linguistic:paraphrasing, linguistic:voice_change
Equivalences

These formulas can be used to simplify expressions involving floors and ceilings.

In the language of order theory, the floor function is a residuated mapping, that is, part of a Galois connection: it is the upper adjoint of the function that embeds the integers into the reals.

These formulas show how adding an integer n to the arguments affects the functions:

The above are never true if n is not an integer; however, for every x and y, the following inequalities hold: