Floor

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. This process can be affected by the setting of the global variable $MaxExtraPrecision.

See The Mathematica Book: Section 3.2.2.

Implementation Notes: see section A.9.4.

See also: Ceiling, Round, IntegerPart, Chop.

Further Examples