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 even.Since p2 is even,we know from Problem 3.1 that p must be ever 你有没有怀疑过 some integer m.This means that 2q2= 这个”therefore" g2 =2m2.But this means that g2 is even. 的正确性？ lem 3.1 that q is even.So p and g have a common facto2,which is completely absurd,since we assumed they had no common factor Therefore our assumption that v2 is rational must be wrong and we have completed the proof of the theorem2 is not rational (Pythagoreans)? 你有没有怀疑过 这个”therefore” 的正确性？