I disagree with the suggested dupe closure. In this question the point is what happens to the floor function when we subtract a small amount from an integer. On the other hand, in the suggested target the point is what happens to the floor function when an integer is added to the argument. Even if it is possible to massage the formula of the target question to yield this identity also, I think ...
Is there a convenient way to typeset the floor or ceiling of a number, without needing to separately code the left and right parts? For example, is there some way to do $\ceil{x}$ instead of $\lce...
Is there a macro in latex to write ceil (x) and floor (x) in short form? The long form \left \lceil {x}\right \rceil is a bit lengthy to type every time it is used.
How to write ceil and floor in latex? - LaTeX Stack Exchange
The height of the floor symbol is inconsistent, it is smaller when the fraction contains a lowercase letter in the numerator and larger when the fraction contains numbers or uppercase letters in the numerator. Why is that the case? How can I produce floor symbols that are always the larger size shown in the picture?
What are some real life application of ceiling and floor functions? Googling this shows some trivial applications.
OR Floor always rounding towards zero. Ceiling always rounding away from zero. E.g floor (x)=-floor (-x) if x<0, floor (x) otherwise If gravity were reversed, the ceiling would become the floor. So from a physics standpoint the standard mathematical definition might be inadequate.