach works best when the number of cases is genuinely finite, so it is rarely usable for statements about infinitely many objects, and it is sometimes criticized as inelegant compared with a shorter, more conceptual proof. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/