送交者: HunHunSheng 于 2005-4-22, 10:17:58:
回答: 请你不要侮辱欧几里德。 由 guoxj 于 2005-4-22, 10:10:50:
I still remmeber a counter-proof method
Assuming sqrt(2) is a rational so that it can be expressed as m/n where m and n do not have any common factor.
sqrt(2)=m/n
therefore
2=m^2/n^2
so m^2=2*n^2
so m must be an even number it can be expressed as
2k
therefore 4k^2=2n^2
2*k^2=n^2
So n is also an even number so that n and m
has a common factor 2, which counter the original
assumptions. So sqrt(2) can not be a rational