Proof by Exhaustion and Disproof by Counterexamples

The video tutorial covers two mathematical proof techniques: proof by exhaustion and disproof by counterexample. It begins with an explanation of proof by exhaustion, demonstrating it with examples such as identifying prime numbers between 10 and 20 and proving the absence of even perfect squares between 800 and 900. The tutorial also discusses the use of computers in proof by exhaustion, citing the four color theorem as an example. The second part introduces disproof by counterexample, illustrating how a single counterexample can invalidate a conjecture. Examples include disproving conjectures about mathematical expressions.

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