质疑第一次数学危机的真相

Query the Truth of the First Mathematical Crisis

摘要: 目的:澄清第一次数学危机的真相。方法:揭示Pythagoras派关于√2不是有理数的证明是非有效的。结果:“α，β互素”是个不相干的假设，它误导人们做非有效推理，它应被更正为“α，β均为整数”。结论:第一次数学危机的真相是:第一对不可公度量的发现，并不是基于对√2不是有理数的有效证明，而是基于非有效证明。

Abstract: Purpose: The purpose is to clarify the truth of the first mathematical crisis. The method is to reveal that the proof of the Pythagoras School on √2 not a rational number is non-effective.The results show that “α and β as relatively primes” is an irrelevant assumption that misleads people to do the non-effective reasoning, which should be corrected to “α and β as integers”. Conclusions are obtained that the truth of the first mathematical crisis is that the first pair of immeasurable discoveries is not based on a valid proof that √2 is not a rational number but is based on a non-effective proof.