**16. Show that -[-x] is the least integer greater than or equal to x when x is a real number.
**Solution: We define the greatest integer, denoted by [x] , as the largest integer less than or equal to x satisfying the inequation

[x]<=x<[x]+1 …..(1)

Where x is a real number

We assume that

y=-x

Then, from (1) we get,

[y]<=y<[y]+1

We take negative sign which will reverse the inequality, so

-[y]>=-y>-[y]-1

Therefore, we get,

-[-x]>=-(-x)>-[-x]-1

-[-x]>=x>-([-x]+1)

This implies -[-x] that is the least integer greater than or equal to x whenever x is a real number.