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Proof by exhaustion, also referred to as proof by cases, proof by case analysis, complete induction or even the brute force process, is a means of mathematical proof where the assertion to become proved is split into a finite variety of cases or sets of equal cases, and where Every single style of case is checked to check out In the event the proposition in query retains.[1] This is a method of direct proof. A proof by exhaustion usually contains two stages:
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Other types of proofs—such as evidence by induction (mathematical induction)—are deemed more tasteful. On the other hand, there are a few significant theorems for which no other way of evidence has actually been discovered, such as
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