V2 is not rational(Pythagoreans)? Proof. Suppose,to the contrary,that v2 is rational.Then there exist inte- gers p and q(with q nonzero)such that v2=p/q.We may assume that p and g have no common factor,for if they did,we would sim- plify and begin again.Now,we have that v2q p.Squaring both sides,we obtain 2g2 =p2.Thus p2 is o s even,we know from Problem 3.1 that p m 你有没有怀疑过 2m for some integer m.This means t 这个"therefore” see that g2 =2m2.But this means that a 的正确性？ m Prob- lem 3.1 that g is even.So p and 2,which is completely absurd,since we assumed re o common factor. Therefore our assumption that v2 is rational must be wrong and we have completed the proof of the theorem. ■2 is not rational (Pythagoreans)? 你有没有怀疑过 这个”therefore” 的正确性？