Definition:Floor Function

Also known as
The floor function of a real number $x$ is usually just referred to as the floor of $x$.

The floor function is sometimes called the entier function, from the French for integer.

The floor of $x$ is also often referred to as the integer part or integral part of $x$, particularly in older treatments of number theory.

Also see

 * Equivalence of Definitions of Floor Function


 * Definition:Ceiling Function

It immediately follows that:


 * $\left \lfloor {x} \right \rfloor$ is an integer;
 * $x - 1 < \left \lfloor {x} \right \rfloor \le x < \left \lfloor {x} \right \rfloor + 1$;
 * $\forall n \in \Z: \left \lfloor {x} \right \rfloor + n = \left \lfloor {x + n} \right \rfloor$.