Go backward to IllustrationGo up to TopGo forward to Floor and Ceiling Rules |

*Proposition:*
For every `x` in **R**, we have:

x-1 < floor(x) <=x<= ceiling(x) <x+1,floor( x) =x<=>xinZ<=> ceiling(x) =x,floor(- x) = -ceiling(x), ceiling(-x) = -floor(x).

- 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.
- Floor and ceiling intersect each other at the diagonal.
- Floor and ceiling are reflections of each other about both axes.

Author: Wolfgang Schreiner

Last Modification: December 14, 1999