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Mathematica Teacher's Edition

Built-in Functions

Mathematical Functions

Numerical Functions

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.
See The Mathematica Book on the web: Section 3.2.2.
Implementation Notes: see Section A.9.4.
See also: Ceiling, Round, IntegerPart, Chop.

Further Examples