存在性的证明 这个集合里，到底是哪 Existence of g and r.Let 些元素？ 定义这个集合，有何用 S={a-bk:k∈Z and a-bk≥0}.2 途？ If 0ES,then b divides a,and we can let g=a/b and r =0.If0S,we can use the Well-Ordering Principle.We must first show that S is nonempty. If a 0,then a-b.0E S.If a 0,then a-b(2a)a(1-26)ES.In either case S0.By the Well-Ordering Principle,S must have a smallest member,say r=a-bg.Therefore,a bg+r,r >0.We now show that r<b.Suppose that r>b.Then a-b(q+1)=a-bq-b=r-b>0. 为什么让=2a? In this case we would have a-b(q+1)in the set S.But then a-b(q+1)< a-bg,which would contradict the fact that r =a-bg is the smallest member ofS.Sor≤b.Since0tS,r≠b and so r<b.存在性的证明 为什么让k=2a? 这个集合里，到底是哪 些元素？ 定义这个集合，有何用 途？