1.設(shè)A,B皆為非空有界數(shù)集,定義數(shù)集A+B={z|z=x+y,x∈A,y∈B}.證明:(1)sup(A+B)=supA+supB;(2)inf(A+B)=infA+infB.2.設(shè)A,B皆為非空有界數(shù)集,且對任何x∈A,y∈B,都有x≥0,y≥0,定義數(shù)集AB={z|z=x·y,x∈A,y∈B}.證明:(1)supAB=supA·supB;(2)infAB=infA·infB.
1.設(shè)A,B皆為非空有界數(shù)集,定義數(shù)集A+B={z|z=x+y,x∈A,y∈B}.證明:(1)sup(A+B)=supA+supB;(2)inf(A+B)=infA+infB.2.設(shè)A,B皆為非空有界數(shù)集,且對任何x∈A,y∈B,都有x≥0,y≥0,定義數(shù)集AB={z|z=x·y,x∈A,y∈B}.證明:(1)supAB=supA·supB;(2)infAB=infA·infB.