previous up next
Go backward to Illustration
Go up to Top
Go forward to Floor and Ceiling Rules
RISC-Linz logo

Floor and Ceiling Rules

Proposition: For every x in R, we have:

x-1 < floor(x) <= x <= ceiling(x) < x+1,
floor(x) = x <=> x in Z <=> ceiling(x) = x,
floor(-x) = -ceiling(x), ceiling(-x) = -floor(x).
  1. Floor lies on or below the first diagonal; ceiling lies above diagonal; if we shift diagonal down one unit, it lies completely below the floor; if we shift it up one unit, it lies completely above the ceiling.
  2. Floor and ceiling intersect each other at the diagonal.
  3. Floor and ceiling are reflections of each other about both axes.

Author: Wolfgang Schreiner
Last Modification: December 14, 1999

previous up next