Question

求两个数学题证明

1.证明：[2x]+[2y]≥[x]+[y]+[x+y]
2.证明：[x/n]=[[x]/n]
取整函数

Answer 1

1
左=[2x-[x]+[y]]+[2y-2[y]]+[x]+[y]
=[[x]+[y]+2(x-[x])]+[2(y-[y])]+[x]+[y]

[x+y]=[x]+[y]+1时，则满足2(x-[x])≥1或2(y-[y])≥1
[[x]+[y]+2(x-[x])]+[2(y-[y])]=[x]+[y]+1或[x]+[y]+2
[[x]+[y]+2(x-[x])]+[2(y-[y])]≥[x]+[y]+1

[x+y]=[x]+[y]时，[2(x-[x]]=1or0,[2(y-[y])]=1or0
[[x]+[y]+2(x-[x])]+[2(y-[y])]≥[x]+[y]+1

综上，[2x]+[2y]≥[x]+[y]+[x+y]

2
[x/n]=[[x]/n+(x-[x])/n]
(x-[x])/n<1
[x/n]=[[x]/n]

Answer 2

题目是取整函数还是绝对值啊？

Answer 3

my dear