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


 * Properties of Floor Function


 * Definition:Ceiling Function


 * Definition:Fractional Part


 * Integers Bounded Above has Greatest Element, which justifies the validity of the definition.