Floor and Ceiling Sum Bounds

We show the analogue of the triangle inequality when floor and ceiling functions replace absolute value. This results in some interesting inequalities that are useful in obtaining approximation results. The floor function one is $$0\le \lfloor x+y \rfloor -\lfloor x \rfloor – \lfloor y \rfloor \le 1.$$

Subscribe to get 4 free e-books!