Floor [x] = greatest integer <= x. Ceiling ceil(x) = smallest integer >= x. Properties: [x] <= x < [x]+1, x-1 < [x] <= x. [x] + [-x] = 0 if x is integer, = -1 otherwise. The fractional part {x} = x - [x] satisfies 0 <= {x} < 1. These functions appear in domain/range problems.