Floor function
The greatest integer function, also known as the floor function, gives the greatest integer less than or equal to its argument. The floor of is usually denoted by or . The action of this function is the same as "rounding down." On a positive argument, this function is the same as "dropping everything after the decimal point," but this is not true for negative values.
Examples
A useful way to use the floor function is to write , where y is an integer and k is the leftover stuff after the decimal point. This can greatly simplify many problems.
Alternate Definition
Another common definition of the floor function is
where is the fractional part of .