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.
参考文献
[1]
|
[美]M.克莱因.古今数学思想[M],第1卷.张理京,张锦炎译.上海:上海科学技术出版社,1979年第1版,第37-38页.
|
[2]
|
马复主编.义务教育教科书数学(八年级上册)[M].北京:北京师范大学出版社,2014年第2版,第24页.
|