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It’s because you can’t create square root of two with a fraction. Pythagoreans were all about fractions (such as their musical tuning).


That's not an argument, that's a restatement of the problem; that's what being irrational means. The problem is to prove that you can't create sqrt(2) with a fraction. How, exactly, would this statement have been obvious to the Pythagoreans? Can you give me an argument for this that they would have found obvious? One that uses the Pythagorean theorem even, perhaps, since you brought that up? Remember, no using concepts they wouldn't have had like prime factorization!




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