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  • 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.
  • See also: Ceiling, Round, IntegerPart, Chop.