Floor and Ceiling Rules
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).
- 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