Floor[x] gives the greatest integer less than or equal to x.
Mathematical function (see Section A.3.10). Examples: Floor[2.4]; Floor[2.6]; Floor[-2.4]; Floor[-2.6].
Floor[x] can be entered in StandardForm and InputForm as x , lf x rf or \[LeftFloor] x \[RightFloor].
Floor[x] returns an integer when x is any numeric quantity, whether or not it is an explicit number. Example: Floor[Pi^2]. For exact numeric quantities, Floor internally uses numerical approximations to establish its result. See The Mathematica Book on the web: Section 3.2.2. Implementation Notes: see Section A.9.4. See also: Ceiling, Round, IntegerPart, Chop.