Definition:Floor Function

Definition
Let $x$ be a real number.

Informally, the floor function of $x$ is the greatest integer less than or equal to $x$.

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.

Some sources give it as the greatest integer function.

Also see

 * Equivalence of Definitions of Floor Function
 * Properties of Floor Function
 * Definition:Ceiling Function
 * Definition:Fractional Part
 * Definition:Nearest Integer Function